Bubbles within an elastic shell,which undergo ultrasound-driven oscillation to treat tumors and soft tissues,are frequently treated as viscoelastic media.Therefore,studying the dynamic behavior of bubbles wrapped in a...Bubbles within an elastic shell,which undergo ultrasound-driven oscillation to treat tumors and soft tissues,are frequently treated as viscoelastic media.Therefore,studying the dynamic behavior of bubbles wrapped in a viscoelastic medium while considering an elastic shell can provide theoretical support for ultrasound biotherapy.Bubbles are always in the form of clusters.Therefore,a model of spherical bubble clusters in a liquid cavity wrapped by an elastic shell was constructed,the coupled oscillation equations of bubbles were obtained by taking into account the dynamic effects of the elastic shell and the viscoelastic media outside the cavity,and the oscillation behaviors of the bubbles were analyzed.Acoustic waves at 1.5 MHz could cause bubbles with a radius of 1μm to resonate.Increasing the number of bubbles increased the suppressing effect of bubble oscillation caused by bubble interaction.The bubble cluster oscillation caused the elastic shell to oscillate and be stressed,and the stress trend was the inverse of the bubble oscillation trend with maximal tensile and compressive stresses.Bubbles with an equilibrium radius of 2μm exhibited the lowest inertial cavitation threshold,making inertial cavitation more likely under high-frequency acoustic excitation.The inertial cavitation threshold of bubbles was heavily influenced by the acoustic wave frequency,bubble number density,and bubble cluster radius.The nonspherical oscillation stability of bubbles was primarily affected by the driving acoustic pressure amplitude and frequency,bubble initial radius,bubble number density,and bubble cluster radius.The acoustic frequency and amplitude exhibited a synergistic effect,with a minimum unstable driving acoustic pressure threshold of approximately 0.13 MPa.The initial radius within the elastic shell affected the minimum unstable driving acoustic pressure threshold.展开更多
Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their m...Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their mechanical characteristics can be tuned by the active feedback control system at low frequency ranges in which the traditional passive control is limited.This work illustrates that the superior performances of the effective mass density and sound pressure level(SPL)of an elastic wave metamaterial can be significantly changed by the active control,in which the periodic array of local resonators and orthogonal stiffeners are included.Significantly,based on the locally resonant mechanism,the negative density occurs over a frequency range.Due to the effects of lattice constant,structural damping and other parameters,the SPL with the function of fluid-solid coupling are illustrated and discussed.展开更多
A motor-driven linkage system with links fabricated from 3-dimensional braided composite materials was studied. A group of coupling dynamic equations of the system, including composite materials parameters, electromag...A motor-driven linkage system with links fabricated from 3-dimensional braided composite materials was studied. A group of coupling dynamic equations of the system, including composite materials parameters, electromagnetism parameters of the motor and structural parameters of the link mechanism, were established by finite element method. Based on the air-gap field of non-uniform airspace of three-phase alternating current motor caused by the vibration eccentricity of rotor, the relation of electromechanical coupling at the actual running state was analyzed. And the motor element, which defines the transverse vibration and torsional vibration of the motor as its nodal displacement, was established. Then, based on the damping element model and the expression of energy dissipation of the 3-dimentional braided composite materials, the damping matrix of the system was established by calculating each order modal damping of the mechanism.展开更多
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increase...Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increased mathematical complexity compared with the single plate structure.In order to study analytically the vibration characteristics and power transmission of the coupled-plate structure,an analytical model consisting of three coupled plates elastically restrained along boundary edges and elastically coupled with arbitrary angle is considered,in which four groups of springs are distributed consistently along each edge of the model to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.With elastic coupling condition and general boundary condition of both flexural and in-plane vibrations taken into account by setting the stiffness of corresponding springs,the double Fourier series solution to the dynamic response of the structure was obtained by employing the Rayleigh-Ritz method.In order to validate the model,the natural frequency and velocity response of the model are firstly checked against results published in literatures and the ANSYS data,and good agreement was observed.Then,numerical simulation of the effects of several relevant parameters on the vibration characteristics and power transmission of the coupled structure were performed,including boundary conditions,coupling conditions,coupling angle,and location of the external forces.Vibration and energy transmission behaviors were analyzed numerically.The results show that the power transmission can be significantly influenced by the boundary restraints and the location of excitation.When the excitation is located at the central symmetry point of the model,the energy flow shows a symmetrical distribution.Once the location deviates from the central symmetry point,the power circumfluence occurs and the vortex energy field is formed at high frequency.展开更多
Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I...Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.展开更多
A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(F...A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.展开更多
Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations ...Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.展开更多
We use neutron powder diffraction to investigate the magnetic and crystalline structure of Cr_(2)GaN.A magnetic phase transition is identified at T≈170 K,whereas no trace of structural transition is observed down to ...We use neutron powder diffraction to investigate the magnetic and crystalline structure of Cr_(2)GaN.A magnetic phase transition is identified at T≈170 K,whereas no trace of structural transition is observed down to 6 K.Combining Rietveld refinement with irreducible representations,the spin configuration of Cr ions in Cr_(2)GaN is depicted as an incommensurate sinusoidal modulated structure characterized by a propagating vector k=(0.365,0.365,0).Upon warming up to the paramagnetic state,the magnetic order parameter closely resembles to the temperature dependence of c-axis lattice parameter,suggesting strong magneto-elastic coupling in this compound.Therefore,Cr_(2)Ga N provides a potential platform for exploration of magnetically tuned properties such as magnetoelectric,magnetostrictive and magnetocaloric effects,as well as their applications.展开更多
The governing equation and energy equations for thermal-elastic coupling vibration of cylindrical shell were developed. The Garlerkin method was used in numerical process. Some useful result can be concluded from nume...The governing equation and energy equations for thermal-elastic coupling vibration of cylindrical shell were developed. The Garlerkin method was used in numerical process. Some useful result can be concluded from numerical result. With the increase of the amplitude of temperature and coupling coefficient, the speed of vibration decaying becomes slower and the coupling effect becomes weaker. The larger the ration of length to radius and length to thickness, the faster the decaying of the vibration amplitude and the vibration frequency increase. It means the coupling effect gets stronger. The larger the coupling coefficient, the smaller the axial stress, the axial force and the bendind moment are.展开更多
Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equ...Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.展开更多
Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditiona...Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.展开更多
To take into account the couple stress effects, a modified Reynolds equation is derived for dynamically loaded journal beatings with the consideration of the elasticity of the liner. The numerical results show that th...To take into account the couple stress effects, a modified Reynolds equation is derived for dynamically loaded journal beatings with the consideration of the elasticity of the liner. The numerical results show that the influence of couple stresses on the bearing characteristics is significant. Compared with Newtonian lubricants, lubricants with couple stresses increase the fluid film pressure, as a result enhance the load-carrying capacity and reduce the friction coefficient. However, since the elasticity of the liner weakens the couple stress effect, elastic liners yield a reduction in the load-carrying capacity and an increase in the friction coefficient. The elastic deformation of the bearing liner should be considered in an accurate performance evaluation of the journal bearing.展开更多
The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in ...The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.展开更多
The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behav...The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.展开更多
Rotating machinery in the aviation industry is increasingly embracing high speeds and miniaturization,and foil dynamic pressure gas bearing has great application value due to its self-lubrication and self-adaptive def...Rotating machinery in the aviation industry is increasingly embracing high speeds and miniaturization,and foil dynamic pressure gas bearing has great application value due to its self-lubrication and self-adaptive deformation characteristics.This study explores the interaction mechanism between micro-scale variable-sectional shearing flow with hyper-rotation speeds and a three-layer elastic foil assembly through bidirectional aero-elastic coupling in a Multi-layer Thrust Gas Foil Bearing(MTGFB).The bearing capacity of the MTGFB varies non-linearly with the decrease of gas film clearance,while the collaborative deformation of the three-layer elastic foil assembly can deal with different load conditions.As the load capacity increases,the enhanced dynamic pressure effect causes the top foil to evolve from a single arch to multiple arches.The hydrodynamic effects in the gas film evolve to form multiple segmented wedges with different pitch ratios,while the peak pressure of the gas film always occurs near the vaults of the top foil.As the rotational speed frequency approaches the natural frequency,the resonance of the gas film and elastic foil assembly system occurs,and a phase delay occurs between the pressure pulsation and the vibration of foils.The load capacity of the MTGFB also depends on the elastic moduli of the elastic foil assembly.Increasing the elastic modulus decreases the deformation amplitude of the top foil,whereas it increases those of the backboard and middle foil,increasing the load capacity.展开更多
The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the sys...The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the system are investigated and analyzed.The various nonlinear dynamical behaviors of the coupling system are obtained,which can further explain the relationship between the physical parameters and the bifurcation solutions.The results provide a theoretical basis to the realization of the parameter optimal control.展开更多
The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation ...The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by po,ver series method. Compared,with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio beta, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.展开更多
In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and ...In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and boundary conditions.Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity.For each nanorod component,its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials,with the aim to make all the spatial differential sufficiently continuous across each rod.All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix.Numerical results are presented for the particular cases of twonanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model.Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature.Based on the model established,influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed.This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.展开更多
The dynamic cumulative damage of rigid-flexible coupling model of high-speed train with flexible bogie frame is performed by using the coupled scheme of elastic and multibody dynamics theories.The motion equations of ...The dynamic cumulative damage of rigid-flexible coupling model of high-speed train with flexible bogie frame is performed by using the coupled scheme of elastic and multibody dynamics theories.The motion equations of the present problem are firstly established by integrating the finite element method and floating frame of reference approach based on the virtual power principle and D'Alembert principle.The process of condensing the elastic DOFs of the obtained finite element model involving the incorporation of the substructure technique and sparse approximate inverse method is tentatively carried out.Then,the motion equations are further solved by virtue of the generalized α method and the Jacobian-free Newton-Krylov technologies.And the superiority of coupled scheme is proven by comparing with the traditional approach.Finally,besides the dynamic behaviors of the considered vehicle model,the time-variations of stresses on the elastic bogie frame's dangerous nodes and the distributions of stresses of bogie frame at some specified moments are synchronously calculated and analyzed.More importantly,the real-time and time-varying cumulative damages of some typical nodes on bogie frame are investigated.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12374441)。
文摘Bubbles within an elastic shell,which undergo ultrasound-driven oscillation to treat tumors and soft tissues,are frequently treated as viscoelastic media.Therefore,studying the dynamic behavior of bubbles wrapped in a viscoelastic medium while considering an elastic shell can provide theoretical support for ultrasound biotherapy.Bubbles are always in the form of clusters.Therefore,a model of spherical bubble clusters in a liquid cavity wrapped by an elastic shell was constructed,the coupled oscillation equations of bubbles were obtained by taking into account the dynamic effects of the elastic shell and the viscoelastic media outside the cavity,and the oscillation behaviors of the bubbles were analyzed.Acoustic waves at 1.5 MHz could cause bubbles with a radius of 1μm to resonate.Increasing the number of bubbles increased the suppressing effect of bubble oscillation caused by bubble interaction.The bubble cluster oscillation caused the elastic shell to oscillate and be stressed,and the stress trend was the inverse of the bubble oscillation trend with maximal tensile and compressive stresses.Bubbles with an equilibrium radius of 2μm exhibited the lowest inertial cavitation threshold,making inertial cavitation more likely under high-frequency acoustic excitation.The inertial cavitation threshold of bubbles was heavily influenced by the acoustic wave frequency,bubble number density,and bubble cluster radius.The nonspherical oscillation stability of bubbles was primarily affected by the driving acoustic pressure amplitude and frequency,bubble initial radius,bubble number density,and bubble cluster radius.The acoustic frequency and amplitude exhibited a synergistic effect,with a minimum unstable driving acoustic pressure threshold of approximately 0.13 MPa.The initial radius within the elastic shell affected the minimum unstable driving acoustic pressure threshold.
基金the supports by the National Natural Science Foundation of China(Grants 11922209,11991031 and 12021002)for this research work.
文摘Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their mechanical characteristics can be tuned by the active feedback control system at low frequency ranges in which the traditional passive control is limited.This work illustrates that the superior performances of the effective mass density and sound pressure level(SPL)of an elastic wave metamaterial can be significantly changed by the active control,in which the periodic array of local resonators and orthogonal stiffeners are included.Significantly,based on the locally resonant mechanism,the negative density occurs over a frequency range.Due to the effects of lattice constant,structural damping and other parameters,the SPL with the function of fluid-solid coupling are illustrated and discussed.
基金Project(50175031) supported by the National Natural Science Foundation of China
文摘A motor-driven linkage system with links fabricated from 3-dimensional braided composite materials was studied. A group of coupling dynamic equations of the system, including composite materials parameters, electromagnetism parameters of the motor and structural parameters of the link mechanism, were established by finite element method. Based on the air-gap field of non-uniform airspace of three-phase alternating current motor caused by the vibration eccentricity of rotor, the relation of electromechanical coupling at the actual running state was analyzed. And the motor element, which defines the transverse vibration and torsional vibration of the motor as its nodal displacement, was established. Then, based on the damping element model and the expression of energy dissipation of the 3-dimentional braided composite materials, the damping matrix of the system was established by calculating each order modal damping of the mechanism.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
基金supported by National Natural Science Foundation of China (Grant No. 10802024)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200802171009)Innovative Talents Fund of Harbin of China(Grant No.2009RFQXG211)
文摘Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increased mathematical complexity compared with the single plate structure.In order to study analytically the vibration characteristics and power transmission of the coupled-plate structure,an analytical model consisting of three coupled plates elastically restrained along boundary edges and elastically coupled with arbitrary angle is considered,in which four groups of springs are distributed consistently along each edge of the model to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.With elastic coupling condition and general boundary condition of both flexural and in-plane vibrations taken into account by setting the stiffness of corresponding springs,the double Fourier series solution to the dynamic response of the structure was obtained by employing the Rayleigh-Ritz method.In order to validate the model,the natural frequency and velocity response of the model are firstly checked against results published in literatures and the ANSYS data,and good agreement was observed.Then,numerical simulation of the effects of several relevant parameters on the vibration characteristics and power transmission of the coupled structure were performed,including boundary conditions,coupling conditions,coupling angle,and location of the external forces.Vibration and energy transmission behaviors were analyzed numerically.The results show that the power transmission can be significantly influenced by the boundary restraints and the location of excitation.When the excitation is located at the central symmetry point of the model,the energy flow shows a symmetrical distribution.Once the location deviates from the central symmetry point,the power circumfluence occurs and the vortex energy field is formed at high frequency.
基金supported by he National Natural Science Foundation of China (No.10872081)the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No.111005)
文摘Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
基金co-supported by the National Key R&D Program of China(Nos.2018YFF01012401-05)the National Natural Science Foundation of China(No.51975243)+2 种基金Jilin Provincial Department of Education(No.JJKH20180084KJ),Chinathe Fundamental Research Funds for the Central Universities and Jilin Provincial Department of Science&Technology Fund Project,China(Nos.20170101043JC and 20180520072JH)Graduate Innovation Fund of Jilin University,China(No.101832018C184).
文摘A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.
基金supported by the National Natural Science Foundation of China (11132007)
文摘Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.
基金supported by the National Natural Science Foundation of China(Grant Nos.11822411,12061130200,11961160699,11974392,and 52101236)the National Key Research and Development Program of China(Grant Nos.2018YFA0704200,2017YFA0303100,and 2020YFA0406003)+4 种基金the Strategic Priority Research Program(B)of the CAS(GrantNo.XDB25000000)K.C.Wong Education Foundation(Grant No.GJTD-2020-01)the Youth Innovation Promotion Association of the CAS(Grant No.Y202001)Beijing Natural Science Foundation(Grant No.JQ19002)the Newton Advanced Fellowship funding from the Royal Society of UK(Grant No.NAFR1201248)。
文摘We use neutron powder diffraction to investigate the magnetic and crystalline structure of Cr_(2)GaN.A magnetic phase transition is identified at T≈170 K,whereas no trace of structural transition is observed down to 6 K.Combining Rietveld refinement with irreducible representations,the spin configuration of Cr ions in Cr_(2)GaN is depicted as an incommensurate sinusoidal modulated structure characterized by a propagating vector k=(0.365,0.365,0).Upon warming up to the paramagnetic state,the magnetic order parameter closely resembles to the temperature dependence of c-axis lattice parameter,suggesting strong magneto-elastic coupling in this compound.Therefore,Cr_(2)Ga N provides a potential platform for exploration of magnetically tuned properties such as magnetoelectric,magnetostrictive and magnetocaloric effects,as well as their applications.
文摘The governing equation and energy equations for thermal-elastic coupling vibration of cylindrical shell were developed. The Garlerkin method was used in numerical process. Some useful result can be concluded from numerical result. With the increase of the amplitude of temperature and coupling coefficient, the speed of vibration decaying becomes slower and the coupling effect becomes weaker. The larger the ration of length to radius and length to thickness, the faster the decaying of the vibration amplitude and the vibration frequency increase. It means the coupling effect gets stronger. The larger the coupling coefficient, the smaller the axial stress, the axial force and the bendind moment are.
基金supported by the National Natural Science Foundation of China (No.10872081)the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No. 111005)
文摘Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.
文摘Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.
基金Project (No. 571123) supported by the Scientific Research SpecialFoundation for the Excellent Youth Teacher of Shanghai University byEducation Committee of Shanghai, China
文摘To take into account the couple stress effects, a modified Reynolds equation is derived for dynamically loaded journal beatings with the consideration of the elasticity of the liner. The numerical results show that the influence of couple stresses on the bearing characteristics is significant. Compared with Newtonian lubricants, lubricants with couple stresses increase the fluid film pressure, as a result enhance the load-carrying capacity and reduce the friction coefficient. However, since the elasticity of the liner weakens the couple stress effect, elastic liners yield a reduction in the load-carrying capacity and an increase in the friction coefficient. The elastic deformation of the bearing liner should be considered in an accurate performance evaluation of the journal bearing.
基金Project supported by the Fundamental Research Funds for the Central Universities(FRF-BR-15-026A)the National Natural Science Foundation of China(No.10972029)
文摘The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.
基金support from the Anusandhan National Research Foundation(ANRF),erstwhile Science and Engineering Research Board(SERB),India,under the startup research grant program(SRG/2022/000566).
文摘The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.
基金the financial support from the National Natural Science Foundation of China(No.52206091)the Aeronautical Science Foundation of China(No.201928052008)the Natural Science Foundation of Jiangsu Province,China(No.BK20210303)。
文摘Rotating machinery in the aviation industry is increasingly embracing high speeds and miniaturization,and foil dynamic pressure gas bearing has great application value due to its self-lubrication and self-adaptive deformation characteristics.This study explores the interaction mechanism between micro-scale variable-sectional shearing flow with hyper-rotation speeds and a three-layer elastic foil assembly through bidirectional aero-elastic coupling in a Multi-layer Thrust Gas Foil Bearing(MTGFB).The bearing capacity of the MTGFB varies non-linearly with the decrease of gas film clearance,while the collaborative deformation of the three-layer elastic foil assembly can deal with different load conditions.As the load capacity increases,the enhanced dynamic pressure effect causes the top foil to evolve from a single arch to multiple arches.The hydrodynamic effects in the gas film evolve to form multiple segmented wedges with different pitch ratios,while the peak pressure of the gas film always occurs near the vaults of the top foil.As the rotational speed frequency approaches the natural frequency,the resonance of the gas film and elastic foil assembly system occurs,and a phase delay occurs between the pressure pulsation and the vibration of foils.The load capacity of the MTGFB also depends on the elastic moduli of the elastic foil assembly.Increasing the elastic modulus decreases the deformation amplitude of the top foil,whereas it increases those of the backboard and middle foil,increasing the load capacity.
基金supported by the National Natural Science Foundation of China (No. 10632040)the Tianjin Natural Science Foundation (No. 09JCZDJC26800)
文摘The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the system are investigated and analyzed.The various nonlinear dynamical behaviors of the coupling system are obtained,which can further explain the relationship between the physical parameters and the bifurcation solutions.The results provide a theoretical basis to the realization of the parameter optimal control.
文摘The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by po,ver series method. Compared,with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio beta, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.
文摘In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and boundary conditions.Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity.For each nanorod component,its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials,with the aim to make all the spatial differential sufficiently continuous across each rod.All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix.Numerical results are presented for the particular cases of twonanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model.Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature.Based on the model established,influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed.This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.
基金support for the research:National Natural Science Foundation of China(Grant No.11872257 and 11572358)Key Project of Natural Science Foundation of Hebei Province(Grant No.A2020210008)Hebei Provincial Department of Education Youth Top Talents Project(Grant No.BJK2023018).
文摘The dynamic cumulative damage of rigid-flexible coupling model of high-speed train with flexible bogie frame is performed by using the coupled scheme of elastic and multibody dynamics theories.The motion equations of the present problem are firstly established by integrating the finite element method and floating frame of reference approach based on the virtual power principle and D'Alembert principle.The process of condensing the elastic DOFs of the obtained finite element model involving the incorporation of the substructure technique and sparse approximate inverse method is tentatively carried out.Then,the motion equations are further solved by virtue of the generalized α method and the Jacobian-free Newton-Krylov technologies.And the superiority of coupled scheme is proven by comparing with the traditional approach.Finally,besides the dynamic behaviors of the considered vehicle model,the time-variations of stresses on the elastic bogie frame's dangerous nodes and the distributions of stresses of bogie frame at some specified moments are synchronously calculated and analyzed.More importantly,the real-time and time-varying cumulative damages of some typical nodes on bogie frame are investigated.
