Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonli...Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.展开更多
Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore th...Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.展开更多
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is...The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.展开更多
The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping r...The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.展开更多
Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-am...Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.展开更多
This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the...This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.展开更多
In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric laye...In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.展开更多
This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force...This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.展开更多
In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates w...In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.展开更多
The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-...The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.展开更多
The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is ...The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender Pipes.展开更多
Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume ...Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0° and 180° for self-excited ease and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.展开更多
In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temper...In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton＇s principle and then computed these equations by using Navier＇s solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutio...The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions： either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature： the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.展开更多
In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic...In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well.展开更多
In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution...In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates.展开更多
In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed...In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.展开更多
The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved....The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.展开更多
Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track a...Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.展开更多
文摘Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.
基金the National Natural Science Foundation of China(Nos.12302007,12372006,and 12202109)the Specific Research Project of Guangxi for Research Bases and Talents(No.AD23026051)。
文摘Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.
基金Project supported by the National Natural Science Foundation of China (No. 10472060)Natural Science Founda-tion of Shanghai Municipality (No. 04ZR14058)Doctor Start-up Foundation of Shenyang Institute of Aeronautical Engineering (No. 05YB04).
文摘The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
基金Project supported by the National Science and Technology Major Project(NMP)of China(No.2013ZX04011-011)
文摘The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.
基金the National Natural Science Foundation of China (Nos. 10702045 and 10872135)the Aerospace Foundation of China (No. 2009ZA018)the Natural Science Foundation of Liaoning Province (No. 2009A572)
文摘Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.
文摘This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.
文摘In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.
基金supported by the National Natural Science Foundation of China (project nos.11772205 , 11202140 , 11402151 , 11572182 , 51305421)the funding support from the Natural Science Foundation of Liaoning Province (201501708)
文摘This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.
文摘In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.
文摘The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.
基金supported by the National Natural Science Foundation of China (Nos. 11622216 and 51409134)
文摘The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender Pipes.
基金supported by the National Natural Science Foundation of China(Grant No.50538050)
文摘Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0° and 180° for self-excited ease and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.
基金the Iranian Nanotechnology Development Committee for their financial supportthe University of Kashan (463855/7)
文摘In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton＇s principle and then computed these equations by using Navier＇s solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Project supported by the Shanghai Leading Academic Discipline Project(No.Y0103)the Natural Science Foundation of Zhejiang Province of China(No.100039)
文摘The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions： either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature： the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.
文摘In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well.
文摘In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates.
文摘In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.
基金Project supported by the National Natural Science Foundation of China (No.10972143)the Shanghai Municipal Education Commission (No.YYY11040)+2 种基金the Shanghai Leading Academic Discipline Project (No.J51501)the Leading Academic Discipline Project of Shanghai Institute of Technology(No.1020Q121001)the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No.YJ2011-26)
文摘The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.
基金funded by the Research Fund of Shanghai Bureau Group Corporation(2021142)Science Foundation of China State Railway Group Corporation Limited(P2021T013)and Science Foundation of China Academy of Railway Sciences Corporation Limited(2021YJ250).
文摘Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.
