Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade compone...Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.展开更多
Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use ...Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare （L-P） method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different condi- tions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parame- ter e, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2 04, different magneto-electro-elastic ma- terials of BaTiO3/CoFe2 04 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects in- volve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.展开更多
To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum poten...To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum potential energy and variational method are used and series functions with unknown coefficients are taken as trial functions of functional to solve the large deflection and non linear bending problem of a thin plate and find relation curves between deflection of plate and loads. The proposed method can capture the buckling and post buckling behaviors of a thin plate in different geometrical and load boundary conditions. The analysis confirms that there occur snap and bifurcation behaviors in the post buckling stage of the plate. And these results show the validity of the variational method for solving buckling problems of thin plate.展开更多
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-f...The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported （S） and clamped （C） boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.展开更多
Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying ...Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.展开更多
Textile reinforced concrete （TRC） is especially suitable for the thin-walled and light-weight structural elements with a high load-bearing capacity. For this thin element, the concrete cover thickness is an importan...Textile reinforced concrete （TRC） is especially suitable for the thin-walled and light-weight structural elements with a high load-bearing capacity. For this thin element, the concrete cover thickness is an important factor in affecting the mechanical and anti-crack performance. Therefore, the influences of the surface treatment of the textile and mixing polypropylene fiber into the concrete on the properties of the components with different cover thickness were experimentally studied with four-point bending tests. The experimental results show that for the components with the same cover thickness, sticking sand on epoxy resin-impregnated textile and adding short fiber into the concrete are helpful to improve their mechanical performance. The 2-3 mm cover thickness is enough to meet the anchorage requirements of the reinforcement fiber and the component has good crack pattern and mechanical behavior at this condition. Comparison between the calculated and the experimental Values of flexural capacity reveals satisfactory agreement. Finally, based on the calculation model of the crack spacing of reinforced concrete structures, the crack extension of this thin-wall component was qualitatively analyzed and the same results with the experimental were obtained.展开更多
We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and me-chanical fields.Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangula...We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and me-chanical fields.Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the ex-pressions of electromagnetic forces,the vibration equations are derived for the mechanical loading in a steady transverse magnetic field.Using the Melnikov function method,the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping.The vibration equations are solved numerically by a fourth-order Runge-Kutta method.Its bifurcation dia-gram,Lyapunov exponent diagram,displacement wave diagram,phase diagram and Poincare section diagram are obtained.展开更多
Photostrictive actuators can produce photodeformation strains under illumination of ultraviolet lights. They can realize non-contact micro-actuation and vibration control for elastic plate structures. Considering the ...Photostrictive actuators can produce photodeformation strains under illumination of ultraviolet lights. They can realize non-contact micro-actuation and vibration control for elastic plate structures. Considering the switching actuation and nonlinear dynamic characteristics of photostrictive actuators, a variable structure fuzzy active control scheme is presented to control the light intensity applied to the actuators. Firstly, independent modal vibration control equations of photoelectric laminated plates are established based on modal analysis techniques. Then, the optimal light switching function is derived to increase the range of sliding modal area, and the light intensity self-adjusting fuzzy active controller is designed. Meanwhile, a continuous function is applied to replace a sign function to reduce the variable structure control （VSC） chattering. Finally, numerical simulation is carried out, and simulation results indicate that the proposed control strategy provides better performance and control effect to plate actuation and control than velocity feedback control, and suppresses vibration effectively.展开更多
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia...The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.展开更多
In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational princi...In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational principle is obtained in a convolutionbilinear form. For application the problems of free vibration, forcedvibration and stability of a viscoelastic simply-supportedrectangular thin plate are considered. The results show thatnumerical solutions agree well with analytical solutions.展开更多
In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were i...In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were investigated. The results show that the optimal bonding strength is up to 20 MPa with a reduction ratio of 40 % and rolling temperature of 400 ℃, superior than that in other one-pass rolling studies with regard to thin lami- nated plates. In addition, a favorable property is achieved with the annealing temperature of 250-300 ℃ or annealing time of 1.5 h. When the annealing temperature exceeds 300 ℃ or annealing time exceeds 1.5 h, respectively, the bonding strength of Al/Mg/Al plate decreases. The scan- ning electron microscopy （SEM） and energy-dispersive spectroscopy （EDS） analyses suggest that the appearance of thin diffusion layers between Al and Mg interfaces is helpful to improve the bonding strength, while the presence of thick diffusion layer would reduce the bonding strength greatly.展开更多
Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelas...Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
The energy variational formula based on the principle of minimum potential energy is proposed for the plates constrained at arbitrary points. As an instance, the orthotropic large deflection rectangular thin plates wi...The energy variational formula based on the principle of minimum potential energy is proposed for the plates constrained at arbitrary points. As an instance, the orthotropic large deflection rectangular thin plates with four free edges and transverse displacement constraints under uniform transverse load are discussed. The generalized Fourier series are used as the trial functions of the transverse displacement and the stress function to establish the essential equations, which are linearized by means of the incremental method of load and displacement constraint. In the end of the paper, several computational results are compared with the former literature. Moreover, one typical example is demonstrated through advanced experimental technique. The result shows the accuracy is satisfied well.展开更多
The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of control...The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.展开更多
Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of visco...Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elasti...Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.展开更多
The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element...The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.展开更多
The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution varia...The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.展开更多
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This fu...The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.展开更多
The knowledge of crack type and dislocation orientation is helpful for the lifetime prediction of thin plates on aircrafts.The moment-tensor inversion utilizes the Acoustic Emission(AE)signals to detect cracks and the...The knowledge of crack type and dislocation orientation is helpful for the lifetime prediction of thin plates on aircrafts.The moment-tensor inversion utilizes the Acoustic Emission(AE)signals to detect cracks and the source mechanisms can be interpreted by the decomposition of moment tensors.Since the traditional moment-tensor inversion is implemented for the AE sources inside infinite elastic bodies,the inversion needs to be modified for the cracks in thin plates.In this study,the moment tensors of cracks in thin plates are derived and the inversion equation is provided based on the Green's function of second kind.A method of modifying the moment tensors to adapt to the existing decomposition processes and source-type plots is provided.By employing the Finite Element Method(FEM),the wave fields generated by the AE sources are computed.The AE sources continuously changing from pure tensile type(Model I)to shear type(Model II)are achieved in the FE models and the moment tensors are recovered.By the comparison between the reference values and recovered solutions,the source type can be accurately identified in the source-type plot and the applicability of the moment-tensor inversion for cracks in thin plates is confirmed.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12372071 and 12372070)the Aeronautical Science Fund of China(No.2022Z055052001)the Foundation of China Scholarship Council(No.202306830079)。
文摘Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.
基金National Natural Science Foundation of China(No.11202190)Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars,Ministry of Education,ChinaResearch Project Supported by Shanxi Scholarship Council of China(No.2013-085)
文摘Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare （L-P） method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different condi- tions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parame- ter e, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2 04, different magneto-electro-elastic ma- terials of BaTiO3/CoFe2 04 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects in- volve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.
文摘To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum potential energy and variational method are used and series functions with unknown coefficients are taken as trial functions of functional to solve the large deflection and non linear bending problem of a thin plate and find relation curves between deflection of plate and loads. The proposed method can capture the buckling and post buckling behaviors of a thin plate in different geometrical and load boundary conditions. The analysis confirms that there occur snap and bifurcation behaviors in the post buckling stage of the plate. And these results show the validity of the variational method for solving buckling problems of thin plate.
基金supported by the National Natural Science Foundation of China (10772014)
文摘The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported （S） and clamped （C） boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.
基金supported by the Natural Science Foundation of Hebei Province of China(No.E2010001254)
文摘Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.
基金Supported by the National Natural Science Foundation of China(No.51108451)the Natural Science Foundation of Jiangsu Province of China(No.BK2011220)+2 种基金the Fundamental Research Funds for the Central Universities of China(Nos.2010QNA45, 2011FZA4017)Postdoctoral Science Foundation of China(No.2012M511817)Postdoctoral Science Foundation of Jiangsu Province(No.1102082C)
文摘Textile reinforced concrete （TRC） is especially suitable for the thin-walled and light-weight structural elements with a high load-bearing capacity. For this thin element, the concrete cover thickness is an important factor in affecting the mechanical and anti-crack performance. Therefore, the influences of the surface treatment of the textile and mixing polypropylene fiber into the concrete on the properties of the components with different cover thickness were experimentally studied with four-point bending tests. The experimental results show that for the components with the same cover thickness, sticking sand on epoxy resin-impregnated textile and adding short fiber into the concrete are helpful to improve their mechanical performance. The 2-3 mm cover thickness is enough to meet the anchorage requirements of the reinforcement fiber and the component has good crack pattern and mechanical behavior at this condition. Comparison between the calculated and the experimental Values of flexural capacity reveals satisfactory agreement. Finally, based on the calculation model of the crack spacing of reinforced concrete structures, the crack extension of this thin-wall component was qualitatively analyzed and the same results with the experimental were obtained.
基金Project(No. A2006000190)supported by the Natural Science Foundation of Hebei Province,China
文摘We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and me-chanical fields.Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the ex-pressions of electromagnetic forces,the vibration equations are derived for the mechanical loading in a steady transverse magnetic field.Using the Melnikov function method,the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping.The vibration equations are solved numerically by a fourth-order Runge-Kutta method.Its bifurcation dia-gram,Lyapunov exponent diagram,displacement wave diagram,phase diagram and Poincare section diagram are obtained.
基金supported by National Natural Science Foundation of China (Nos. 10872090 and 50830201)Qing Lan Project
文摘Photostrictive actuators can produce photodeformation strains under illumination of ultraviolet lights. They can realize non-contact micro-actuation and vibration control for elastic plate structures. Considering the switching actuation and nonlinear dynamic characteristics of photostrictive actuators, a variable structure fuzzy active control scheme is presented to control the light intensity applied to the actuators. Firstly, independent modal vibration control equations of photoelectric laminated plates are established based on modal analysis techniques. Then, the optimal light switching function is derived to increase the range of sliding modal area, and the light intensity self-adjusting fuzzy active controller is designed. Meanwhile, a continuous function is applied to replace a sign function to reduce the variable structure control （VSC） chattering. Finally, numerical simulation is carried out, and simulation results indicate that the proposed control strategy provides better performance and control effect to plate actuation and control than velocity feedback control, and suppresses vibration effectively.
基金Supported by the National Natural Science Foundation of China under Grant No.10962004the Natural Science Foundation of Inner Mongolia under Grant No.2009BS0101+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002the Cultivation of Innovative Talent of "211 Project"of Inner Mongolia University
文摘The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.
基金the National Natural Science Foundation of China (No.19772027)the Shanghai Municipal Development Foundation of Science and Technology(No.98JC14032)
文摘In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational principle is obtained in a convolutionbilinear form. For application the problems of free vibration, forcedvibration and stability of a viscoelastic simply-supportedrectangular thin plate are considered. The results show thatnumerical solutions agree well with analytical solutions.
基金financially supported by the National Natural Science Foundation of China (Nos.51301118 and 51175363)the Specialized Research Fund for the Doctoral Program of Higher Education (No.20050112001)the Natural Science Foundation of Shanxi Province (No. 2006011051)
文摘In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were investigated. The results show that the optimal bonding strength is up to 20 MPa with a reduction ratio of 40 % and rolling temperature of 400 ℃, superior than that in other one-pass rolling studies with regard to thin lami- nated plates. In addition, a favorable property is achieved with the annealing temperature of 250-300 ℃ or annealing time of 1.5 h. When the annealing temperature exceeds 300 ℃ or annealing time exceeds 1.5 h, respectively, the bonding strength of Al/Mg/Al plate decreases. The scan- ning electron microscopy （SEM） and energy-dispersive spectroscopy （EDS） analyses suggest that the appearance of thin diffusion layers between Al and Mg interfaces is helpful to improve the bonding strength, while the presence of thick diffusion layer would reduce the bonding strength greatly.
文摘Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
文摘The energy variational formula based on the principle of minimum potential energy is proposed for the plates constrained at arbitrary points. As an instance, the orthotropic large deflection rectangular thin plates with four free edges and transverse displacement constraints under uniform transverse load are discussed. The generalized Fourier series are used as the trial functions of the transverse displacement and the stress function to establish the essential equations, which are linearized by means of the incremental method of load and displacement constraint. In the end of the paper, several computational results are compared with the former literature. Moreover, one typical example is demonstrated through advanced experimental technique. The result shows the accuracy is satisfied well.
文摘The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.
文摘Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
文摘Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.
基金supported by National Natural Science Foundation of China (Grant No. 50775044, Grant No. 50975050)Guangdong Provincial and Ministry of Education Industry-University-Research Integration Project of China (Grant No. 2009B090300044)
文摘The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.
文摘The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.
文摘The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.
基金financial supports provided by the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA22000000)National Natural Science Foundation of China(No.41804134)。
文摘The knowledge of crack type and dislocation orientation is helpful for the lifetime prediction of thin plates on aircrafts.The moment-tensor inversion utilizes the Acoustic Emission(AE)signals to detect cracks and the source mechanisms can be interpreted by the decomposition of moment tensors.Since the traditional moment-tensor inversion is implemented for the AE sources inside infinite elastic bodies,the inversion needs to be modified for the cracks in thin plates.In this study,the moment tensors of cracks in thin plates are derived and the inversion equation is provided based on the Green's function of second kind.A method of modifying the moment tensors to adapt to the existing decomposition processes and source-type plots is provided.By employing the Finite Element Method(FEM),the wave fields generated by the AE sources are computed.The AE sources continuously changing from pure tensile type(Model I)to shear type(Model II)are achieved in the FE models and the moment tensors are recovered.By the comparison between the reference values and recovered solutions,the source type can be accurately identified in the source-type plot and the applicability of the moment-tensor inversion for cracks in thin plates is confirmed.
