The control of the piezoelastic laminated cylindrical shell's vibration under hydrostatic pressure was discussed. From Hamilton's principle nonlinear dynamic equations of the piezoelastic laminated cyl...The control of the piezoelastic laminated cylindrical shell's vibration under hydrostatic pressure was discussed. From Hamilton's principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which, the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using veloctity feedback control, a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system, the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.展开更多
This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are d...This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.展开更多
Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is in...Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.展开更多
Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is invest...Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.展开更多
The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of...The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.g.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.展开更多
文摘The control of the piezoelastic laminated cylindrical shell's vibration under hydrostatic pressure was discussed. From Hamilton's principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which, the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using veloctity feedback control, a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system, the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.
基金supported by the National Natural Science Foundation of China (No. 10572049)
文摘This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.
基金Project supported by the National Nature Science Foundation of China(Nos.11262012,11262017,11462020,and 10761005)the Scientific Research Key Program of Inner Mongolia University of Technology(No.ZD201219)
文摘Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.
基金supported by the National Natural Science Foundation of China (Nos.11262012, 11462020, 10761005 and 11262017)the Scientific Research Key Program of Inner Mongolia University of Technology of China (No.ZD201219)+1 种基金the Natural Science Foundation of Inner Mongolia Department of Public Education of China (No.NJZZ13037)the Inner Mongolia Natural Science Foundation of China (No.2013MS0114)
文摘Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.
基金supported by the Linz Institute of Technology[MiFESMS].
文摘The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.g.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.
