Shen Yapeng

Finite element approach of vibration control using self-sensing piezoelectric actuators

The general finite element formulations for piezoelectric sensors and actuators are derived by using the virtual work principle, and are verified mathematically and numerically. The amplitude-frequency and the phase-frequency charactersitics of the closed-loop system are studied in detail, and the control effects owing to the distributions of the segmented piezoelectric patches are also investigated. Several numerical results are presented.

Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent

Abstract The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to deal with a thermoelastic–piezoelectric coupled two-dimensional thermal shock problem of a thick piezoelectric plate of infinite extent by means of the hybrid Laplace transform-finite element method. The generalized thermoelastic–piezoelectric coupled finite element equations are formulated. By using Laplace transform the equations are solved and the solutions of the temperature, displacement and electric potential are obtained in the Laplace transform domain. Then the numerical inversion is carried out to obtain the temperature, displacement and electric potential distributions in the physical domain. The distributions are represented graphically. From the distributions, it can be found the wave type heat propagation in the piezoelectric plate. The heat wavefront moves forward with a finite speed in the piezoelectric plate with the passage of time. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in media.

Stability Analysis of Piezoelectric Circular Cylindrical Shells

A study on the problem of linear buckling of piezoelectric circular cylindrical shells subjected to external pressure as well as on an electric field is presented. In this paper, the structure is treated as a three-dimensional one. The results reveal that the piezoelectric effect has significant effect on the critical load, while the stress due to the uniformly applied electric field alone is not likely to cause elastic buckling. In addition, they can also be used to assess the limitation of shell theories in predicting buckling of piezoelectric smart shell structures.

Vibration and damping analysis of a composite plate with active and passive damping layer

The equations of motion and boundary conditions governing the vibration of nonsymmetric composite plates with active and passive dampings layer are derived. The analytical solution is first obtained for frequencies and loss factors of the plates with active constrained layer damping treatments. The distributions of electric potential across, the thickness of piezoelectric, layer and relevant governing equations are obtained when the direct and inverse, piezolectric effects are considered. The influence of the direct and inverse piezoelectric effects on the frequencies and loss factors are investigated.

THE ANALYSIS OF CRACK PROBLEMS WITH NON-LOCAL ELASTICITY *

In this paper, the displacement discontinuity fundamental solutions (DDFS) corresponding to the unit concentrated displacement discontinuity for plane problems of non-local elasticity are obtained. Based on the displacement discontinuity boundary integral equation (DDBIE) and boundary element method (BEM), a method of analysis of crack problems in non-local elasticity with generalized purpose is proposed. By using this method, several important problems in fracture mechanics such as edge crack are studied. The study of edge crack shows that the stress concentration factor (SCF) near the crack tip is not a constant but varies with the crack length. With this result the effect of crack length on the fracture toughness KI c is studied. The results obtained in this paper are in accordance with the published ones.

Gradient surface ply model of SH wave propagation in SAW sensors

Investigation of the propagation of the wave in SAW sensors is a basis for the research and design of the sensors. With the advance of the sensor, both the effect of environment on the surface ply and the geometry of waveguide are complicated. To consider the complication, a model with gradient surface ply and multilayer waveguide of SH wave propagation in sensor is proposed. The equation of wave velocity is derived by a transfer matrix method. Through the equation, the function of wave velocity increment via the change of parameters in the surface ply is obtained. The effect of the inhomogeneity on the function is also studied. Finally, some influencing factors of the behavior of the sensor are discussed.

Scattering of anti-plane shear waves by a single crack in an unbounded trasversely isotropic electro-magneto-elastic medium

A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.

The Finite Element Method of Viscoelastic Large Deformation Plane Problem with Kirchhoff Stress Tensors-Green Strain Tensors Constitutive Relation

The stress analysis of viscoelastic large deformation plane problem had been completed in [1]. Because the Eular stress tensors are used in the viscoelastic differential constitutive relation, when the rigid-body rotation can not be negligible the accuracy of results is relatively poor.

Some Faults in the Stress Analysis of Power-Hardening Materials With Pseudo-Stress Function Method

A new analytic method was suggested and described by Lee(1987), which is known as the pseudo-stress function method similar to the Airy stress function method in linear elasticity. Here the serious errors of Lees theory are presented

Electromechanical Coupling Multiaxial Experimental and Micro-Constitutive Model Study of Pb(Mg1/3Nb2/3)O3- 0.32PbTiO3 Ferroelectric Single Crystal

Compared to polycrystalline ferroelectric ceramics such as Pb(Zr1/2Ti1/2)-O3 (PZT), domain en‐ gineered relaxor ferroelectric single crystals Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-xPT) and Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) show greatly enhanced electromechanical properties: the piezoelectric coefficient d33 and electrically induced strain of <001> oriented single crystals direction can respectively reach 2500pC/N and 1.7%, or even greater [1],[2]. PZN-xPT and PMN-xPT with outstanding properties are usually near the morphotropic phase boundary (MPB), separating rhombohedra (R) and tetragonal (T) phases [1], [4], [5]. For example, the MPB is located within a range of x=0.275-0.33 for PMN-xPT [6], [7]. Recent investigations have also shown that the MPB of PMN-xPT and PZN-xPT is actually in a multi-phase state at room temperature [8], [9]. e.g., the coexistence of rhombohedra (R) and monoclinic (M) phases at x=0.33 or rhombohedra and tetragonal phases at x=0.32. Other phases can also exist near MPB under stress and/or electric field loading. Experiment studies [10], [11], [12] and first-princi‐ ples calculations [4], [13]reveal that two different homogeneous polarization rotation path‐ ways are present between rhombohedra and tetragonal phases under an electric field. It is found that three kinds of intermediate monoclinic phases MA, MB and MC are associated with the two pathways [9], [10]. Orthorhombic phase has also been observed between the rhombo‐ hedra and tetragonal phases when PMN-PT is loaded with strong electric field along the <110> direction [9],[14]. Although the mechanism underlying the high performance of these crystals is not completely clear, the existence of the intermediate phases and the associated phase tran‐ sitions are believed to be one of the main reasons [1], [3], [4], [8], [10].