Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.     

Exact solution of orthotropic cylindrical shell with piezoelectric layers under cylindrical bending

An exact elasticity solution for an orthotropic cylindrical shell with piezoelectric layers is obtained in this paper. The stress and displacement distributions are presented. The influence of the piezoelectric layers on the mechanical behavior of structures is studied. Both the direct piezoelectric effect and the converse piezoelectrical effect of the piezoelectric material are investigated. Results presented in this paper can be used to study various approximate shell theories used in the numerical simulations of piezoelectric structures.     

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory (FSDT) of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young’s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.     

Analysis of wave propagation in piezoelectric coupled cylinder affected by transverse shear and rotary inertia

In this paper, we examine the wave propagation in a piezoelectric coupled cylindrical shell affected by the shear effect and rotary inertia. A complete mathematical analysis of wave propagation solution in this piezoelectric coupled cylindrical shell is provided. The dispersion characteristics are derived through the solving an eigenvalue problem. Results are validated by the classical solution of a metallic cylinder. Besides providing and discussing the dispersion curves for different wave modes, we also examine the piezoelectric effects on the dispersion curves. Further to the above investigation, comparison of dispersion solutions from different shell theories is also conducted. This work may serve as a benchmark for wave propagation in piezoelectric coupled cylindrical shells.     

Three-dimensional solution of smart laminated anisotropic circular cylindrical shells with imperfect bonding

This paper presents an exact solution for a simply-supported and laminated anisotropic cylindrical shell strip with imperfect bonding at the off-axis elastic layer interfaces and with attached anisotropic piezoelectric actuator and sensor subjected to transverse loading. In this research, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective discontinuities in displacements. The solution for an elastic (or piezoelectric) layer of the smart laminated cylindrical shell strip is obtained in terms of the six-dimensional (or eight-dimensional) pseudo-Stroh formalism, solution for multilayered system is then derived based on the transfer matrix method. Finally, a numerical example is presented to demonstrate the effect of imperfect interface on the static response of the smart laminated cylindrical shell. The derived solutions can serve as benchmark results to assess various approximate shell theories and numerical methods.     

恒磁场作用下压磁/压电半导体复合圆柱壳的耦合响应分析

本文针对由压磁材料和压电半导体材料组成的无限长复合圆柱壳结构,理论研究了其在径向恒磁场作用下结构内的多场耦合力学响应问题。为解析求解方便,文中分别采用单向耦合法和线性全耦合法,导出复合圆柱壳内位移场、电场、载流子等物理量的解析表达式。利用导出的解析表达式,数值分析了磁场大小和半导体层厚度比对结构内电势、电场和载流子的影响。计算结果表明：磁场和厚度比均可用来有效调控半导体层内的电学量,复合圆柱壳结构的厚度比有一个最优区间。     

恒磁场作用下压磁/压电半导体复合圆柱壳的耦合响应分析

本文针对由压磁材料和压电半导体材料组成的无限长复合圆柱壳结构,理论研究了其在径向恒磁场作用下结构内的多场耦合力学响应问题。为解析求解方便,文中分别采用单向耦合法和线性全耦合法,导出复合圆柱壳内位移场、电场、载流子等物理量的解析表达式。利用导出的解析表达式,数值分析了磁场大小和半导体层厚度比对结构内电势、电场和载流子的影响。计算结果表明：磁场和厚度比均可用来有效调控半导体层内的电学量,复合圆柱壳结构的厚度比有一个最优区间。     

AN ANALYSIS OF A CYLINDRICAL THIN SHELL AS A PIEZOELECTRIC TRANSFORMER

The vibration of a circular cylindrical piezoelectric ceramic shell with tangential poling is investigated for transformer application and an analytical solution is obtained.Numer- ical calculations of the output voltage,input admittance and the efficiency of the transformer are presented.The results indicate that the structure analyzed can be used as a piezoelectric transformer with a certain harmonic driving frequency and matching load impedance.     

ACTIVE CONTROL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL''''S VIBRATION UNDER HYDROSTATIC PRESSURE

IntroductionDuetotheintrinsicdirectandconversepiezoelectriceffects,piezoelectricmaterialscanbeeffectivelyusedtoproducesensorsoractuatorsfortheactiveshapeorvibrationcontrolostructures.Therefore,theuseofpiezoelectricmaterialsinintelligentstructuresattractedmanyattentionsinrecentyears.Thedesignofsuchactivesystemsrequiresgoodunderstandingofthemechanical_electricinteractionbetweenthestructuresandpiezoelectricmaterials.Manyinvestigationshavebeendoneinthisfield[1].However,mostofthesestudiesarebasedo…     

含压电层的功能梯度柱壳的自由振动分析

基于三维弹性理论,导出了带有压电层的圆柱形梯度壳的动力学方程以及相应的边界条件,用幂级数展开法得到了求解该圆柱形梯度壳自由振动的三维精确公式．通过实例模型求解了该壳体的自由振动的固有频率;分析了不同电学边界条件对壳体的振动频率的影响。结果可评估各种近似理论解和数值解的正确性。     

Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators

A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Kármán–Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

Wave propagation in Reissner–Mindlin piezoelectric coupled cylinder with non-constant electric field through the thickness

In a recent paper by Berg et al. [Berg, M., Hagedorn, P., Gutschmidt, S., 2004. On the dynamics of piezoelectric cylindrical shell, Journal of Sound and Vibration 274, 91–109], equations for the piezo-ceramic cylindrical shell are derived. These equations differ from known equations because the electric field is not assumed to be constant over the thickness, but is obtained by solving the Maxwell’s equation. The considered shell model is the so-called Flugge’s shell theory where the transverse shear deformations is not considered, and the Maxwell’s equation is reduced in form. In this paper the analysis of wave propagation in Reissner–Mindlin piezoelectric coupled cylinder is studied. The shear strain is modelled and the Maxwell’s equation is fully considered.     

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: Part II– Applications

A comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties is developed and applied to examples of practical importance. Details on derivation of a general homogenized smart shell model are provided in Part I of this work. The present paper solves the obtained unit cell problems and develops expressions for the effective elastic, piezoelectric and thermal expansion coefficients for the grid reinforced smart composite shell. Thus obtained effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The applicability of the model is illustrated by means of several examples including cylindrical reinforced smart composite shells, and multi-layer smart shells. The derived expressions allow tailoring the effective properties of a smart grid-reinforced shell to meet the requirements of a particular application by changing certain geometric or physical parameters.     

Low-energy impact of adaptive cylindrical piezoelectric–composite shells

A theoretical framework for analyzing low-energy impacts of laminated shells with active and sensory piezoelectric layers is presented, including impactor dynamics and contact law. The formulation encompasses a coupled piezoelectric shell theory mixing first order shear displacement assumptions and layerwise variation of electric potential. An exact in-plane Ritz solution for the impact of open cylindrical piezoelectric–composite shells is developed and solved numerically using an explicit time integration scheme. The active impact control problem of adaptive cylindrical shells with distributed curved piezoelectric actuators is addressed. The cases of optimized state feedback controllers and output feedback controllers using piezoelectric sensors are analyzed. Numerical results quantify the impact response of cylindrical shells of various curvatures including the signal of curved piezoelectric sensors. Additional numerical studies quantify the impact response of adaptive cylindrical panels and investigate the feasibility of actively reducing the impact force.     

压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状,着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法;（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发,不引进任何变形假设,因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。     

功能梯度压电、压磁柱对称问题的振动分析

本文在不考虑体力、体电流和体电荷的情况下, 假定压电、压磁柱壳的材料参数沿圆柱厚度方向呈幂函数分布时, 研究了径向载荷作用下功能梯度压电、压磁空心柱壳的空间柱对称径向振动问题. 首先在柱坐标系下, 由功能梯度材料的参数、本构、梯度和平衡方程推导得出外激励作用下以Bessel函数表示圆柱壳的应力、电势、磁势等物理量的稳态解, 进而对空间柱对称的压电、压磁功能梯度材料动力控制问题进行了理论分析. 可以看出, 当梯度参数时, 即完全退化为横观各项同性压电、压磁柱对称的振动问题, 与文献[16]的基本方程为柱坐标下得出的结果一致. 最后给出数值算例, 结果表明材料不均匀性对沿径向振动各物理量的显著影响, 且用一个特定不均匀性参数值可以优化电磁力耦合的性能, 这在现代工程设计中尤为重要.     

功能梯度压电、压磁柱对称问题的振动分析

本文在不考虑体力、体电流和体电荷的情况下, 假定压电、压磁柱壳的材料参数沿圆柱厚度方向呈幂函数分布时, 研究了径向载荷作用下功能梯度压电、压磁空心柱壳的空间柱对称径向振动问题. 首先在柱坐标系下, 由功能梯度材料的参数、本构、梯度和平衡方程推导得出外激励作用下以Bessel函数表示圆柱壳的应力、电势、磁势等物理量的稳态解, 进而对空间柱对称的压电、压磁功能梯度材料动力控制问题进行了理论分析. 可以看出, 当梯度参数时, 即完全退化为横观各项同性压电、压磁柱对称的振动问题, 与文献[16]的基本方程为柱坐标下得出的结果一致. 最后给出数值算例, 结果表明材料不均匀性对沿径向振动各物理量的显著影响, 且用一个特定不均匀性参数值可以优化电磁力耦合的性能, 这在现代工程设计中尤为重要.     

复合材料层板构件气弹振动控制实验研究

飞机局部复合材料构件存在着因涡流作用诱发的弹性振动问题。本文首先研究了表面粘贴型压电元件对复合材料构件的传感和驱动原理;针对结构待控模态的要求,采用了D-准则优化确定同位压电传感/驱动器在构件中的布置方案;应用自适应振动前馈控制原理和方法,构造了闭环控制系统;分别利用正弦和方波信号激发气动声场,对玻纤/环氧圆筒构件进行激振和振动控制实验;结果表明：构件主要待控模态的振动得到了有效抑制,但也出现了高阶模态被激发的问题,导致结构辐射噪声上升。     

Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load

Summary An exact axisymmetric piezothermoelastic solution is presented for a simply-supported hybrid cylindrical shell made of cross-ply composite laminate and piezoelectric layers. Numerical results for hybrid shells are presented for sinusoidal and central band thermal and electrical loads. The effect of the loading, the radius-to-thickness ratio, the span-to-radius ratio and the number of layers of the substrate on the response is investigated. The interface between the substrate and the actuated piezoelectric layer has been found to be subjected to high shear stress. It has been shown that the maximum values of the deflection and the stresses, due to thermal load, can be appreciably reduced by appropriate application of actuation potential. Accepted for publication 13 October 1996     

Buckling and post-buckling analyses for an axially compressed laminated cylindrical shell of FGM with PFRC in thermal environments

In this paper, investigation on buckling and post-buckling behaviors of a laminated cylindrical shell of functionally graded material (FGM) with the piezoelectric fiber reinforced composite (PFRC) actuators subjected to thermal and axial compressed loads is presented. Based on the Donnell assumptions, the material properties of the FGM layer vary smoothly through the laminated cylindrical shell thickness according to a power law distribution of the volume fraction of constituent materials. In the present study, a numerical procedure for the laminated cylindrical shell is used based on the Ritz energy method and the nonlinear strain–displacement relations. Some useful discussion and numerical examples are presented to show various effects of temperature field, volume fraction and geometric parameters on the buckling and post-buckling behaviors of the laminated cylindrical shell with PFRC.