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横观各向同性热电材料简支矩形板的自由振动
引用本文:皓江,国凤林,侯鹏飞.横观各向同性热电材料简支矩形板的自由振动[J].力学学报,2000,32(4):402-411.
作者姓名:皓江  国凤林  侯鹏飞
作者单位:浙江大学土木系,杭州 310027
基金项目:国家自然科学基金资助项目(1987206).
摘    要:从耦合的三维压电热弹性理论出发分析了横观各向同性热电材料简支矩板的自由振动,证明其存在两类振动,即解耦的第一类振动和耦合的第二类振动,如果板的结构和上下表面边界条件关于中面对称,则第二类振动又可进一步分解为对称振和反对称振动,给出了热电材料简支矩形板自由振动的三维精确解,采用Monte Carlo法克服了超越方程求复根的困难。对于PZT-4矩形板给出了数值结果,分析了耦合效应对振动频率的影响,计算

关 键 词:横观各向异性  热电材料  矩形板  自由振动
修稿时间:1998年7月20日

FREE VIBRATION OF SIMPLY-SUPPORTED TRANSVERSELY ISOTROPIC PYROELECTRIC RECTANGULAR PLATES
Ding Haojiang,Guo Fenglin,Hou Pengfei.FREE VIBRATION OF SIMPLY-SUPPORTED TRANSVERSELY ISOTROPIC PYROELECTRIC RECTANGULAR PLATES[J].chinese journal of theoretical and applied mechanics,2000,32(4):402-411.
Authors:Ding Haojiang  Guo Fenglin  Hou Pengfei
Abstract:Free vibration of rectangulax pyroelectric plates of transverse isotropy is analyzed based on the three-dimensional coupled piezothermoelasticity theory.It has been proved that there exist two classes of vibrations for a pyroelectric plate of this type, that is, the uncoupled first class of vibration and the coupled second class of vibration. The first class of vibration includes the thickness-shear motion. If the structure of the plate and boundary conditions on the top and bottom surfaces are symmetric about the middle plane, the second class of vibration can be further decomposed into symmetric vibration and antisymmetric vibration. Three dimensional exact solutions are obtained for free vibration of rectangular pyroelectric plates. Monte Carlo method is utilized to overcome the difficulty of solving transcendental equations for complex roots.Numerical results are presented for a rectangular PZT-4 plate. The results of calculation show good agreement with those given by other researchers. The results also show that frequencies for vibration of the first class are always real while frequencies for the second class axe complex when thermo-mechanical and electro-thermal coupling effects are accounted. The imaginary parts of complex frequencies, which represent thermal damping, are all very small over the low and medium frequency range, which is commonly encountered in engineering. The effects of thermomechanical and electro-thermal coupling on natural frequencies are discussed. It is observed that the frequencies obtained in the open condition are still higher that those in closed condition when thermo-mechanical and electro-thermal coupling effects are considered. In addition, in the second class vibration frequencies of antisymmetric mode are higher than those of symmetric mode. Although numerical calculation is only carried out on a single-layer PZT-4 plate, the method proposed in this paper is also applicable for laminated pyroelectric plates.
Keywords:coupled piezothermoelasticity  rectangular pyroelectric plates  freevibration  thermal damping  pyroelectric effect
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