CAJ | 학술논문

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形板的自由振动,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动和反对称振动,给出了热电材料简支矩形板自由振动的三维精确解.采用MonteCarlo 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,计算结果与有关文献的结果一致.
종우합적삼유압전열탄성이론출발분석료횡관각향동성열전재료간지구형판적자유진동,증명기존재량류진동,즉해우적제일류진동화우합적제이류진동,여과판적결구화상하표면변계조건관우중면대칭,칙제이류진동우가진일보분해위대칭진동화반대칭진동,급출료열전재료간지구형판자유진동적삼유정학해.채용MonteCarlo 법극복료초월방정구복근적곤난,대우PZT-4구형판급출료수치결과,분석료우합효응대진동빈솔적영향,계산결과여유관문헌적결과일치.
Free vibration ofrectangular pyroelectric plates of transverse isotropy is analyzed basedon the three-dimensional coupled piezothermoelasticity theory. It hasbeen proved that there exist two classes of vibrations for apyroelectric plate of this type, that is, the uncoupled first class ofvibration and the coupled second class of vibration. The first class ofvibration includes the thickness-shear motion. If the structure of theplate and boundary conditions on the top and bottom surfaces aresymmetric about the middle plane, the second class of vibration can befurther decomposed into symmetric vibration and antisymmetric vibration.Three dimensional exact solutions are obtained for free vibration ofrectangular pyroelectric plates. Monte Carlo method is utilized toovercome the difficulty of solving transcendental equations for complexroots. Numerical results are presented for a rectangular PZT-4 plate.The results of calculation show good agreement with those given by otherresearchers. The results also show that frequencies for vibration of thefirst class are always real while frequencies for the second class arecomplex when thermo-mechanical and electro-thermal coupling effects areaccounted. The imaginary parts of complex frequencies, which representthermal damping, are all very small over the low and medium frequencyrange, which is commonly encountered in engineering. The effects ofthermo-mechanical and electro-thermal coupling on natural frequenciesare discussed. It is observed that the frequencies obtained in the opencondition are still higher that those in closed condition whenthermo-mechanical and electro-thermal coupling effects are considered.In addition, in the second class vibration frequencies of antisymmetricmode are higher than those of symmetric mode. Although numericalcalculation is only carried out on a single-layer PZT-4 plate, themethod proposed in this paper is also applicable for laminatedpyroelectric plates.