%0 Journal Article
%T Wave mode characteristics on piezo-electric stepped beam<br>阶梯压电层合梁的波动动力学特性
%A Ren Jianting Jiang Jiesheng Institute of Vibration Engineering
%A Northwest Polytechnic University
%A Xi''''an
%A China
%A <br>任建亭
%A 姜节胜
%J 力学学报
%D 2004
%I 
%X In this paper, a systematic approach for the free vibration analysis and forced-response of the beam bonded with PZT patches is presented employing the travelling wave method. The wave propagation characteristic of the stepped beam bonded with PZT patches is studied based on distributed parameters theories. Neglecting the effect of transverse shear and rotary inertia, harmonic wave solutions are found for both flexible and axial vibration of beam models. Then, the system is simplified into a node model considering multiple point discontinuities due to attached masses, and actuated moment of PZT patches. And wave scattering matrices including wave reflection and transmission matrices in nodes are formulated by applying the compatibility of displacements and equilibrium of forces at the junctions. Based on the above work, the concept of the wave loop, which is the process when the vibration wave comes through a periods along the wave propagation paths, is introduced, and wave loops and transmission matrices are derived accounting for general boundary conditions. Therefore, the wave loops matrices combined with the aid of field transfer matrices provides a concise and efficient method to solve the free vibration problem of beam bonded with PZT patches. The frequencies and response solutions are exact since the effects of attenuating wave components are included in the formulation. Furthermore, the general relations between the flexural wave transmission factor and the position of the PZT actuator in structures is discussed too. The numerical results give two major conclusions: 1) the PZT patch bonded position near by the fixed-end in beam has the powerful actuated capability, because the attenuating wave components created by the active wave incident upon the discontinuities boundary enhance the transmission effectiveness of the active traveling wave propagation; 2) the modulus of the mode transmission factor has a close relation with the sensitivity of the nature frequencies. The bigger modulus of the mode transmission factor, the bigger sensitivities factor of the nature frequencies is. In addition, a comparison of eigenvalues and frequency response function obtained by finite element method (FEM) and the wave method respectively is also presented. It is indicated that the result by the wave method is more exact than one by FEM.
%K wave propagation
%K wave reflection and transmission
%K wave loops
%K stepped beam<br>行波
%K 波循环
%K 波传递
%K 层合梁
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=DAB2E841698AA0A9&yid=D0E58B75BFD8E51C&vid=933658645952ED9F&iid=94C357A881DFC066&sid=DFBC046213B3DD86&eid=E5D85F291CED2DA6&journal_id=0459-1879&journal_name=力学学报&referenced_num=1&reference_num=9