The Dynamic Characteristical Analytication Of L-shaped Structure-cavity Coupled System And The Investigation Of Investigation

In this paper, the dynamic behavior of a three-dimensional rectangular closed cavitycoupled with L-shaped flexible plates is investigated. The modified Fourier series are given toexpress the displacement of the plate and the sound pressure in the cavity. The equations ofmatrices for determining the modal characteristics and the dynamic response of the coupledsystem are obtained using the Rayleigh-Ritz procedure.First, the models of L-shaped structure-cavity coupled system are constructed to illustratethe free vibration features and the dynamic response of the coupled system. The displacementpresentation for the out-of-plane transverse vibration and the in-plane displacements in x-andy-directions for the transverse vibration of L-shaped plates with general elastic boundarysupports are given through the2D improved Fourier series. A3D modified Fourier series areadopted to expand the sound pressure inside the cavity.The sound pressure distribution function inside the cavity are given for the rectangularcavity with rigid walls. At the conncetion between structures, four kinds of spring areintrouded to describe the out-of plane shear force, the transverse force, the in-planelongitudinal force and the in-plane shear force. The coupling effect of the plates is describedby these internal forces which can be artificially regulated by changing the stiffness ofcorresponding springs. All the unknown coefficients are obtained obtained using theRayleigh-Ritz procedure based on the energy expressions for the L-shaped structure-cavitycoupled system.The modal characterictics and the dynamic response of the L-shaped structure-cavitycoupled system are calculated by Matlab and the results are compared with the ones obtainedby Ansys. The results show the difference for the first20natural frequencies of the coupledsystem is less than1.5%. A nice agreement for the fist6order mode shapes for the coupedsystem can be observed in this paper. The accuracy for the method of the paper is validatedthrough comparison. At the same time, the comparison of the velocity responses of the plateand the sound pressure responses inside the cavity obtained from the current method and fromAnsys are given. The nice agreement illustrate the prediction of the velocity responses of theplate and the sound pressure responses inside the cavity of the current method is acceptable.In the end, a laser test system was used to obtain the natural frequencies of the coupledsystem and the velocity responses of the plate and the sound pressure responses inside the cavity. The results obtained from the current method and the ones obtained throughexperimental measurement are compared to demonstrate the accuracy of the current method.