|
|
|
| The free vibration characteristics analysis of rectangular plate with central opening using in arbitrary boundary conditions |
| QIU Yong-kang1 LI Tian-yun1,2,3 ZHU Xiang1,2 GUO Wen-jie1 MAO Yi-da1 |
1.School of Naval Architecture and Ocean Engineering，Huazhong University of Science and Technology，Wuhan 430074，China;
2.Hubei Provincial Key Laboratory of Ship and Marine Hydrodynamics, Wuhan 430074,China;
3.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240,China |
|
|
|
Abstract This paper based on the improved Fourier series method to establish a free vibration analysis model and calculate the natural frequency of rectangular plate with a central opening. When considering the opening, only a quarter of the plate is researched by using the symmetry of rectangular plate with central opening，which is divided into three regions. The admissible function displacement of each region is expressed by the improved Fourier series. By using the linear spring, which is uniform distribution along the border, simulate arbitrary boundary conditions. And through the continuous conditions of displacements determine the relationship of each regional plate. According to the Rayleigh-Ritz energy functional and variational method, we can get the overall energy functional. We can get the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. Solving the equation can obtain the natural frequencies and the corresponding vibration modes of rectangular plate with central opening. Finally, according to the calculation of numerical examples, comparing the calculated results with the finite element method to verify the accuracy and effectiveness of the method in this paper.
|
|
Received: 04 March 2016
Published: 15 October 2017
|
|
|
|
[1] Leissa A W. The free vibration of rectangular plates[J]. Journal of Sound and vibration, 1973, 31(3): 257-293.
[2] Lam K Y, Hung K C. Vibration study on plates with stiffened openings using orthogonal polynomials and partitioning method[J]. Computers & Structures, 1990, 37(3): 295-301.
[3] Paramasivam P. Free vibration of square plates with square openings[J]. Journal of Sound and Vibration, 1973, 30(2): 173-178.
[4] Ali R, Atwal S J. Prediction of natural frequencies of vibration of rectangular plates with rectangular cutouts[J]. Computers & Structures, 1980, 12(6): 819-823.
[5] Reddy J N. Large amplitude flexural vibration of layered composite plates with cutouts[J]. Journal of Sound and Vibration, 1982, 83(1): 1-10.
[6] Rajamani A, Prabhakaran R. Dynamic response of composite plates with cut-outs, part II: Clamped-clamped plates[J]. Journal of Sound and Vibration, 1977, 54(4): 565-576.
[7] Hegarty R F, Ariman T. Elasto-dynamic analysis of rectangular plates with circular holes[J]. International Journal of Solids and Structures, 1975, 11(7): 895-906.
[8] Aksu G, Ali R. Determination of dynamic characteristics of rectangular plates with cutouts using a finite difference formulation[J]. Journal of Sound and Vibration, 1976, 44(1): 147-158.
[9] Sivasubramonian B, Kulkarni A M, Rao G V, et al. Free vibration of curved panels with cutouts[J]. Journal of Sound and Vibration, 1997, 200(2): 227-234.
[10] Takahashi S. Vibration of rectangular plates with circular holes[J]. Bulletin of JSME, 1958, 1(4): 380-385.
[11] Li W L. Free vibrations of beams with general boundary conditions[J]. Journal of Sound and Vibration, 2000, 237(4): 709-725.
[12] Li W L. Vibration analysis of rectangular plates with general elastic boundary supports[J]. Journal of Sound and Vibration, 2004, 273(3): 619-635.
[13] Dai L, Yang T, Du J, et al. An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions[J]. Applied Acoustics, 2013, 74(3): 440-449.
|
|
|
|
