A method based on improved Fourier series method (IFSM) was proposed to solve free vibration characteristics of rectangular thin plates under arbitrary boundary conditions. The plate vibration displacement function was expressed as a linear combination of 2-D Fourier cosine series and auxiliary series to overcome the defect of vibration displacement function being dis-continuous at boundary using the traditional Fourier series method. A plate’s energy functional was established based on vibration displacement function. Using Hamilton principle, a rectangular thin plate’s natural frequencies and the corresponding displacement function’s coefficients were solved. The calculation results agreed well with those published in literature and using the finite element method to verify the correctness and reliability of the proposed method. Boundary restraint springs’ stiffness values were changed to simulate arbitrary boundary conditions. A lot of calculation results showed that in combination of fixed boundary conditions and elastic ones, dimensionless frequencies of a rectangular thin plate grow with increase in the range of fixed boundary conditions; in combination of simply supported and free boundary conditions and elastic ones, dimensionless frequencies of a rectangular thin plate grow with increase in the range of elastic boundary conditions.
Key words
Rectangular Thin Plates /
Vibration Characteristic /
Improved Fourier Series Method /
Elastic boundary condition
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References
[1] Liew K M, Xiang Y, Kitipornchai S. Transverse vibration of thick rectangular plates—I. Comprehensive sets of boundary conditions[J]. Computers & structures, 1993, 49(1): 1-29.
[2] Li J J, Cheng C J. Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect[J]. Journal of sound and vibration, 2005, 281(1): 295-309.
[3] Xiaofei Y W C Z H. ANALYTICAL SOLUTION FOR THE FORCED VIBRATION OF ORTHOTROPIC RECTANGULAR THIN PLATES [J][J]. Journal of Dynamics and Control, 2011, 1: 004.
[4] Shen Y, Gibbs B M. An approximate solution for the bending vibrations of a combination of rectangular thin plates[J]. Journal of sound and vibration, 1986, 105(1): 73-90.
[5] Cho D S, Vladimir N, Choi T M. Approximate natural vibration analysis of rectangular plates with openings using assumed mode method[J]. International Journal of Naval Architecture and Ocean Engineering, 2013, 5(3): 478-491.
[6] Reddy J N. Large amplitude flexural vibration of layered composite plates with cutouts[J]. Journal of Sound and Vibration, 1982, 83(1): 1-10.
[7] 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.
[8] D.J.Gorman. Free vibration analysis of Mindlin plates with uniform elastic edge support by the superposition method[J]. Journal of Sound and Vibration, 1997, 207, 335-350.
[9] Li H, Pang F, Wang X, et al. Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions[J]. Shock and Vibration, 2017, 2017. WOS：000411576100001
[10] Li W L, Zhang X, Du J, et al. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports[J]. Journal of Sound and Vibration, 2009, 321(1): 254-269.Hu, W.C.L. and J.P. Raney. Experimental and analytical study of vibrations of joined shells. Aiaa Journal 2012; 5(5): 976-980.
[11] Xie X, Zheng H, Jin G. Free vibration of four-parameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions[J]. Composites Part B: Engineering, 2015, 77: 59-73.
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