×

zbMATH — the first resource for mathematics

Free vibration analysis of thin isotropic and anisotropic rectangular plates by the discrete singular convolution algorithm. (English) Zbl 1235.74330
Summary: This paper presents the free vibration analysis of thin isotropic and anisotropic rectangular plates with various boundary conditions by using the discrete singular convolution (DSC) algorithm. Based on Taylor’s series expansion, a unique scheme is proposed to handle various boundary conditions, including the simply supported (S), clamped (C) and free (F) edge. To validate the proposed method, the non-dimensional frequency parameters of isotropic, orthotropic and angle-ply symmetric laminated rectangular plates with various combinations of boundary conditions are obtained by using the DSC algorithm and compared with the analytical and/or numerical solutions. Comparisons reveal that the proposed method can handle the zero bending moment and zero shear force conditions for the isotropic as well as anisotropic plates. The proposed method provides an alternative way for applying the simply supported boundary conditions in applications of the DSC algorithm to plate structures. This investigation extends the application range of the DSC algorithm to vibration analysis of anisotropic plates with various combinations of boundary conditions.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Leissa, The free vibration of rectangular plates, Journal of Sound and Vibration 31 pp 257– (1973) · Zbl 0268.73033 · doi:10.1016/S0022-460X(73)80371-2
[2] Leissa, Vibration studies for simply supported symmetrically laminated rectangular plates, Composite Structures 12 pp 113– (1989) · doi:10.1016/0263-8223(89)90085-8
[3] Chow, Transverse vibration of symmetrically laminated rectangular composite plates, Composite Structures 20 pp 213– (1992) · doi:10.1016/0263-8223(92)90027-A
[4] Bellman, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications 34 pp 235– (1971) · Zbl 0236.65020 · doi:10.1016/0022-247X(71)90110-7
[5] Wang, A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates, Journal of Sound and Vibration 162 (3) pp 566– (1993) · Zbl 0958.74527 · doi:10.1006/jsvi.1993.1143
[6] Bert, Differential quadrature for static and free vibration analyses of anisotropic plates, International Journal of Solids and Structures 30 (13) pp 1737– (1993) · Zbl 0800.73182 · doi:10.1016/0020-7683(93)90230-5
[7] Wang, Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method, International Journal for Numerical Methods in Engineering 59 pp 1207– (2004) · Zbl 1041.74563 · doi:10.1002/nme.913
[8] Wei, Discrete singular convolution for the solution of the Fokker-Planck equations, Journal of Chemical Physics 110 pp 8930– (1999) · doi:10.1063/1.478812
[9] Wei, A new algorithm for solving some mechanical problems, Computer Methods in Applied Mechanics and Engineering 190 (15-17) pp 2017– (2001) · Zbl 1013.74081 · doi:10.1016/S0045-7825(00)00219-X
[10] Wei, Vibration analysis by discrete singular convolution, Journal of Sound and Vibration 244 (3) pp 535– (2001) · Zbl 1237.74095 · doi:10.1006/jsvi.2000.3507
[11] Wei, The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, International Journal of Mechanical Sciences 43 (8) pp 1731– (2001) · Zbl 1018.74017 · doi:10.1016/S0020-7403(01)00021-2
[12] Zhao, Plate vibration under irregular internal supports, International Journal of Solids and Structures 39 (5) pp 1361– (2002) · Zbl 1090.74603 · doi:10.1016/S0020-7683(01)00241-4
[13] Wei, Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: theory and algorithm, International Journal for Numerical Methods in Engineering 55 pp 913– (2002) · Zbl 1058.74643 · doi:10.1002/nme.526
[14] Xiang, Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: applications, International Journal for Numerical Methods in Engineering 55 pp 947– (2002) · Zbl 1058.74644 · doi:10.1002/nme.527
[15] Zhao, Discrete singular convolution for the prediction of high frequency vibration of plates, International Journal of Solids and Structures 39 (1) pp 65– (2002) · Zbl 1090.74604 · doi:10.1016/S0020-7683(01)00183-4
[16] Zhao, DSC analysis of rectangular plates with non-uniform boundary conditions, Journal of Sound and Vibration 255 (2) pp 203– (2002) · doi:10.1006/jsvi.2001.4150
[17] Ng, Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates, Computer Methods in Applied Mechanics and Engineering 193 (23-26) pp 2483– (2004) · Zbl 1067.74600 · doi:10.1016/j.cma.2004.01.013
[18] Yu, Matched interface and boundary (MIB) method for the vibration analysis of plates, Communications in Numerical Methods in Engineering 25 pp 923– (2009) · Zbl 1307.74043 · doi:10.1002/cnm.1130
[19] Civalek, Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight-sided quadrilateral plates, Communications in Numerical Methods in Engineering 24 pp 1475– (2008) · Zbl 1153.74022 · doi:10.1002/cnm.1046
[20] Civalek, Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach, Finite Elements in Analysis and Design 43 pp 1013– (2007) · doi:10.1016/j.finel.2007.06.014
[21] Civalek, Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach, Journal of Computational and Applied Mathematics 205 pp 251– (2007) · Zbl 1115.74058 · doi:10.1016/j.cam.2006.05.001
[22] Gürses, Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory, International Journal for Numerical Methods in Engineering 79 pp 290– (2009) · Zbl 1171.74464 · doi:10.1002/nme.2553
[23] Seçgin, Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification, Journal of Sound and Vibration 315 (1-2) pp 197– (2008) · doi:10.1016/j.jsv.2008.01.061
[24] Wang, Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution, Journal of Sound and Vibration 329 (10) pp 1780– (2010) · doi:10.1016/j.jsv.2009.12.006
[25] Gockel, MSC/NASTRAN Handbook for Dynamic Analysis: MSC/NASTRAN (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.