Mesh-free least-squares-based finite difference method for large-amplitude free vibration analysis of arbitrarily shaped thin plates

Journal of Sound and Vibration

Volumn 317, Issue 3-5, 2008, Pages 955-974

  Wu, W X ^a   Shu, C ^a   Wang, C M ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

AIRCRAFT ENGINES; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL MECHANICS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FUNCTIONS; LATTICE VIBRATIONS; LEAST SQUARES APPROXIMATIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); VIBRATIONS (MECHANICAL);

APPROXIMATE NUMERICAL METHOD; COMPLEX DOMAINS; COMPLEX SHAPES; DISPLACEMENT COMPONENTS; FINITE DIFFERENCE (FD); FREE VIBRATION ANALYSES; FREE VIBRATION PROBLEM; FUNCTION VALUES; LARGE DEFLECTIONS; LEAST SQUARES (LS); LOCAL APPROXIMATION; MESH FREE; MESH FREE METHODS; NON LINEAR PDE; ORDINARY DIFFERENTIAL EQUATION (ODE); PARTIAL DIFFERENTIAL; SPATIAL DERIVATIVES; THIN PLATES; VIBRATION FREQUENCIES;

FINITE DIFFERENCE METHOD;

EID: 48349105784     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2008.03.050     Document Type: Article

References (26)

1. Timoshenko S.P., and Woinowsky-Krieger S. Theory of Plates and Shells. second ed. (1959), McGraw-Hill, New York
2. Ugural A.C. Stresses in Plates and Shells. second ed (1999), McGraw-Hill, New York
3. Leissa A.W. Vibration of Plates (1993), NASA
4. Chu H.N., and Herrmann G. Influence of large amplitudes on free flexural vibrations of rectangular elastic plates. Journal of Applied Mechanics 23 (1956) 532-540
5. Yamaki N. Influence of large amplitudes on flexural vibrations of elastic plates. ZAMM 41 (1961) 501-510
6. Berger H.M. A new approach to the analysis of large deflections of plates. Journal of Applied Mechanics 22 (1955) 465-472
7. Wah T. Large amplitude flexural vibration of rectangular plates. International Journal of Mechanical Sciences 5 (1963) 425-438
8. Mei C. Finite element displacement method for large amplitude free flexural vibrations of beams and plates. Computers and Structures 3 (1973) 163-174
9. Rao G.V., Raju I.S., and Raju K.K. A finite element formulation for large amplitude flexural vibrations of thin rectangular plates. Computers and Structures 6 (1976) 163-167
10. Rao G.V., Raju K.K., and Raju I.S. Finite element formulation for the large amplitude free vibrations of beams and orthotropic circular plates. Computers and Structures 6 (1976) 169-172
11. Mei C., Narayanaswami R., and Rao G.V. Large amplitude free flexural vibrations of thin plates of arbitrary shapes. Computers and Structures 10 (1979) 675-681
12. Wang X.X., Qian J., and Huang M.K. A boundary integral equation formulation for large amplitude nonlinear vibration of thin elastic plates. Computer Methods in Applied Mechanics and Engineering 86 (1991) 73-86
13. Shi Y., and Mei C. A finite element time domain modal formulation for large amplitude free vibrations of beams and plates. Journal of Sound and Vibration 193 (1996) 453-464
14. Kurpa L., Pilgun G., and Ventsel E. Application of the R-function method to nonlinear vibrations of thin plates of arbitrary shape. Journal of Sound and Vibration 284 (2005) 379-392
15. Barik M., and Mukhopadhyay M. A new stiffened plate element for the analysis of arbitrary plates. Thin-Walled Structures 40 (2002) 625-639
16. Ding H., Shu C., Yeo K.S., and Xu D. Development of least square-based two-dimensional finite difference schemes and their application to simulate natural convection in a cavity. Computers and Fluids 33 (2004) 137-154
17. Shu C., Wu W.X., Ding H., and Wang C.M. Free vibration analysis of plates using least-square-based finite difference method. Computer Methods in Applied Mechanics and Engineering 196 (2007) 1330-1343
18. C.M. Wang, W.X. Wu, C. Shu, T. Utsunomiya, LSFD method for vibration analysis of plates with free edges, Advances in Steel Structures, ICASS'05, 2005, pp. 1715-1722.
19. Wu W.X., Shu C., and Wang C.M. Computation of modal stress resultants for completely free vibrating plates by LSFD method. Journal of Sound and Vibration 297 (2006) 704-726
20. Wang C.M., Wu W.X., Shu C., and Utsunomiya T. LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS. Computers and Structures 84 (2006) 2329-2339
21. Shu C., Wu W.X., and Wang C.M. Least squares finite difference method for vibration analysis of plates. In: Shanmugam N.E., and Wang C.M. (Eds). Analysis and Design of Plated Structures: Dynamics vol. 2 (2006), Woodhead Publishing Limited, Cambridge, England (Chapter 4)
22. Chen J.S., Pan C.H., Wu C.T., and Liu W.K. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering 139 (1996) 195-227
23. Li Q.S., and Huang Y.Q. Moving least-squares differential quadrature method for free vibration of antisymmetric laminates. Journal of Engineering Mechanics 130 12 (2004) 1447-1457
24. Liew K.M., Huang Y.Q., and Reddy J.N. Moving least squares differential quadrature method and its application to the analysis of shear deformable plates. International Journal for Numerical Methods in Engineering 56 15 (2003) 2331-2351
25. Liu W.K., Jun S., Li S.F., Adee J., and Belytschko T. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering 38 (1995) 1655-1679
26. Peng L.X., Liew K.M., and Kitipornchai S. Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method. Journal of Sound and Vibration 289 (2006) 421-449