New exact solutions for free vibrations of thin orthotropic rectangular plates
Source abstract
Abstract
In this paper, a novel separation of variables is presented for solving the exact solutions for the free vibrations of thin orthotropic rectangular plates with all combinations of simply supported (S) and clamped (C) boundary conditions, and the correctness of the exact solutions are proved mathematically. The exact solutions for the three cases SSCC, SCCC, and CCCC are successfully obtained for the first time, although it was believed that they are unable to be obtained. The new exact solutions are further validated by extensive numerical comparisons with the solutions of FEM and those available in the literature.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Vibration and Dynamic Analysis · Structural Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (50)
Show source-provided references
1. Approximate solution for free vibrations of thin orthotropic rectangular plates10.1016/j.jsv.2005.01.005 ↗
2. Vibrations of a rectangular orthotropic plate with a free edge a comparison of analytical and numerical results10.1016/S0029-8018(97)00022-X ↗
3. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported10.1016/j.compstruct.2004.05.015 ↗
4. Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation10.1006/jsvi.1996.9999 ↗
5. Chladni · 1802
6. Lord · 1877 · vol. 1
7. Uber eine neue methode zur losung gewisser variations probleme der mathematischen physic10.1515/crll.1909.135.1 ↗
8. Research on thick plate vibration: a literature survey10.1006/jsvi.1995.0072 ↗
9. Leissa · 1969
10. Recent research in plate vibrations, 1973–1976: classical theory10.1177/058310247700901005 ↗
11. Recent research in plate vibrations, 1973–1976: complicating effects10.1177/058310247801001204 ↗
12. Plate vibration research, 1976–1980: complicating effects10.1177/058310248101301004 ↗
13. Recent studies in plate vibration, 1981–1985: complicating effects10.1177/058310248701900304 ↗
14. Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges10.1016/S0263-8223(03)00132-6 ↗
15. Szilard · 1974
16. Lekhnitskii · 1968
17. Meirovitch · 1986
18. The frequency of flexural vibration of rectangular orthotropic plates with clamped or supported edges10.1115/1.4012107 ↗
19. Natural frequencies of rectangular plates using characteristic orthogonal polynomials in the Rayleigh–Ritz method10.1016/S0022-460X(85)80109-7 ↗
20. On the use of orthogonal polynomials in the Reyleigh–Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates10.1016/S0022-460X(86)80310-8 ↗
21. Upper and lower bounds to the natural frequencies of vibration of clamped rectangular orthotropic plates10.1016/0020-7683(78)90001-X ↗
22. Bazely NW, Fox DW, Stadter JT. Upper and lower bounds for frequencies of rectangular clamped plates. Applied Physics Laboratory, Technical Memo, TG-626. The John Hopkins University, Baltimore; 1965.
23. Timoshenko · 1959
24. Gorman · 1982
25. Accurate free vibration analysis of clamped orthotropic plates by the method of superposition10.1016/0022-460X(90)90758-R ↗
26. Accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition10.1006/jsvi.1993.1267 ↗
27. Accurate free vibration analysis of completely free symmetric cross-ply rectangular laminated plates10.1016/S0263-8223(02)00337-9 ↗
28. Free vibration analysis of point supported orthotropic plates10.1061/(ASCE)0733-9399(1994)120:1(58) ↗
29. Accurate free vibration analysis of laminated symmetric cross-ply rectangular plates by the superposition-Galerkiin method10.1016/0263-8223(95)00008-9 ↗
30. Gorman · 1999
31. Generic free vibration of orthotropic rectangular plates with clamped and simply supported edges10.1006/jsvi.1993.1180 ↗
32. Generic buckling curves for specially orthotropic rectangular plates10.2514/3.8219 ↗
33. Untruncated infinite series superposition method for accurate flexural analysis of isotropic/orthotropic rectangular plates with arbitrary edge conditions10.1016/j.compstruct.2007.04.001 ↗
34. Accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series10.1016/j.jsv.2008.01.013 ↗
35. Kantorovich · 1964
36. Application of the extended Kantorovich method to the vibration of clamped rectangular plates10.1016/0022-460X(76)90390-4 ↗
37. Plate characteristic functions and natural frequencies of vibration of plates by iterative reduction of partial differential equation10.1115/1.2930328 ↗
38. Natural vibration analysis of clamped rectangular orthotropic plates10.1006/jsvi.1996.0026 ↗
39. Free vibration solution for clamped orthotropic plates using the Kantorovich method10.1006/jsvi.1996.0479 ↗
40. Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation10.1006/jsvi.1996.9999 ↗
41. Free vibrations of rectangular orthotropic plates with a pair of parallel edges simply supported10.1016/0045-7949(90)90363-7 ↗
42. Free vibration solution for clamped orthotropic plates using Lagrangian mulitplier technique10.2514/3.9594 ↗
43. Free vibration analysis of orthotropic plates by the initial value method10.1016/0045-7949(89)90483-5 ↗
44. Evaluation of fundamental vibration frequency of an orthotropic bending plate by using an iterative approach10.1016/S0045-7825(97)00321-6 ↗
45. Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions10.1016/j.jsv.2005.01.052 ↗
46. Free vibration analysis of thin coplanar rectangular plate assemblies – Part I: theory, and initial results for specially orthotropic plates10.1016/0263-8223(95)00139-5 ↗
47. Free vibration analysis of thin coplanar rectangular plate assemblies – Part II: theory, and initial results for specially orthotropic plates10.1016/0263-8223(95)00138-7 ↗
48. Bending, stability and free vibrations of thin orthotropic plates by simplified mixed finite elements10.1016/0022-460X(78)90511-4 ↗
49. Free vibration, buckling, and static deflections of functionally graded plates10.1016/j.compscitech.2006.02.032 ↗
50. Levy-type piezothermoelastic solution for hybrid plate by using first-order shear deformation theory10.1016/S1359-8368(96)00071-6 ↗