Free vibration analyses of axially loaded laminated composite beams using a unified higher-order shear deformation theory and dynamic stiffness method
Source abstract
Abstract
Abstract Free vibration characteristics and buckling behaviors of generally laminated composite beams subjected to the concentrated axial force and various classical end conditions are investigated in this paper. The analysis is based on a unified higher-order shear deformation beam theory. The Poisson effect, axial force, extensional deformation, bending deformation, shear deformation, and rotary inertia are all incorporated in the formulation. The dynamic stiffness method is employed to perform the exact vibration and buckling analyses of laminated composite beams. The dynamic stiffness matrix is developed from the complete analytical solutions of the homogeneous governing differential equations. Numerical results for the natural frequencies and buckling loads of particular laminated beams are presented and compared with previously published results. The effects of shear deformation, axial force and end condition on the natural frequencies, buckling loads and/or mode shapes of the laminated beams are thoroughly analyzed.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Structural Load-Bearing Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (71)
Show source-provided references
1. The vibration of cantilever beams of fiber reinforced material10.1177/002199837200600406 ↗
2. An analytic means of determining the flexural and torsional resonant frequencies of generally orthotropic beams10.1016/S0022-460X(75)80107-6 ↗
3. Recent advances in analysis of laminated beams and plates: Part I. Shear effects and buckling; Part II. Vibrations and wave propagation10.2514/3.10202 ↗
4. Free vibration of composite beams – an exact method using symbolic computation10.2514/3.46767 ↗
5. Spectral-element-based solutions for wave propagation analysis of multiply connected unsymmetric laminated composite beams10.1006/jsvi.2000.3078 ↗
6. The vibration of beams of fibre reinforced material10.1016/S0022-460X(77)80044-8 ↗
7. The vibrations of generally orthotropic beams, a finite element approach10.1016/0022-460X(79)90021-X ↗
8. Static and dynamic formulation of symmetrically laminated beam finite element for microcomputer10.1177/002199838501900505 ↗
9. Free vibration of composite beams including rotary inertia and shear deformation10.1016/0263-8223(90)90010-C ↗
10. Analytical solutions to vibration of generally layered composite beams10.1016/0022-460X(92)90452-4 ↗
11. Free vibration of non-symmetric cross-ply laminated composite beams10.1006/jsvi.1994.1401 ↗
12. A generalized element for the free vibration analysis of composite beams10.1016/0045-7949(94)90068-X ↗
13. Dynamic stiffness analysis of laminated beams using first order shear deformation theory10.1016/0263-8223(95)00091-7 ↗
14. Free vibration of generally layered composite beams using symbolic computations10.1016/0263-8223(95)00112-3 ↗
15. Vibrations and buckling of cross-ply nonsymmetric laminated composite beams10.2514/3.13188 ↗
16. Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method10.1016/S0045-7949(98)00114-X ↗
17. Free vibration analysis of symmetric cross-ply laminated composite beams with the help of the transfer matrix approach10.1002/(SICI)1099-0887(199909)15:9<651::AID-CNM279>3.0.CO;2-Y ↗
18. Investigation of the rotary inertia and shear deformation effects on the out-of-plane bending and torsional natural frequencies of laminated beams10.1016/S0263-8223(00)00063-5 ↗
19. Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities10.1016/S0263-8223(01)00130-1 ↗
20. A spectral finite element model for analysis of axial-flexural-shear coupled wave propagation in laminated composite beams10.1016/S0263-8223(02)00228-3 ↗
21. A spectral element for laminated composite beams: theory and application to pyroshock analysis10.1016/S0022-460X(03)00488-7 ↗
22. A shear-deformable beam element for the analysis of laminated composites10.1016/j.finel.2006.11.011 ↗
23. An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia10.1016/j.ijmecsci.2012.09.007 ↗
24. Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams10.1177/0021998311432946 ↗
25. Some observations on the modeling of laminated composite beams with general lay-ups10.1016/0263-8223(91)90082-A ↗
26. A transverse shear and normal deformable orthotropic beam theory10.1016/0022-460X(92)90717-C ↗
27. Free vibration of composite beams using a refined shear flexible beam element10.1016/0045-7949(92)90514-Z ↗
28. Random response of symmetric cross-ply composite beams with arbitrary boundary conditions10.2514/3.11030 ↗
29. Free vibration of cross-ply laminated beams with arbitrary boundary conditions10.1016/0020-7225(94)90093-0 ↗
30. Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modelling10.1006/jsvi.1996.0362 ↗
31. Buckling of cross-ply laminated beams with arbitrary boundary conditions10.1016/S0263-8223(97)00048-2 ↗
32. Effects of shear deformation on buckling and free vibration of laminated composite beams10.1016/S0263-8223(97)00067-6 ↗
33. Analytical solution to the dynamic analysis of laminated beams using higher order refined theory10.1016/S0263-8223(97)00133-5 ↗
34. Bending, buckling and free vibration of laminated composite with a transverse shear stress continuity model10.1016/S1359-8368(97)00024-3 ↗
35. Free vibration analysis of two layered cross-ply laminated beams using layer-wise trigonometric shear deformation theory
36. Finite element vibration analysis of composite beams based on higher-order beam theory10.1006/jsvi.1998.1903 ↗
37. A review of refined shear deformation theories for isotropic and anisotropic laminated beams10.1177/073168401772678283 ↗
38. Vibration and buckling of multilayered composite beams according to higher order deformation theories10.1006/jsvi.2000.3627 ↗
39. Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity10.1016/S0020-7683(02)00647-9 ↗
40. Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams10.1016/j.compstruct.2003.08.013 ↗
41. A refined higher order finite element for asymmetric composite beams10.1016/j.compstruct.2004.01.005 ↗
42. Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method10.1016/j.compscitech.2005.10.029 ↗
43. Free vibration analysis of angle-ply laminated beams with general boundary conditions10.1177/0731684406066752 ↗
44. Dynamic analysis of laminated composite beams using higher order theories and finite elements10.1016/j.compstruct.2005.02.002 ↗
45. An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams10.1016/j.compstruct.2007.10.005 ↗
46. A family of sinus finite elements for the analysis of rectangular laminated beams10.1016/j.compstruct.2007.06.009 ↗
47. Vibration of multilayered beams using sinus finite elements with transverse normal stress10.1016/j.compstruct.2009.10.009 ↗
48. A sine finite element using a zig-zag function for the analysis of laminated composite beams10.1016/j.compositesb.2011.03.012 ↗
49. Free vibration of axially loaded rectangular composite beams using refined shear deformation theory10.1016/j.compstruct.2012.05.012 ↗
50. Vibration and buckling of composite beams using refined shear deformation theory10.1016/j.ijmecsci.2012.06.001 ↗
51. Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory10.1007/s00419-012-0707-4 ↗
52. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates10.1016/S0263-8223(00)00099-4 ↗
53. Assessment of theories for free vibration analysis of homogeneous and multilayered plates10.1155/2004/493584 ↗
54. Analysis of thickness locking in classical, refined and mixed multilayered plate theories10.1016/j.compstruct.2007.02.002 ↗
55. A study of transverse normal stress effect on vibration of multilayered plates and shells10.1006/jsvi.1999.2271 ↗
56. A Reissner’s mixed variational theorem applied to vibration analysis of multilayered shell10.1115/1.2789171 ↗
57. Theories and finite elements for multilayered plates and shells A unified compact formulation with numerical assessment and benchmarking10.1007/BF02736224 ↗
58. Unified formulation applied to free vibrations finite element analysis of beams with arbitrary section10.1155/2011/706541 ↗
59. Hierarchical theories for the free vibration analysis of functionally graded beams10.1016/j.compstruct.2011.07.016 ↗
60. Free vibration and stability analysis of three-dimensional sandwich beams via hierarchical models10.1016/j.compositesb.2012.11.017 ↗
61. Free vibration analysis of composite beams via refined theories10.1016/j.compositesb.2012.03.005 ↗
62. Exact dynamic stiffness elements based on one-dimensional higher-order theories for free vibration analysis of solid and thin-walled structures10.1016/j.jsv.2013.06.023 ↗
63. Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions10.1016/j.compstruct.2013.12.010 ↗
64. A general algorithm for computing natural frequencies of elastic structures10.1093/qjmam/24.3.263 ↗
65. A unified formulation of laminated composite, shear deformable five-degrees-of-freedom cylindrical shell theories10.1016/0263-8223(93)90162-J ↗
66. Jones · 1976
67. Wolfram · 1991
68. Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams10.1016/j.compstruct.2007.07.007 ↗
69. Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory10.1007/s11012-010-9388-7 ↗
70. A dynamic stiffness approach for vibration analysis of a laminated composite beam
71. Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method10.1007/s00419-008-0276-8 ↗