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Abstract

In this study, vibration analysis of angle-ply laminated beams subjected to different sets of boundary conditions is investigated. The analysis is based on a three-degrees-of-freedom shear deformable beam theory. The governing equations are obtained by means of Hamilton's principle. Six different combinations of free, clamped, and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different lay-ups are presented and compared with that available in the literature.

Keywords

angle-ply beams vibration Ritz method general boundary conditions

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References

Kapani, R. K. and Raciti, S. (1989). Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation , AIAA Journal, 27: 935–946 .

Chandrashekhara, K. , Krishnamurty, K. and Roy, S. (1990). Free Vibration of Composite Beams Including Rotary Inertia and Shear Deformation , Composite Structures, 14(4): 269–279 .

Chandrashekhara, K. and Bangera, K. M. (1992). Free Vibration of Composite Beams using a Refined Shear Flexible Beam Element , Computers and Structures, 43(4): 719–727 .

Krishnaswamy , Chandrashekhara, K. and Wu, W. Z. B. (1992). Analytical Solutions to Vibration of Generally Layered Composite Beams , Journal of Sound and Vibration, 159(1): 85–99 .

Chen, W. Q. , Lv, C. F. and Bian, Z. G. (2004). Free Vibration Analysis of Generally Laminated Beams via State-space-based Differential Quadrature , Composite Structures, 63(1): 417–425 .

Soldatos, K. P. and Timarci, T. (1993). A Unified Formulation of Laminated Composite, Shear Deformable, Five Degrees of Freedom Cylindrical Shell Theories , Composite Structures, 25(14): 165–171 .

Jones, R. M. (1975). Mechanics of Composite Materials, Hemisphere Publishing Corporation, New York , pp. 31–59.

Aydogdu, M. and Timarci, T. (2003). Vibration Analysis of Cross-ply Laminated Square Plates with General Boundary Conditions , Composites Science and Technology, 63(7): 1061–1070 .

Timarci, T. and Soldatos, K. P. (1995). Comparative Dynamic Studies for Symmetric Cross-ply Circular Cylindrical Shells on the Basis of a Unified Shear Deformable Shell Theory , Journal of Sound and Vibration, 187(4): 609–624 .

10.

Reddy, J. N. (1984). A Simple Higher-order Theory for Laminated Composite Plates , Journal of Applied Mechanics, 51(4): 745–752 .

11.

Karama, M. , Afaq, K. S. and Mistou, S. (2003). Mechanical Behaviour of Laminated Composite Beam by the New Multi-layered Laminated Composite Structures Model with Transverse Shear Stress Continuity , Int. Jour. Solids and Structures, 40(3): 1525–1546 .

12.

Soldatos, K. P. and Sophocles, C. (2001). On Shear Deformable Beam Theories: The Frequency and Normal Mode Equations of the Homogeneous Orthotropic Bickford Beam , Journal of Sound and Vibration, 242(2): 215–245 .

13.

Kantrovich, L. V. and Krylov, V. I. (1958). Approximate Methods in Higher Analysis, Noordhoff, Groningen , pp. 258–262.

14.

Leissa, A. W. and Narita, Y. (1989). Vibration Studies for Simply Supported Symmetrically Laminated Rectangular Plates , Compos. Struct., 12(2): 113–132 .

15.

Baharlou, B. and Leissa, A. W. (1987). Vibration and Buckling of Generally Laminated Composite Plates with Arbitrary Boundary Conditions , Int J mech. Sci., 29(8): 545–555 .

16.

Bhat, R. B. (1985). Natural Frequencies of Rectangular Plates using Characteristics Orthogonal Polynomials in Rayleigh-Ritz Method , J Sound and Vibration, 102: 493–499 .

17.

Chen, C. C. , Liew, K. M. , Lim, C. W. and Kitipornchai, S. (1997). Vibration Analysis of Symmetrically Laminated Thick Rectangular Plates using the Higher Order Theory and p-Ritz Method , J. Acoust. Soc. Am., 102(3): 1600–1611 .

18.

Narita, Y. (2000). Combinations for Free-vibration Behaviors of Anisotropic Rectangular Plates under General Edge Boundary Conditions , J. Appl. Mech., 67(3): 568–573 .

19.

Leissa, A. W. (1973). On a Curve Veering Aberration , Z. Angew. Math. Phys., 25: 99-99 .

Free Vibration Analysis of Angle-ply Laminated Beams with General Boundary Conditions

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