In-plane Vibration Analysis of Symmetric Angle-ply Laminated Composite Arches

Abstract

The in-plane free vibration analysis of symmetric angle-ply laminated composite arches is carried out by finite elements method. The rotary inertia and shear deformation effects have been included in the analysis. Arches with opening angle (α) from 30° to 270° are taken into consideration. Parametric studies are performed to study the effects of fiber orientation angle, boundary conditions, material orthotropicity, radius-to-width ratio and number of layers on natural frequencies. The validity of the finite element model is shown by comparing the results with those available in the literature. Mode shapes are presented for two different cases. It is found that fundamental in-plane natural frequency of laminated composite arches can be substantially increased by 30 to 60%, by using angle-ply instead of cross-ply. This percent increase offers a considerable advantage that, for arch beams, angle-ply lamination can be preferable to cross-ply lamination.

 

 Key Words: Arch, in-plane vibration, angle-ply laminated composite.

Keywords

• Arch, in-plane vibration, angle-ply laminated composite

References

1. Chidamparam, P. and Leissa, A.W., "Vibrations of Planar Curved Beams, Rings, and Arches", Appl. Mechanics Review, 46(3-5): 467-483 (1993).
2. Howson, W.P. and Jemah, A.K., "Exact Out-of- Plane Natural Frequencies of Curved Timoshenko Beams", ASCE J. of Eng. Mechanics, 125(1): 19- 25 (1999).
3. Eisenberger, M. and Efraim, E., "In-Plane Vibrations of Shear Deformable Curved Beams", Int. J. for Numerical Methods in Eng., 52(11): 1221-1234 (2001).
4. Wu, J.-S. and Chiang, L.-K., "Free Vibration Analysis of Arches Using Curved Beam Elements", Int. J. for Numerical Methods in Eng., 58(13): 1907-1936 (2003).
5. Karami, G. and Malekzadeh, P., "In-Plane Free Vibration Analysis of Circular Arches with Varying Cross Sections Using Differential Quadrature Method", J. Sound and Vibration, 274(3-5): 777- 799 (2004).
6. Chen, C.-N., "DQEM Analysis of In-Plane Vibration of Curved Beam Structures", Advances in Engineering Software, 36(6): 412-424 (2005).
7. Oz, H.R. and Daş, M.T., "In-Plane Vibrations of Circular Curved Beams with a Transverse Open Crack", Math. and Computational Applications, 11(1): 1-10 (2006).
8. Khdeir, A.A. and Reddy, J.N., "Free and Forced Vibration of Cross-ply Laminated Composite Shallow Arches", Int. J. of Solids & Structures, 34(10): 1217-1234 (1997).

9. Qatu, M.S., Elsharkawy, A., "Vibration of Laminated Composite Arches with Deep Curvature and Arbitrary Boundaries", Computers & Structures, 47(2): 305-311 (1993).
10. Bhimaraddi, A., "Generalized Analysis of Shear Deformable Rings and Curved Beams", Int. J. of Solids & Structures, 24(4): 363-373 (1988).
11. Yıldırım, V., "Common Effects of the Rotary Inertia and Shear Deformation on the Out-of-plane Natural Frequencies of Composite Circular Bars", Composites Part B: Engineering, 32(8):687-695 (2001).
12. Matsunaga, H., "Free Vibration and Stability of Laminated Composite Circular Arches Subjected to Initial Axial Stress", J. Sound and Vibration, 271(3-5):651-670 (2004).
13. Qatu, M.S., "In-Plane Vibration of Slightly Curved
14. Laminated Composite Beams", J. Sound and
15. Vibration, 159(2): 327-338 (1992).
16. Yıldırım, V., "Rotary Inertia, Axial and Shear Deformation Effects on the In-Plane Natural Frequencies of Symmetric Cross-ply Laminated Circular Arches", J. Sound and Vibration, 224(4): 575-589 (1999).
17. Yıldırım, V., "In-Plane Free Vibration of Symmetric Cross-ply Laminated Circular Bars", ASCE J. of Eng. Mechanics, 125(6): 630-636 (1999).
18. Tseng, Y.P., Huang, C.S. and Kao, M.S., "In- Plane Vibration of Laminated Curved Beams with Variable Curvature by Dynamic Stiffness Analysis", Composite Structures, 50(2): 103-114 (2000).
19. Ecsedi, I. and Dluhi, K., "A Linear Model for the Static and Dynamic Analysis of Non- homogeneous Curved Beams", Appl. Math. Modeling, 29(12):1211-1231 (2005).
20. Tanrıöver, H. and Şenocak, E., “Large Deflection Analysis of Unsymmetrically Laminated Composite Plates: Analytical-numerical Type Approach”, Non-Linear Mechanics, 39(8):1385- 1392 (2004).
21. Yalçın, O.F., Mengi, Y. and Turhan, D., “Higher Order Approximate Dynamic Models for Layered Composites”, Eur. J. of Mechanics A/Solids, 26(3): 418-441 (2007).
22. Malekzadeh, P., Setoodeh, A.R. and Barmshouri, E., “A Hybrid Layerwise and Differential Quadrature Method for In-plane Free Vibration of Laminated Thick Circular Arches”, J. Sound and Vibration, 315(1-2): 212-225 (2008).
23. Lü, Q. and Lü, C.F., “Exact Two-dimensional Solutions for In-plane Natural Frequencies of Laminated Circular Arches”, J. Sound and Vibration, 318(4-5): 982-990 (2008).
24. Malekzadeh, P. and Setoodeh, A.R., “DQM In- plane Free Vibration of Laminated Moderately Thick Circular Deep Arches”, Advances in Eng. Software, 40(9): 798-803 (2009).
25. Moleiro, F., Mota Soares, C.M., Mota Soares, C.A. and Reddy, J.N., “Mixed Least-Squares Finite Element Models for Static and Free Vibration Analysis of Laminated Composite Plates”, Comp. Meth. In Appl. Mech. And Eng., 198 (21-26): 1848-1856 (2009).
26. Jun, L., Hongxing, H. and Rongying, S., "Free Vibration of Laminated Composite Circular Arches by Dynamic Stiffness Analysis", J. Reinforced Plastics and Composites, 27(8):851- 870 (2008).
27. ANSYS 10.0 User’s Manual (2005).