The Influence of Axial Compression on the Free Vibration Frequencies of Cross-ply Laminated and Moderately Thick Cylinders

Öz

In this study, the free vibration behavior of axially compressed cross-ply laminated composite cylinders is investigated using a semi-analytical shell finite element based on a consistent first order shear deformable shell theory, which includes the influences of rotatory inertia and thickness coordinate/radius ratio. First, a verification study is conducted to validate the axisymmetric shell finite element used in this study and, for the non-compressed cases, the free vibration frequencies obtained using the finite element developed are found out to be in excellent agreement with the published results found in the literature. The same element is also validated for first-ply failure analysis and good agreement is observed with the first-ply failure loads obtained using a shear deformable and curved shell element. Then, numerical results for free vibration analyses are presented for axially compressed composite cylinders having different boundary conditions and for which the level of axial compression is kept below the corresponding linear buckling and first ply failure loads. It is observed that, the fundamental free vibration frequencies decrease sharply for axial load levels higher than about 60~80% of the buckling loads of the cylindrical structures considered. It is also determined that the first-ply failure load is lower than the buckling load for some of the thicker cylinders.

Anahtar Kelimeler

• composite cylinder,finite elements,compression,Vibration,buckling

The Influence of Axial Compression on the Free Vibration Frequencies of Cross-ply Laminated and Moderately Thick Cylinders

Öz

In this study, the free vibration behavior of axially compressed cross-ply laminated composite cylinders is investigated using a semi-analytical shell finite element based on a consistent first order shear deformable shell theory, which includes the influences of rotatory inertia and thickness coordinate/radius ratio. First, a verification study is conducted to validate the axisymmetric shell finite element used in this study and, for the non-compressed cases, the free vibration frequencies obtained using the finite element developed are found out to be in excellent agreement with the published results found in the literature. The same element is also validated for first-ply failure analysis and good agreement is observed with the first-ply failure loads obtained using a shear deformable and curved shell element. Then, numerical results for free vibration analyses are presented for axially compressed composite cylinders having different boundary conditions and for which the level of axial compression is kept below the corresponding linear buckling and first ply failure loads. It is observed that, the fundamental free vibration frequencies decrease sharply for axial load levels higher than about 60~80% of the buckling loads of the cylindrical structures considered. It is also determined that the first-ply failure load is lower than the buckling load for some of the thicker cylinders.

Anahtar Kelimeler

• Vibration,buckling,composite cylinder,finite elements,compression

Kaynakça

1. Qatu, Mohamad S. "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells." Applied Mechanics Reviews 55(4): 325-350, (2002)
2. Khdeir, A. A., J. N. Reddy, and D. Frederick. "A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories." International Journal of Engineering Science 27(11):1337-1351, (1989)
3. Jones, Robert M., and Harold S. Morgan. "Buckling and vibration of cross-ply laminated circular cylindrical shells." AIAA journal 13(5):664-671, (1975).
4. Armenàkas, Anthony E. "Influence of initial stress on the vibrations of simply supported circular cylindrical shells." AIAA Journal 2(9):1607-1612, (1964)
5. Rosen, Aviv, and Josef Singer. "Vibrations of axially loaded stiffened cylindrical shells." Journal of Sound and Vibration 34(3): 357-IN3, (1974)
6. Bradford, L. G., and S. B. Dong. "Natural vibrations of orthotropic cylinders under initial stress." Journal of Sound and Vibration 60(2): 157-175, (1978)
7. Greenberg, J. B., and Y. Stavsky. "Vibrations of axially compressed laminated orthotropic cylindrical shells, including transverse shear deformation." Acta Mechanica 37(1-2) : 13-28, (1980)
8. Yamada, Gen, Toshihiro Irie, and Mitsuo Tsushima. "Vibration and stability of orthotropic circular cylindrical shells subjected to axial load." The Journal of the Acoustical Society of America 75(3): 842-848, (1984)

9. Chang, Jeng-Shian, and Chen-Hong Lin. "Buckling and free vibration of cross-ply laminated circular cylindrical shells subjected to axial thrust and lateral pressure loading according to a higher order displacement field." Thin-walled structures 13(3) 177-196, (1992)
10. Greenberg, J. B., and Y. Stavsky. "Vibrations and buckling of composite orthotropic cylindrical shells with nonuniform axial loads." Composites Part B: Engineering 29(6): 695-70, (1998)
11. Matsunaga, H. "Free vibration of thick circular cylindrical shells subjected to axial stresses." Journal of sound and vibration 211(1):1-17, (1998)
12. Skukis, E., K. Kalnins, and A. Chate. "Preliminary assessment of correlation between vibrations and buckling load of stainless steel cylinders." Shell structures theory and applications, CRC Press, London, (2013)
13. Arbelo, Mariano A., et al. "Vibration correlation technique for the estimation of real boundary conditions and buckling load of unstiffened plates and cylindrical shells." Thin-Walled Structures 79: 119-128, (2014)
14. Qatu, Mohamad S. "Accurate equations for laminated composite deep thick shells." International Journal of Solids and Structures 36(19) : 2917-2941, (1999)
15. Cagdas, Izzet U. "Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element." Thin-Walled Structures 49(6): 732-742, (2011)
16. Cagdas, Izzet U., and Sarp Adali. "Buckling of cross-ply cylinders under hydrostatic pressure considering pressure stiffness." Ocean engineering 38(4) : 559-569, (2011)
17. Cagdas, Izzet U. "Optimal design of filament wound truncated cones under axial compression." Composite Structures 170: 250-260, (2017)
18. Cagdas, Izzet U. "Optimal design of variable stiffness laminated composite truncated cones under lateral external pressure." Ocean Engineering 145: 268-276, (2017)
19. Cagdas, Izzet U., and Sarp Adali. "Effect of Fiber Orientation on Buckling and First-Ply Failures of Cylindrical Shear-Deformable Laminates." Journal of Engineering Mechanics 139(8) : 967-978, (2013)
20. Ochoa, Ozden O., and Junuthula Narasimha Reddy. "Finite element analysis of composite laminates." Finite Element Analysis of Composite Laminates. Springer, Dordrecht, (1992)