Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019
Example 7: Perforated composite skew plates with different number of layers.
In this example, a simply supported angle ply skew laminate with skew cut out (0.2a × 0.2b) at the center is analysed (Figure. 1b). In this analysis different number of layers is considered and the results are presented in Table 8. Both symmetric and anti-symmetric plates are analysed. As the number of layer increases, stiffness of the laminate increases and thus, frequencies increase.
Example 8: Perforated composite skew plates with corner point constraints and having different cut-out sizes.
In the last example an angle-ply skew laminate (30/-30/30) with skew cut out having different sizes at the center is analysed (Figure. 1e). The skew laminate is fixed along the left edge and the opposite two corner points A and B are also restrained with all the five degrees of freedom. The results are presented in Table 9. Here it is seen that as the cut-out size increases the frequency decreases.
Table 9. Frequencies = 2√ 2⁄ /ℎ of an angle-ply skew laminate (30/-30/30) having skew cutout at the plate center (a=b, h/a=0.01, α = 45°)
Cut out size 1
First five natural frequencies 2
3 4 5
0.1a × 0.1a 10.01 17.12 17.62 34.71 40.43 0.2a × 0.2a 0.3a × 0.3a
9.89 16.89 17.32 34.05 39.68 9.80 16.46 16.84 33.94 38.21
10. 6. CONCLUSION
In this research, the equivalent single layer theories are critically discussed. A brief cross-section of the literature on equivalent single layer theories is reviewed. An exhaustive survey on works related to the analysis of skew composite laminates is also presented. A finite element analysis on free vibration behavior of skew laminates is then carried out. The shear deformation across the thickness is included by considering a first-order shear deformation theory. The rotary inertia effects are also included. Certain numerical examples are solved using the formulation which will serve as benchmark results for future studies.
7. 1.
REFERENCES 15.
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AMBARTSUMIAN, S. A., 1960. On the theory of bending of anisotropic plates and shallow shells. Journal of Applied Mathematics and Mechanics, Volume 24, pp. 500-514.
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AMBARTSUMIAN, S. A., 1970. Theory of anisotropic plates: strength, stability, vibration. s.l.:Technomic Publishing Company.
ANLAS, G. & GÖKER, G., 2001. Vibration analysis of skew fiber-reinforced composite laminated plates. Journal of sound and vibration, Volume 242, pp. 265-276.
ARDESTANI, M. M., ZHANG, L. W. & LIEW, K. M., 2017. Isogeometric analysis of the effect of CNT orientation on the static and vibration behaviors of CNT-reinforced skew composite plates. Computer Methods in Applied Mechanics and Engineering, Volume 317, pp. 341-379.
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ASEMI, K., SALAMI, S. J., SALEHI, M. & SADIGHI, M., 2014. Dynamic and static analysis of FGM skew plates with 3D elasticity based graded finite element modeling. Latin American Journal of Solids and Structures, Volume 11, pp. 504-533.
ASHOUR, A. S., 2009. The free vibration of symmetrically angle-ply laminated fully clamped skew plates. Journal of Sound and Vibration, Volume 323, pp. 444-450.
ASHTON, J. E. & WHITNEY, J. M., 1970. Theory of laminated plates. s.l.:CRC Press.
AURICCHIO, F. & TAYLOR, R. L., 1995. A triangular thick plate finite element with an exact thin limit. Finite Elements in Analysis and Design, Volume 19, pp. 57-68.
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©2019: The Royal Institution of Naval Architects
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