The Effect of Winkler-Pasternak Foundation Coefficients on the Natural Frequency of Cylindrical Lattice Structures Using Galerkin Method

Document Type : Original Article

Authors

• Amir Hossein Hashemian ¹
• Ehsaneh Mohammadpour Hamedani ²

¹ Department of Aerospace Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran

² Department of Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

10.22067/jacsm.2022.73646.1069

Abstract

Composite Lattice structures are one of the most widely used structures in the aerospace industry in recent years. These structures are composed of a large number of oblique and circumferential ribs with specific distances from each other and in addition to strength, they are very light in terms of weight. The present study includes an analytical expression and a solution to the problem of free vibrations of a composite lattice cylindrical shell. The continuous formula for calculating the natural frequency of a cylindrical lattice structure was obtained by considering the Winkler-Pasternak elastic foundation from the governing equations of the shell based on Galerkin methods. This formula, in addition to being used to estimate the frequency in the initial design phase, is also a tool for evaluating the vibration analysis of composite lattice shells in mechanical analysis. The results have been calculated analytically in two cases with and without elastic foundation and the accuracy of the results has been confirmed by finite element modeling. For finite element method simulations, Winkler and Pasternak coefficients have been replaced by shear and radial springs, respectively. The natural base frequency of the system depends on the properties of the elastic substrate, so changing the stiffness of the radial and shear springs causes a change in the natural frequencies.

Keywords

• Lattice Composite Structure
• Natural Frequency
• Fourier Method
• Galerkin method
• FEM

Main Subjects

• Vibrations

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References

1. Wang, T.M. and Stephens, J.E., “Natural Frequencies of Timoshenko Beams on Pasternak Foundations”, Journal of Sound and Vibration, Vol. 51, No. 2, Pp. 149-155, (1977).
2. Khalifa Ahmed M., “Natural Frequencies and Mode Shapes of Variable Thickness Elastic Cylindrical Shells Resting on a Pasternak Foundation”, Journal of Vibration and Control, 17, No. 8, Pp. 1158–1172, (2016).
3. Paliwal, D.N. and Pandey, R., “Free Vibrations of An Orthotropic Thin Cylindrical Shell on a Pasternak Foundation”, AIAA Journal, Vol. 39, No. 11, (2001).
4. Lopatin, A.V., Morozov, E.V. and Shaatov, A.V., “An Analytical Expression for Fundamental Frequency of The Composite Lattice Cylindrical Shell with Clamped Edges”, Journal of Composite Structures, Vol. 141, No. 1, Pp. 232-239, (2016).
5. Lopatin, A.V., Morozov, E.V. and Shaatov, A.V., “Fundamental Frequency of a Cantilever Composite Filament-Wound Anisogrid Lattice Cylindrical Shell”, Journal of Composite Structures, 133, Pp. 564–575, (2015).
6. Vasiliev, V.V and Brayan, V.A., “Anisogrid Composite Lattice Structures-Development and Aerospace Applications”, Journal of Composite Structures, Vol. 94, No. 3, 1117-1127, (2012).
7. Vasiliev, V.V., Brayan, V.A. and Rasin, A.F.,  “Anisogrid Lattice Structures-Survey of Development and Application”, Journal of Composite Structures, Vol. 54, No. 2–3,  361-370, (2001).
8. Hou, A. and Gramoll, K., “Compressive Strength of Composite Lattice Structures”, Journal of Reinforced Plastics and Composites, Vol. 17, No. 5, (1998).
9. Totaro, G., “Local Buckling Modelling of Isogrid and Anisogrid Lattice Cylindrical Shells with Hexagonal Cells”, Journal of Composite Structures, Vol.  95, Pp. 403–410, (2013).
10. Xu, M. and Qiu, Z., “Free Vibration Analysis and Optimization of Composite Lattice Truss Cores and Sandwich Beams with Interval Parameters”, Journal of Composite Structures, Vol. 106, No.1, Pp. 85–95, (2013).
11. Frulloni, E., Conti, K. and Torre, L., “Experimental Study and Finite Element Analysis of The Elastic Instability of Composite Lattice Structures for Aeronautic Applications”, Journal of Composite Structures, Vol. 78, Pp. 519–528, (2007).
12. Iwata Y. , Yokozeki T., “ Shock wave filtering of two-dimensional CFRP X-lattice structures: A numerical investigation”, Composite Structures, Vol. 265, (2021).
13. Mikaeili, E, Heydarnabi, M., Eskandari Jam, J, “Analysis of free vibrations of smart FGM lattice plates in thermal environments”, Journal of Mechanical Eng. University of Tabriz, Vol. 92, No. 50, Issue 3, Autumn, (1399). (In persian)
14. Li, M., Fan, H., "Free vibration behaviors and vibration correlation technique of hierarchical Isogrid stiffened composite cylindricals”, Thin-Walled Structures, Vol. 159, (2020).
15. Banijamali, S. M. and Jafari, A., "Free vibration analysis of rotating functionally graded conical shells reinforced by lattice structure”, Mechanics Based Design of Structures and Machines, (2021).