A STUDY ON THE FREQUENCY RESPONSE OF A COMPOSITE PRE-STRESSED SYSTEM UNDER AN INCLINED HARMONIC LOADING

Abstract

Goal for the present research is investigating the dynamic behaviors regarding forced vibration of an elastic composite body on the rigid ground for four different material designations. For this purpose, the effects of the initial stress state and frequency response parameter on the forced vibration of the model are studied. Based on the linearized theory of elasticity, the nonlinear forced vibration of composite material on the rigid ground is considered. The nonlinear governing equations are linearized and boundary-contact conditions are derived using Hamilton’s principle. Total energy functional is constructed based on the principle of the variational formulation, and then the forced vibration of elastic composite plate-strip is analyzed using the finite element method (FEM). Moreover, the numerical examples related to the influences of important problem factors on our mathematical model are given. The observations show that the selection of more soft material in the upper layers has a great potential for the structural stability of the system. For the softer upper layer relatively, the wave oscillation in the plate-strip exhibits becomes more regular. In addition, the resonance values of the system decrease with the increase of the initial compressing parameter but with the initial stretching parameter.

Keywords

• Composite material
• Initial stress
• Finite element method
• Frequency response
• Forced vibration

References

1. Abo-el-Nour, N., Al-sheikh, F., & Al-Hossain, A. Y. (2009). Effect of initial stresses on dispersion relation of transverse waves in a piezoelectric layered cylinder. Materials Science and Engineering: B, 162(3), 147-154.
2. Abd-Alla, A. M., Mahmoud, S. R., Abo-Dahab, S. M., & Helmy, M. I. (2011). Propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field. Applied Mathematics and Computation, 217(9), 4321-4332.
3. Akbarov, S. D. (2015). Dynamics of pre-strained bi-material elastic systems: Linearized three-dimensional approach. Springer, New York, NY, USA.
4. Babych, S. Y., & Glukhov, Y. P. (2021). On One Dynamic Problem for a Multilayer Half-Space with Initial Stresses. International Applied Mechanics, 57(1), 43-52.
5. Biswas, S., & Abo-Dahab, S. (2018). Effect of phase-lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium. Applied Mathematical Modelling, 59, 713-727.
6. Daşdemir, A. (2017). Effect of imperfect bonding on the dynamic response of a pre-stressed sandwich plate-strip with elastic layers and a piezoelectric core. Acta Mechanica Solida Sinica, 30(6), 658-667.
7. Ejaz, K., & Shams, M. (2019). Love waves in compressible elastic materials with a homogeneous initial stress. Mathematics and Mechanics of Solids, 24(8), 2576-2590.
8. Farhan, A. M. (2013). Effect of Initial Stress on Wave Propagation in an Infinite Generalized Thermoelastic Circular Cylinder. Journal of Computational and Theoretical Nanoscience, 10(9), 2269-2275.

9. Guz, A. N. (1999). Fundamentals of the three-dimensional theory of stability of deformable bodies. Springer, New York, NY, USA. [Translated from Russian by M. Kashtalian.]
10. Güven, U. (2012). A more general investigation for the longitudinal stress waves in microrods with initial stress. Acta Mechanica, 223(9), 2065-2074.
11. Hutton, D. (2004). Fundamentals of Finite Element Analysis. McGraw-Hills, New York, 2004
12. Kundu, S., Gupta, S., & Manna, S. (2014). Propagation of Love wave in fiber‐reinforced medium lying over an initially stressed orthotropic half‐space. International Journal for Numerical and Analytical Methods in Geomechanics, 38(11), 1172-1182.
13. Li, X., & Tao, M. (2015). The influence of initial stress on wave propagation and dynamic elastic coefficients. Geomechanics & Engineering, 8(3), 377-390.
14. Nam, N. T., Merodio, J., Ogden, R. W., & Vinh, P. C. (2016). The effect of initial stress on the propagation of surface waves in a layered half-space. International Journal of Solids and Structures, 88, 88-100.
15. Panja, S. K., & Mandal, S. C. (2022). Propagation of Love wave in multilayered viscoelastic orthotropic medium with initial stress. Waves in Random and Complex Media, 32(2), 1000-1017.
16. Sharma, M. D. (2020). Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity. Journal of Vibration and Control, 26(21-22), 2070-2080.
17. Singh, B. (2013). Rayleigh wave in an initially stressed transversely isotropic dissipative half-space. Journal of Solid Mechanics, 5(3), 270-277.
18. Uflyand, Y. S. (1963). Integral Transformations in the Theory of Elasticity, Nauka, Moscow-Leningrad, 1963
19. Wang, Y. Z., Li, F. M., & Kishimoto, K. (2010). Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress. Applied Physics A, 99(4), 907-911.
20. Zienkiewicz O. C., & R. L. Taylor, R. L. (1989). The Finite Element Method, Basic Formulation and Linear Problems, vol. 1 (4th ed.), McGraw-Hill, London.