Free Vibration Analysis of Sandwich Beams with FG Face Sheets Based on the High Order Sandwich Beam Theory

Subject Areas :

Mohsen Rahmani ¹ , Sajjad Dehghanpour ² , Ali Barootiha ³

1 - Department of Mechanics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran
2 - Department of Mechanics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran
3 - Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran

Received: 2020-04-29 Accepted : 2020-07-19 Published : 2020-05-01

Keywords: Vibration, FGM, Sandwich beam, Galerkin, High order sandwich beam theory,

Abstract :

In this paper, the vibration behavior of the sandwich beams with functionally graded face-sheets is investigated based on the high order sandwich beam theory.The properties of the FGM are varied gradually across the thickness of the structures in accordant with the power-law rule. First-order shear deformation theory and polynomial patterns are used to model the displacements of the face-sheets and the core, respectively. The governing equations of the motion are obtained based on Hamilton’s energy principle and solved by a Galerkin method. An algebraic method is used to reduce the number of equations. Boundary conditions are considered as simply supported and clamped.The effect of the power-law index and geometrical variations are surveyed on the fundamental frequency parameter for different sandwich beams in some numerical examples. In order to verify the results of the present study, they are compared with special cases of the literature.

References:

[1] Laura, P. and Rossit, C. 2001. The Behavior of Sandwich Structures of Isotropic and Composite Materials-by Jack r. Vinson. Technomic Publishing Company, Ocean Engineering. 10(28): 1437-1438.

[2] Mahamood, R. and Akinlabi, E. 2017. Functionally Graded Materials, Topics in Mining. Metallurgy and Materials Engineering. Springer International Publishing, Cham.

[3] Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. 2019. Buckling analysis of truncated conical sandwich panel with porous functionally graded core in different thermal conditions. Amirkabir Journal of Mechanical Engineering. 52(10): 141-150.

[4] Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. 2020. Vibration analysis of different types of porous fg conical sandwich shells in various thermal surroundings. Journal of Applied and Computational Mechanics. 6(3): 416-432.

[5] Jafari Fesharaki, J., Madani, S.G. and Seydali, D. 2017. Stress concentration factor in a functionally graded material plate around a hole. Journal of Modern Processes in Manufacturing and Production. 6(1): 69-81.

[6] Bouderba, B. 2018. Bending of fgm rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory. Steel and Composite Structures. 27(3): 311-325.

[7] Rahmani, M., Mohammadi, Y. and Kakavand, F. 2020. Buckling analysis of different types of porous fg conical sandwich shells in various thermal surroundings.  Journal of the Brazilian Society of Mechanical Sciences and Engineering. 42(4): 1-16.

[8] Reddy, J. 2000. Analysis of functionally graded plates.  International Journal for numerical methods in engineering. 47(1‐3): 663-684.

[9] Hu, H., Belouettar, S., Potier-Ferry, M. and Makradi, A. 2009. A novel finite element for global and local buckling analysis of sandwich beams.  Composite Structures. 90(3): 270-278.

[10] Vo, T.P., Thai, H.-T., Nguyen, T.-K., Maheri, A. and Lee, J. 2014. Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory.  Engineering Structures. 64: 12-22.

[11] Adámek, V. 2018. The limits of timoshenko beam theory applied to impact problems of layered beams.  International Journal of Mechanical Sciences. 145: 128-137.

[12] Frostig, Y., Baruch, M., Vilnay, O. and Sheinman, I. 1992. High-order theory for sandwich-beam behavior with transversely flexible core.  Journal of Engineering Mechanics. 118(5): 1026-1043.

[13] Mohammadi, Y. and Rahmani, M. 2020. Temperature-dependent buckling analysis of functionally graded sandwich cylinders.  Journal of Solid Mechanics. 12(1): 1-15.

[14] Rahmani, M., Mohammadi, Y. and Kakavand, F. 2019. Vibration analysis of sandwich truncated conical shells with porous fg face sheets in various thermal surroundings.  Steel and Composite Structures. 32(2): 239-252.

[15] Rahmani, M., Mohammadi, Y. and Kakavand, F. 2019. Vibration analysis of different types of porous fg circular sandwich plates. ADMT Journal. 12(3): 63-75.

[16] Salami, S. J. 2016. Extended High Order Sandwich Panel Theory for Bending Analysis of Sandwich Beams with Carbon Nanotube Reinforced Face Sheets. Physica E: Low-dimensional Systems and Nanostructures. 76: 187-197.

[17] Salami, S. J. 2017. Low velocity impact response of sandwich beams with soft cores and carbon nanotube reinforced face sheets based on extended high order sandwich panel theory.  Aerospace Science and Technology. 66: 165-176.

[18] Dariushi, S. and Sadighi, M. 2014. A New Nonlinear High Order Theory for Sandwich Beams: An Analytical and Experimental Investigation. Composite Structures. 108: 779-788.

[19] Canales, F. and Mantari, J. 2016. Buckling and Free Vibration of Laminated Beams with Arbitrary Boundary Conditions using a Refined Hsdt. Composites Part B: Engineering. 100: 136-145.

[20] Khalili, S., Nemati, N., Malekzadeh, K. and Damanpack, A. 2010. Free vibration analysis of sandwich beams using improved dynamic stiffness method.  Composite structures. 92(2): 387-394.

[21] Arikoglu, A. and Ozkol, I. 2010. Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method.  Composite Structures. 92(12): 3031-3039.

[22] Amirani, M.C., Khalili, S. and Nemati, N. 2009. Free vibration analysis of sandwich beam with fg core using the element free galerkin method.  Composite Structures. 90(3): 373-379.

[23] Tossapanon, P. and Wattanasakulpong, N. 2016. Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation. Composite Structures. 142: 215-225.

[24] Khdeir, A. and Aldraihem, O. 2016. Free vibration of sandwich beams with soft core. Composite Structures. 154: 179-189.

[25] Goncalves, B.R., Karttunen, A., Romanoff, J. and Reddy, J. 2017. Buckling and free vibration of shear-flexible sandwich beams using a couple-stress-based finite element. Composite Structures. 165: 233-241.

[26] Zhang, Z.-j., Han, B., Zhang, Q.-c. and Jin, F. 2017. Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores. Composite Structures. 171: 335-344.

[27] Chen, D., Kitipornchai, S. and Yang, J. 2016. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures. 107: 39-48.

[28] Xu, G.-d., Zeng, T., Cheng, S., Wang, X.-h. and Zhang, K. 2019. Free vibration of composite sandwich beam with graded corrugated lattice core. Composite Structures. 229: 111466.

[29] Reddy, J.N. 2003. Mechanics of laminated composite plates and shells: Theory and analysis. ed. CRC press,

[30] Reddy, J. 1998. Thermomechanical behavior of functionally graded materials.

[31] Şimşek, M. 2010. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories.  Nuclear Engineering and Design. 240(4): 697-705.

[32] Nguyen, T.-K., Vo, T.P. and Thai, H.-T. 2013. Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory.  Composites Part B: Engineering. 55: 147-157.