Frequency responses analysis of clamped-free sandwich beams with porous FG face sheets

Document Type : English

Author

Department of Mechanics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran

Abstract

In this paper, the frequency responses analysis of the sandwich beams with functionally graded face sheets and homogeneous core is investigated based on the high order sandwich beam theory. All materials are temperature dependent and the functionally graded materials properties are varied gradually by a power law rule which is modified by considering the even and uneven porosity distributions. The nonlinear Lagrange strain and the thermal stresses of the face sheets and in-plane strain and transverse flexibility of the core are considered. Hamilton’s principle and Galerkin method are used to obtain and solve the equations for the clamped-free boundary condition. To verify the results of this study, they compared with special cases of the literatures. Based on the numerical results, it is concluded that by increasing the temperature, power law index, length, thickness, porosity volume fraction the fundamental frequency parameter decreases and increasing the wave number causes the frequency increases.

Keywords


 
[1] Vinson, J. (2018). The behavior of sandwich structures of isotropic and composite materials: Routledge.
[2] Rahmani, M., Mohammadi, Y., & 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.
[3] Frostig, Y., Baruch, M., Vilnay, O., & Sheinman, I. (1992). High-order theory for sandwich-beam behavior with transversely flexible core. Journal of Engineering Mechanics, 118(5), 1026-1043.
[4] Fazzolari, F. A. (2018). Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Composites Part B: Engineering, 136, 254-271.
[5] Chen, D., Kitipornchai, S., & Yang, J. (2016). Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, 39-48.
[6] Akbaş, Ş. D. (2017). Thermal effects on the vibration of functionally graded deep beams with porosity. International Journal of Applied Mechanics, 9(05), 1750076.
[7] Bourada, F., Bousahla, A. A., Bourada, M., Azzaz, A., Zinata, A., & Tounsi, A. (2019). Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory. Wind and Structures, 28(1), 19-30.
[8] Li, C., Shen, H.-S., & Wang, H. (2019). Nonlinear vibration of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core. International Journal of Structural Stability and Dynamics, 19(03), 1950034.
[9] Wu, H., Kitipornchai, S., & Yang, J. (2015). Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. International Journal of Structural Stability and Dynamics, 15(07), 1540011.
[10] Xu, G.-d., Zeng, T., Cheng, S., Wang, X.-h., & Zhang, K. (2019). Free vibration of composite sandwich beam with graded corrugated lattice core. Composite Structures, 229, 111466.
[11] Li, M., Du, S., Li, F., & Jing, X. (2020). Vibration characteristics of novel multilayer sandwich beams: Modelling, analysis and experimental validations. Mechanical Systems and Signal Processing, 142, 106799.
[12] Li, Y., Dong, Y., Qin, Y., & Lv, H. (2018). Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam. International Journal of Mechanical Sciences, 138, 131-145.
[13] Şimşek, M., & Al-Shujairi, M. (2017). Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads. Composites Part B: Engineering, 108, 18-34.
[14] Nguyen, T.-K., Vo, T. P., Nguyen, B.-D., & Lee, J. (2016). An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, 156, 238-252.
[15] Kahya, V., & Turan, M. (2018). Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering, 146, 198-212.
[16] Tossapanon, P., & Wattanasakulpong, N. (2016). Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation. Composite Structures, 142, 215-225.
[17] Amirani, M. C., Khalili, S., & Nemati, N. (2009). Free vibration analysis of sandwich beam with FG core using the element free Galerkin method. Composite Structures, 90(3), 373-379.
[18] Pradhan, S., & Murmu, T. (2009). Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. Journal of Sound and Vibration, 321(1-2), 342-362.
[19] Mashat, D. S., Carrera, E., Zenkour, A. M., Al Khateeb, S. A., & Filippi, M. (2014). Free vibration of FGM layered beams by various theories and finite elements. Composites Part B: Engineering, 59, 269-278.
[20] Nguyen, T.-K., Nguyen, T. T.-P., Vo, T. P., & Thai, H.-T. (2015). Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering, 76, 273-285.
[21] Vo, T. P., Thai, H.-T., Nguyen, T.-K., Inam, F., & Lee, J. (2015). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119, 1-12.
[22] Yang, Y., Lam, C., Kou, K., & Iu, V. (2014). Free vibration analysis of the functionally graded sandwich beams by a meshfree boundary-domain integral equation method. Composite Structures, 117, 32-39.
[23] Abdolahi, I., & Yas, M. (2014). Vibration Analysis of Timoshenko Beam Reinforced With Boron-Nitride Nanotube on Elastic Bed. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 7(3), 1-12.
[24] Farahani, H., Barati, F., Nejati, M., & Batmani, H. (2013). Vibration Analysis of Thick Functionally Graded Beam under Axial Load Based on Two-Dimensional Elasticity Theory and Generalized Differential Quadrature. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 6(2), 59-71.
[25] Pirmoradian, M., & Karimpour, H. (2017). Parametric resonance and jump analysis of a beam subjected to periodic mass transition. Nonlinear Dynamics, 89(3), 2141-2154.
[26] Pirmoradian, M., Torkan, E., & Toghraie, D. (2020). Study on size-dependent vibration and stability of DWCNTs subjected to moving nanoparticles and embedded on two-parameter foundations. Mechanics of Materials, 142, 103279.
[27] Pirmoradian, M., Torkan, E., Zali, H., Hashemian, M., & Toghraie, D. (2020). Statistical and parametric instability analysis for delivery of nanoparticles through embedded DWCNT. Physica A: Statistical Mechanics and Its Applications, 554, 123911.
[28] Torkan, E., Pirmoradian, M., & Hashemian, M. (2017). Occurrence of parametric resonance in vibrations of rectangular plates resting on elastic foundation under passage of continuous series of moving masses. Modares Mechanical Engineering, 17(9), 225-236.
[29] Torkan, E., Pirmoradian, M., & Hashemian, M. (2019). Dynamic instability analysis of moderately thick rectangular plates influenced by an orbiting mass based on the first-order shear deformation theory. Modares Mechanical Engineering, 19(9), 2203-2213.
[30] Torkan, E., & Pirmoradian, M. (2019). Efficient higher-order shear deformation theories for instability analysis of plates carrying a mass moving on an elliptical path. Journal of Solid Mechanics, 11(4), 790-808.
[31] Heydari, E., Mokhtarian, A., Pirmoradian, M., Hashemian, M., & Seifzadeh, A. (2020). Sound transmission loss of a porous heterogeneous cylindrical nanoshell employing nonlocal strain gradient and first-order shear deformation assumptions. Mechanics Based Design of Structures and Machines, 1-22.
[32] Heydari, E., Mokhtarian, A., Pirmoradian, M., Hashemian, M., & Seifzadeh, A. (2021). Acoustic wave transmission of double-walled functionally graded cylindrical microshells under linear and nonlinear temperature distributions using modified strain gradient theory. Thin-Walled Structures, 169, 108430.
[33] Mohammadi, Y., H Safari, K., & Rahmani, M. (2016). Free vibration analysis of circular sandwich plates with clamped FG face sheets. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 9(4), 631-646.
[34] Rahmani, M., Mohammadi, Y., Kakavand, F., & 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.
[35] Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: theory and analysis: CRC press.
[36] Dariushi, S., & Sadighi, M. (2014). A new nonlinear high order theory for sandwich beams: An analytical and experimental investigation. Composite Structures, 108, 779-788.
[37] Rahmani, M., Mohammadi, Y., & 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.
[38] Rahmani, M., & Dehghanpour, S. (2021). Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers. International Journal of Structural Stability and Dynamics, 21(02), 2150016.
[39] Mohammadi, Y., & Rahmani, M. (2020). Temperature-dependent buckling analysis of functionally graded sandwich cylinders. Journal of Solid Mechanics, 12(1), 1-15.
[40] Rahmani, M., & Mohammadi, Y. (2021). Vibration of two types of porous FG sandwich conical shell with different boundary conditions. Structural Engineering and Mechanics, 79(4), 401-413.
[41] 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.
[42] Nguyen, T.-K., Vo, T. P., & 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.
[43] Vo, T. P., Thai, H.-T., Nguyen, T.-K., Maheri, A., & 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.