Vibration Analysis of Different Types of Porous FG Circular Sandwich Plates

Document Type: Original Article


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran


For the first time, by applying a modified high order sandwich plates theory, vibration behaviour of two types of porous FG circular sandwich plates are investigated. In the first type, the face sheets and in the second one, the core is made of FGM which is modelled by power law rule that is modified by considering two types of porosity distributions. All materials are temperature dependent and uniform temperature distribution is used to model the effect of the temperature changing in the sandwiches. Governing equations are obtained by the Hamilton's energy principle and solved by Galerkin method for a clamped boundary condition. To verify the results, they are compared with FEM results obtained by Abaqus software and for special cases with the results in literatures.


Main Subjects

[1]    Fazzolari, F. A., Sandwich Structures. In Stability and Vibrations of Thin Walled Composite Structures, Woodhead Publishing, 2017, pp. 49-90.

[2]    Mahamood, R. M., Akinlabi, E. T., Functionally Graded Materials, Springer, Gewerbestrasse, Switzerland, 2017, pp. 1-118.‏

[3]    Boutahar, L., Benamar, R., A Homogenization Procedure for Geometrically Non-linear Free Vibration Analysis of Functionally Graded Annular Plates with Porosities, Resting on Elastic Foundations, Ain Shams Engineering Journal, Vol. 7, No. 1, 2016, pp. 313-333.

[4]    Reddy, J. N., Analysis of Functionally Graded Plates. International Journal for Numerical Methods in Engineering. Vol. 47, No. 1‐3, 2000, pp. 663-684.

[5]    Frostig, Y., Baruch, M., Vilnay, O., and Sheinman, I., High-Order Theory for Sandwich-Beam Behavior with Transversely Flexible Core, Journal of Engineering Mechanics, Vol. 118, No. 5, 1992, pp. 1026-1043.

[6]    Najafizadeh, M. M., Shoughi, P., Three Dimensional Free Vibration of FGM Circular Plates Using Semi-Analytical Method, Advance Design and Manufacturing Technology, Vol. 3, No. 1, 2009, pp. 41-49.‏

[7]    Zenkour, A. M., Sobhy, M., Thermal Buckling of Various Types of FGM Sandwich Plates, Composite Structures, Vol. 93, No.1, 2010, pp. 93-102.‏

[8]    Amininejad, R., Mohajerani, A. R., Samsami A. R., and Amininejad, S., Free Vibration Analysis of S-FGM-Coated and S-FGM-Undercoated Plates with Classical Boundary Conditions, Advance Design and Manufacturing Technology, Vol. 3, No. 1, 2009, pp. 19-30.‏

[9]    Davar, A., Khalili, S. M. R., and Hadavinia, H., Free Vibrations of Functionally Graded Circular Cylindrical Shells under Internal Pressure, Advance Design and Manufacturing Technology, Vol. 6, No. 4, 2013, pp. 49-58.‏

[10] Kamarian, S., Volume Fraction Optimization of Four-Parameter FGM Beams Resting on Elastic Foundation, Advance Design and Manufacturing Technology, Vol. 6, No. 4, 2013, pp. 75-82.

[11] Wang, Y. Q., Jean W. Z., Vibration Behaviors of Functionally Graded Rectangular Plates with Porosities and Moving in Thermal Environment, Aerospace Science and Technology, Vol. 69, 2017, pp. 550-562.

[12] Barati, M. R, Shahverdi, H., Aero-Hygro-Thermal Stability Analysis of Higher-order Refined Supersonic FGM Panels with Even and Uneven Porosity Distributions, Journal of Fluids and Structures, Vol. 73, 2017, pp. 125-136.

[13] Chen, D., Yang, J., and Kitipornchai, S., Elastic Buckling and Static Bending of Shear Deformable Functionally Graded Porous Beam, Composite Structures, Vol. 133, 2015, pp. 54-61.

[14] Prakash, T., Ganapathi, M., Asymmetric Flexural Vibration and Thermo Elastic Stability of FGM Circular Plates using Finite Element Method, Composites Part B: Engineering, Vol. 37, 2006, pp. 642–649.

[15] Heydari, A., Analytical Solutions for Buckling of Functionally Graded Circular Plates under Uniform Radial Compression by using Bessel Function, Advance Design and Manufacturing Technology, Vol. 6, No. 4, 2013, pp. 41-47.

[16] Jandaghian, A., Jafari, A., Investigating Effect of Using Piezoelectric layers on the Forced Vibration of Circular Plates, Advance Design and Manufacturing Technology, Vol. 5, No. 5, 2012, pp. 1-9.

[17] Morovat, F., Analytical Solution for Buckling of Composite Sandwich Truncated Conical Shells subject to Combined External Pressure and Axial Compression Load, Advance Design and manufacturing Technology, Vol. 8, No. 4, 2015, pp. 83-94.

[18] Mantari J. L., Granados E. V., and Guedes S. C., Vibrational Analysis of Advanced Composite Plates Resting on Elastic Foundation, Composites Part B: Engineering, Vol. 66, 2014, pp. 407–19.

[19] Khalili, S. M. R., Mohammadi, Y., Free Vibration Analysis of Sandwich Plates with Functionally Graded Face Sheets and Temperature-Dependent Material Properties: A New Approach, European Journal of Mechanics - A/Solids, Vol. 35, 2012, pp. 61-74.

[20] Salami, S. J., Dariushi, S., Sadighi, M., and Shakeri, M., An Advanced High-order Theory for Bending Analysis of Moderately Thick Faced Sandwich Beams, European Journal of Mechanics - A/Solids, Vol. 56, 2016, pp. 1–11.

[21] Frostig, Y., Birman, V., and Kardomateas, G. A., Non-Linear Wrinkling of a Sandwich Panel with Functionally Graded Core–Extended High-order Approach, International Journal of Solids and Structures, Vol. 148, 2018, pp. 122-139.‏

[22] Shahrjerdi, A., Mustapha, F., Bayat, M., and Majid, D. L. A., Free Vibration Analysis of Solar Functionally Graded Plates with Temperature-Dependent Material Properties using Second Order Shear Deformation Theory, Journal of Mechanical Science and Technology, Vol. 25, No. 9, 2011, p.  2195.

[23] Frostig, Y., Thomsen, O. T., On the Free Vibration of Sandwich Panels with a Transversely Flexible and Temperature Dependent Core Material-Part II: Numerical Study, Composites Science and Technology, Vol. 69, 2009, pp. 863–869.

[24] Pandey, S., Pradyumna, S., Free Vibration of Functionally Graded Sandwich Plates in Thermal Environment using a Layer-Wise Theory, European Journal of Mechanics - A/Solids, Vol. 51, 2015, pp. 55–66.

[25] Sherif, H. A., Free Flexural Vibrations of Clamped Circular Sandwich Plates, Journal of Sound and Vibration, Vol. 157, No. 3, 1992, pp. 531-537.

[26] Chan, P., Frequency Equation for the In-plane Vibration of a Clamped Circular Plate, Journal of Sound and Vibration, Vol. 313, 2008, pp. 325–333.

[27] Nie, G. J., Zhong, Z., Semi-Analytical Solution for Three-Dimensional Vibration of Functionally Graded Circular Plates. Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 49-52, 2007, pp. 4901-4910.‏

[28] Ebrahimi, F., Rastgoo, A., and Kargarnovin, M. H., Analytical Investigation on Axisymmetric Free Vibrations of Moderately Thick Circular Functionally Graded Plate Integrated with Piezoelectric Layers, Journal of mechanical science and technology, Vol. 22, No. 6, 2008, pp. 1058-1072.‏

[29] Lal, R., Rani, R., On Radially Symmetric Vibrations of Circular Sandwich Plates of Non-Uniform Thickness, International Journal of Mechanical Sciences, Vol. 99, 2015, pp. 29-39.‏

[30] Heshmati, M., Jalali, S. K., Effect of Radially Graded Porosity on the Free Vibration Behavior of Circular and Annular Sandwich Plates, European Journal of Mechanics-A/Solids, Vol. 74, 2019, pp. 417-430.‏

[31] Reddy, J. N., Mechanics of Laminated Composite Plates and Shells, Theory and Application, CRC Press, New York, USA, 2003.

[32] Shen, H. S., Functionally Graded Materials Nonlinear Analysis of Plates and Shells, CRC Press, New York, 2009.

[33] Kiani, Y., Eslami, M.R., Instability of Heated Circular FGM Plates on a Partial Winkler-type Foundation, Acta Mechanica, Vol. 224, No. 5, 2013, pp. 1045-1060.‏

[34] Kim, Y. W., Temperature Dependent Vibration Analysis of Functionally Graded Rectangular Plates, Journal of Sound and Vibration, Vol. 284, No. 3-5, 2005, pp. 531-549.‏

[35] Es'haghi, M., Hashemi, S. H., and Fadaee, M., Vibration Analysis of Piezoelectric FGM Sensors using an Accurate Method, International Journal of Mechanical Sciences, Vol. 53, No. 8, 2011, pp. 585-594.‏

[36] Wu, T. Y., Wang, Y. Y., Liu, and G. R., Free Vibration Analysis of Circular Plates using Generalized Differential Quadrature Rule, Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 46, 2002, pp. 5365-5380.‏