Frequency analysis of sandwich plates with temperature dependent flexible core based on the unified hybrid formulation

Authors

1 Assistant professor, Department of Mechanical Engineering, Islamic Azad University of Qazvin Branch

2 Assistant Professor, Department of Mechanical Engineering, Islamic Azad University, Qazvin Branch

3 Assistant professor Department of Mechanical Engineering,, Islami Azad University of Quazvin.

Abstract

In this study a frequency analysis of a sandwich plate with multilayered composite face-sheets and flexible core under thermal conditions is investigated for different boundary conditions. In this regard, thermal effects and temperature dependent properties of the core are considered. In this study, for driving the equations of motion, a hybrid LW/ESL finite element formulation, considering the thermal effects is proposed by which the number of unknowns is independent on the number of layers. This new formulation is in the framework of Carrera’s Unified Formulation (CUF). The CUF unify many theories in a unified form which can be differed by the order of expansion and definition of the variables in the thickness direction. In order to satisfy the interlaminar continuity of transverse stresses between the layers the Reissner Mixed Variational Theorem (RMVT) is employed. In this research for considering the thermal effects, the nonlinear strains are used. Results of this formulation are compared with available results which show the high accuracy with low computational cost of the proposed formulation. Results show that with increasing the temperature, the frequency of structure decreases significantly, due to the degradation of the properties of the core. In this study, some new results are presented for different thermal conditions and also different boundary conditions.

Keywords

Main Subjects


[1] Singh, A.V., "Free Vibration Analysis of Deep Doubly Curved Sandwich Panels", Computers and Structures, Vol. 73, pp. 385-394, (1999).
 
[2] Kant, T., and Swaminathan, K., "Analytical Solution for Free Vibrations for Laminated Composite and Sandwich Plates Based on a Higher-order Refined Theory", Composite Structures, Vol. 53, pp. 73–85, (2001).
 
[3] Rao, M.K., and Desai, Y.M., "Analytical Solutions for Vibrations of Laminated and Sandwich Plates using Mixed Theory", Composite Structures, Vol. 63. pp. 361–373, (2004).
 
[4] Morozov, E.V., and Lopatin, A.V., "Fundamental Frequency of the CCCF Composite Sandwich Plate", Composite Structures, Vol. 92, Vol. 11, pp. 2747–2757, (2010).
 
[5] Matsunaga, H., "Free Vibration and Stability of Angle-ply Laminated Composite and Sandwich Plates under Thermal Loading", Composite Structures, Vol. 77, pp. 249–262, (2007).
 
[6] Frostig, Y., and Thomsen, O.T., " On the Free Vibration of Sandwich Panels with a Transversely Flexible and Temperature-dependent Core Material– Part I: Mathematical Formulation", Composites Science and Technology, Vol. 69, pp. 856–862, (2009).
 
[7] Frostig, Y., and 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, pp. 863–869, (2009).
 
[8] Carrera, E., "A Class of Two-dimensional Theories for Anisotropic Multilayered Plates Analysis", Atti Accad Sci Torino Mem Sci Fis, 19–20, pp.1–39, (1995).
 
[9] Zhang, S., Dulieu-Barton, J.M., Fruehmann, R.K., and Thomsen, O.T., "A Methodology for Obtaining Material Properties of Polymeric Foam at Elevated Temperatures", Experimental Mechanics, Vol. 52, pp. 3–15, (2012).
 [10] Reddy, J.N., "An Introduction to the Finite Element Method", 2nd ed, McGraw-Hill, New York, (1993).
 
[11] Carrera, E., and Brischetto, S., "A Survey with Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates", Applied Mechanics Reviews, Vol. 62, 010803, (17 pages), (2009).
 
[12] Kulkarni, S.D., and Kapuria, S., "Free Vibration Analysis of Composite and Sandwich Plates using an Improved Discrete Kirchhoff Quadrilateral Element Based on Third Order Zigzag Theory", Computation Mechanics, Vol. 42, Vol. 6, pp. 803–824, (2008).
Volume 18, Issue 1 - Serial Number 42
System Dynamics and Solid Mechanics
June 2016
Pages 61-90
  • Receive Date: 19 January 2015
  • Revise Date: 31 January 2016
  • Accept Date: 01 March 2016