Free Vibration and Buckling Analysis of Sandwich Panels with Flexible Cores Using an Improved Higher Order Theory

Document Type : Research Paper


1 Department of Mechanical Engineering, Malek Ashtar University, Tehran, Iran

2 Department of Mechanical Engineering Bu-Ali Sina University, Hamedan, Iran


In this paper, the behavior of free vibrations and buckling of the sandwich panel with a flexible core was investigated using a new improved ‎high-order sandwich panel theory. In this theory, equations of motion were formulated based on shear stresses in the core. First-order shear deformation theory was ‎applied for the procedures. In this theory, for the first time, incompatibility problem of velocity and acceleration field existing in Frostig's ‎first theory was solved using a simple analytical method. The main advantage of this theory is its simplicity and less number of equations than the ‎second method of Frostig's high-order theory. To extract dynamic equations of the core, three-dimensional elasticity theory was utilized. ‎Also, to extract the dynamic equations governing the whole system, Hamilton's principle was used. In the analysis of free vibrations, the ‎panel underwent primary pressure plate forces. Results demonstrated that, as plate pre-loads got closer to the critical buckling loads, the natural frequency of the panel tended zero. The results obtained from the present theory were in good correspondence with the ‎results of the most recent papers. 


[1] Kameswara Rao M., Desai Y.M., Chitnis M.R., 2001, Free vibrations of laminated beams using mixed theory, Composite Structures 52(2): 149-160.
[2] Kant T., Swaminathan K., 2001, Free vibrations of laminated beams using mixed theory, Composite Structures 53(1): 73-85.
[3] Meunier M., Shenoi R.A., 2001, Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory, Composite Structures 54(2-3): 243-254.
[4] Nayak A.K., Moy S. S. J., Shenoi R.A., 2002, Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory, Composites Part B: Engineering 33(7): 505-519.
[5] Frostig Y., Thomsen O.H., 2004, High-order free vibration of sandwich panels with a flexible core, International Journal of Solids and Structures 41(5-6): 1697-1724.
[6] Malekzadeh K., Khalili K. M. R., Mittal R. K., 2005, Local and global damped vibrations of plates with a viscoelastic soft flexible core: an improved high-order approach, Journal of Sandwich Structures and Materials 7(5): 431-456.
[7] Frostig Y., Baruch M., 1990, Bending of sandwich beams with transversely flexible core, American Institute of Aeronautics and Astronautics 28(3): 523-531.
[8] Frostig Y., Baruch M., 1994, Free vibrations of sandwich beams with a transversely flexible core: a high order approach, Journal of Sound and Vibration 176(2): 195-208.
[9] Frostig Y., 1998, Buckling of sandwich panels with a flexible core—high-order theory, International Journal of Solids and Structures 35(3): 183-204.
[10] Frostig Y., Thomsen O.H., 2007, Buckling and nonlinear response of sandwich panels with a compliant core and temperature-dependent mechanical properties, Journal of Mechanics of Materials and Structures 2(7): 1355-1380.
[11] Dafedar J.B., Desai Y.M., Mufti A. A., 2003, Stability of sandwich plates by mixed, higher-order analytical formulation, International Journal of Solids and Structures 40(17): 4501-4517.
[12] Pandit M.K., Singh B.N., Sheikh A.H., 2008, Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, Thin-Walled Structures 46(11): 1183-1191.
[13] Ćetković M., Vuksanović D.J., 2009, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layer wise displacement model, Composite Structures 88(2): 219-227.
[14] Yao S., Kuo., Le-Chung Shiau., 2009, Buckling and vibration of composite laminated plates with variable fiber spacing, Composite Structures 90(2): 196-200.
[15] Fiedler L., Lacarbonara W., Vestroni F., 2010, A generalized higher-order theory for buckling of thick multi-layered composite plates with normal and transverse shear strains, Composite Structures 92(12): 3011-3019.
[16] Shariyat M., 2010, A generalized high-order global–local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads, Composite Structures 92(1): 130-143.
[17] Dariushi S., Sadighi M., 2015, Analysis of composite sandwich beam with enhanced nonlinear high order sandwich panel theory, Modares Mechanical Engineering 14(16): 1-8.
[18] Rao M.K., Scherbatiuk K., Desai Y.M., Shah A.H., 2004, Natural vibrations of laminated and sandwich plates, Journal of Engineering of Mechanics 130(11): 1268-1278.
[19] Zhen W., Wanji C., Xiaohui R., 2010, An accurate higher-order theory and C0 finite element for free vibration analysis of laminated composite and sandwich plates, Composite Structures 92(6): 1299-1307.
[20] Zhen W., Wanji C., 2007, Thermo mechanical buckling of laminated composite and sandwich plates using global–local higher order theory, International Journal of Mechanical Sciences 49(6): 712-721.