Large amplitude free vibration of symmetrically laminated magneto-electro-elastic rectangular plates on Pasternak type foundation

Abstract Nonlinear free vibration of symmetrically laminated magneto-electro-elastic rectangular plate resting on an elastic foundation is studied analytically. The plate is considered to be simply supported on all edges. It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces. To model the motion of the plate, the first order shear deformation theory along with the Gauss's equations for electrostatics and magnetostatics are used. Then equations of motion are reduced to a single nonlinear ordinary differential equation which is solved analytically by multiple scales method. The results are compared with the published results and good agreement is found. Some numerical examples are presented to investigate the effects of several parameters on the linear and nonlinear behavior of these plates.

[1]  Chih‐Ping Wu,et al.  A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates , 2009 .

[2]  H. Hu.  Solution of a mixed parity nonlinear oscillator: Harmonic balance , 2007 .

[3]  Alberto Milazzo,et al.  Layer-wise and equivalent single layer models for smart multilayered plates , 2014 .

[4]  Ernian Pan,et al.  Free vibration response of two-dimensional magneto-electro-elastic laminated plates , 2006 .

[5]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[6]  Yansong Li,et al.  Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation , 2014 .

[7]  Ernian Pan,et al.  The MLPG analyses of large deflections of magnetoelectroelastic plates , 2013 .

[8]  Carlos A. Mota Soares,et al.  Analyses of magneto-electro-elastic plates using a higher order finite element model , 2009 .

[9]  Ernian Pan,et al.  Large deflection of a rectangular magnetoelectroelastic thin plate , 2011 .

[10]  Paul R. Heyliger,et al.  Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions , 2014 .

[11]  Xing-chun Huang,et al.  Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations , 2003 .

[12]  Alberto Milazzo,et al.  Refined equivalent single layer formulations and finite elements for smart laminates free vibrations , 2014 .

[13]  Yang Xiang,et al.  Vibration Of Thick Skew Plates Based On Mindlin Shear Deformation Plate Theory , 1993 .

[14]  Marco Amabili,et al.  On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells , 2011 .

[15]  E. Pan,et al.  Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates , 2001 .

[16]  Alberto Milazzo,et al.  Large deflection of magneto-electro-elastic laminated plates , 2014 .

[17]  Ernian Pan,et al.  FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES , 2002 .

[18]  Ivano Benedetti,et al.  A finite element formulation for large deflection of multilayered magneto-electro-elastic plates , 2014 .