Analytical solutions for nonlinear magneto-electro-elastic vibration of smart sandwich plate with carbon nanotube reinforced nanocomposite core in hygrothermal environment
An analytical approach on the nonlinear magneto-electro-elastic vibration of smart sandwich plate in hygrothermal environment is presented.
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The sandwich plate comprises of a carbon nanotube reinforced nanocomposite (CNTRC) core integrated with two magneto-electro-elastic face sheets.
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The coupled constitutive relations are derived based on the Hamilton's principle.
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The Galerkin method is used to obtain the closed form expressions of natural frequency and the relation between the frequency ratio and dimensionless amplitude.
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The effect of geometrical parameters, CNT volume fraction, temperature and moisture increment, electric and magnetic potentials on the nonlinear vibration of smart sandwich plate is discussed in details.
Abstract
This paper presents an analytical approach on the nonlinear magneto-electro-elastic vibration of smart sandwich plate. The sandwich plate consists of a carbon nanotube reinforced nanocomposite (CNTRC) core integrated with two magneto-electro-elastic face sheets. For core layer, three types of carbon nanotube (CNT) distribution such as FG-O, FG-V, FG-X are considered while the volume fraction of BaTiO3 − CoFe2O4 in each face sheet is chosen to be 0.5. It is assumed that the smart sandwich plate is rested on Pasternak-type elastic foundations and subjected to the combination of external pressure, thermal, electric and magnetic loads. The coupled constitutive relations are derived based on the Hamilton's principle in which the kinematic nonlinearity is defined using Reddy's higher order shear deformation theory. The analytical solutions which satisfy the boundary conditions are assumed to have the trigonometric form. The Galerkin method is used to obtain the closed form expressions of natural frequency, the relation between the frequency ratio and dimensionless amplitude and the dynamic response of the sandwich plate. The numerical results are conducted to illustrate the effect of geometrical parameters, CNT volume fraction, temperature and moisture increment, electric and magnetic potentials on the nonlinear vibration of smart sandwich plate. The reliability of present results is evaluated by comparing with the previous results based on different approach.
