Abstract
Based on the theory of magneto-electro-elastic (MEE) multilayered plate and by using the state-vector and propagator matrix approach, the natural characteristics (i.e. modal analyses) of the hard-coating plates are investigated. The hard-coating plates in this study are composed of a purely elastic substrate and one magneto-elastic or electro-elastic coating layer of which the thickness is much smaller compared to the substrate layer. Firstly, every field variable of the hard-coating multilayered plate is written into one of the two state vectors, which are related to each other by the form of matrix-production; Secondly, all the field variables are expanded into the form of infinite trigonometric series, and then the field variables of two adjacent layers are connected by the propagator matrix which is the expression of the unknown natural frequencies; Finally, by applying the boundary conditions at top and bottom surfaces, the natural frequencies can be exactly solved. Numerical examples are provided in the last part, and effect of both coating thickness and coating material properties (with either magnetic or electric effect involved) on the natural frequencies and mode shapes are discussed. The results are also compared with some finite element results.
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