Wave motion in thick damped laminated orthotropic plates

Abstract

Exact closed form solutions are presented for the harmonic plane wave motion in thick single and three layered isotropic/orthotropic plates together with the approximate solution for a general multilayered orthotropic plate. These allow for transverse direct strain through the thickness of the plate together with shear deformation and transverse and longitudinal inertias in all layers. Studies are made of the wavespeeds, wavemodes and the corresponding wave loss factors when some or all of the layers are damped. The forced harmonic response to an external harmonic pressure field with both normal and tangential components is also examined. The exact analyses solve the linear equations of equilibrium and compatibility for each layer. Sinusoidal lengthwise motion is assumed in the layer but no restriction is placed on displacement variation through the layer thickness. In contrast, the approximate theory restricts the through-the-thickness variations to linear forms and each layer is allowed four degrees of freedom. Hamilton's principle is used to set up the equations of motion. Special attention is given to plates with a lengthwise axis of symmetry, and extensive computed results are presented and discussed for the wavespeeds and loss factors of the many different types of wave which can exist. Where possible, the results from the approximate theories are compared with those from the exact theories, and also from previous approximate theories. Experimental methods are also developed to measure the high frequency properties of orthotropic composite materials. These are applied to a particular glass fibre reinforced plastic material and its dynamic mechanical properties are determined successfully up to a frequency of 20kHz.

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