Mode localization in composite laminates

Abstract

a b s t r a c t We study free vibrations of monolithic and composite thin rectangular plates; the former are made of linear elastic, homogeneous, isotropic materials and the latter of fiber reinforced laminas. The plates are clamped on all four edges and interior points on a transverse normal to the plate midsurface are rigidly tied together and have either null displacements and null rotations (Type-I constraint) or only null transverse displacements (Type-II constraint). Depending upon the location of the point on the midsurface through which the transverse normal passes, modes localize in different regions of the plate. Plates of various aspect ratios (length/width) and stacking sequences of 0°, 45°and 90°leading to symmetric and anti-symmetric configurations about their midsurfaces are considered. The problem is studied using the first order shear deformable (or the Mindlin) plate theory. It is found that both the Type-I and Type-II constraints divide the plate into two vibrating regions with amplitudes of transverse vibration localized in a particular region on either side of the clamped interior points. It is found that the mode localization in laminates is governed by the mode localization characteristics of constituent laminas. For symmetric cross ply laminates the localization of modes is found to decrease with the increase in the number of 0°p lies. For anti-symmetric cross ply laminates and those made of all 45°plies the mode localization is found to be independent of the number of plies. For isotropic plates made of a monolithic material the mode localization phenomenon is stronger for Type-I constraint compared to that for Type-II constraints. Also, for these plates the mode localization occurs when lumped masses are placed at these interior points. The significance of the work lies in providing an alternative and an economical way of annulling plate vibrations in selected parts of the plate, and confining the energy of vibration in desired regions of the plate