A mathematical model for wave propagation in bilaminar composite plates

Abstract

Refined models for plate deformation allow for new types of thickness and extensional displacements not currently feasible in the classical or Timoshenko‐Mindlin plate theories. An infinite bilaminar composite plate is fabricated in such a way that the two plates, made of different isotropic, homogeneous materials, are perfectly bonded. A new mathematical model of the vibration of an infinite bilaminar composite plate has been obtained by using energy methods. The displacement field is based on symmetric and antisymmetric displacement functions in both the thickness stretch and the thickness shear of each layer. From this model, the Timoshenko‐Mindlin thick plate theory and the Bernoulli‐Euler classic plate theory for a single plate can be recovered as special limiting cases. For this model, a six‐branched frequency‐wavenumber spectrum of the composite layer is computed. This allows the introduction of suitable correction coefficients to correct the resulting frequency spectra so that they correspond to t...