A refined two-dimensional theory of anisotropic plates (Q1309781)

The theory includes the effects of transverse normal strain and transverse shear deformation. Hamilton's mixed variational principle is used to derive the basis equation of motion of an anisotropic plate subjected to a surface traction field. The in-plane displacements are expanded as linear functions of the thickness coordinate, only the transverse deflection is quadratic. Specially the influence of the transverse normal strains on frequencies is studied. Numerical results for an anisotropic square plate (thickness \(h\), length \(a\)) show that classical and shear deformation theories overestimate the frequencies. The errors increase with increasing wave numbers \(m,n\). This effect is less significant when \(h/a \leq 1\) and \((m,n) \leq 3\).