Vibration of variable thickness orthotropic plates using eigensensitivity analysis

An approximate closed-form expression is presented which can be used to compute the fundamental frequency of orthotropic laminates of variable thickness. The quadratic expression is derived for a laminate with a general thickness variation in one direction, and explicit results are provided for a laminate with a linear thickness variation. The desired expression is determined by casting the governing differential equation into discrete form using the Ritz method and expanding the discrete equations in a Maclaurin series about the off-diagonal elements of both the stiffness and mass matrices. Simply supported and clamped boundary conditions are analyzed using both beam shape functions and orthogonal polynomials. Results are compared with those obtained numerically using the Rayleigh-Ritz approach for several laminate tapers xi and plate aspect ratios R.