A Numerical–Analytical Solution for Dynamics of Composite Delaminated Beam with Piezoelectric Actuator,with Account of Nonpenetration Constraint for the Delamination Crack Faces

Abstract

In this work, a new approach is developed for the dynamic analysis of a composite beam with an interply crack, in which a physically impossible interpenetration of the crack faces is prevented by imposing a special constraint, leading to nonlinearity of the formulated boundary value problem and taking account of a contact interaction of the crack faces. A variational formulation of the problem and partial differential equations of motion with boundary conditions are developed, and solutions of example problems for a piezo-actuated cantilever beam are presented in the form of a series in terms of eigenfunctions of the associated nonself-adjoint eigenvalue problem. A noticeable difference of forced vibrations of the delaminated and undelaminated beams due to the contact interaction of the crack faces is predicted by the developed model.

Keywords

composite beam delamination nonpenetration constraint for the crack faces nonlinear dynamics series solution modal analysis

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