Investigations on the linear vibration characteristics of bistable unsymmetrical laminates

Linear vibration characteristics of bistable unsymmetric laminates have been explored in this study. An experimental strategy to capture the natural frequencies of a bistable composite laminate is presented. An unsymmetric cross-ply laminate supported at its centre and free at all boundaries has been used for the experimental testing. The present study considers the small-amplitude natural vibrations around the static equilibrium shapes where the vibrations are measured using miniature integrated electronics piezoelectric (IEPE) accelerometer sensors. An improved semi-analytical framework where Hamilton’s principle is applied in combination with the Rayleigh-Ritz approach is proposed to analyse the vibration characteristics of the selected bistable laminate. In this framework, the membrane and bending energies are decoupled by a semi-inverse constitutive equation. The in-plane stress components are expressed as differential equations in terms of curvatures using the in-plane equilibrium equations and the compatibility conditions, and the obtained equations are converted into the form of a standard finite element elasticity problem. The in-plane stress components are separately evaluated by solving the obtained finite element elasticity problem using a standard numerical approach. As a result, the total potential energy is expressed in terms of the unknown coefficients of the assumed out-of-plane displacement function. In the subsequent dynamic analysis, perturbations are imposed on the static equilibrium configurations to simulate the eigenfrequencies and corresponding eigenmodes. The proposed semi-analytical model is computationally efficient and very effective to predict the linear vibration characteristics of bistable unsymmetric laminates. The solutions are further compared with a fully geometrically nonlinear FE calculation.