Free Vibration Analysis of Beams with Piezo-Patches Using a One-Dimensional Model with Node-Dependent Kinematic

The electro-mechanical analysis of beams with piezo-patches requires accurate models to be used. The interface between the beam and the patch has to be modeled properly to provide accurate results. The use of refined one-dimensional models may lead to a high accuracy in the solution when an appropriate kinematic model is used, as shown by Miglioretti and Carrera [1]. Nevertheless, refined kinematic models require a high number of degrees of freedoms that increase the computational cost of the analyses. The use of advanced models only in the portion of the structure where high accuracy is required, e.g. the patch area, could reduce the computational cost preserving the results accuracy. Biscani et al. [2] proposed the use of the Arlequin method to study the two-dimensional structures with piezopatches coupling models with different kinematics. This paper presents a new class of advanced one-dimensional models with nodedependent kinematics for the dynamic analysis of beam structures with piezopatches. ESL (Equivalent Single-layer) models and LW (Layer-wise) models have been taken into account. The Carrera Unified Formulation [3], has been used to derive the model in a compact and general form. The Finite Elements Method has been used to solve the one-dimensional problem. The cross-sectional kinematic approximation has been considered as a function of the one-dimensional element node [4], that is, no ad-hoc techniques have been used to derive the nodedependent kinematic model. Governing equations for beam models with nodedependent kinematics accounting for electromechanical effects are derived from the Principle of Virtual Displacement (PVD). The free vibration analysis of various beams structures with piezo-patches has been performed. The results obtained have been compared with solutions taken from literature. When used in the analysis of structures with local components or effects to be accounted for, the proposed advanced models can bridge the locally refined model to the global model and reduce the computational costs significantly while guarantying accuracy without employing special global-local coupling method.