Dynamic modelling and analysis of smart cantilever beam using FEM

This study presents the dynamic analysis of a smart cantilever beam subjected to impact loading with and without tip mass. The smart beam is fabricated by placing a layer of viscoelastic material between the host structure and a piezoelectric (constraining) layer. The viscoelastic layer contributes passive damping, whereas the piezoelectric layer contributes active damping. The mechanical behaviors of the viscoelastic material are incorporated by the fractional derivative model. The Euler Bernoulli beam theory is used in conjunction with Hamilton's principle to derive the system's governing equations of motion and boundary conditions. The solution of the system is obtained through the use of the finite element method and Newmark scheme of time integration. Velocity feedback control gain is applied to get the control response. The system's natural frequencies and tip displacement are determined using the finite element method (FEM). The proposed FEM model is compared with the results available in the literature in order to assess the accuracy in the dynamic behaviour of the sandwich cantilever beam. It is found that the proposed FEM model results deviated by less than 5% error with the existing results. Parametric studies are conducted to examine the effects of some potential design variables on system vibrational behavior. The obtained results show the improvement in the system responses with the incorporation of active-passive damping rather than passive damping. The results presented in the paper can be useful to design a smart structure that would be able to sense the vibration and generate a controlled actuation to it, so that the vibration can be minimized. As a consequence, smart materials are used to manufacture advanced actuators and sensors in the manufacturing industries.