Topology Optimization Method Applied to the Design of a Vibrational Piezo-Structure Subjected to Active Control Law

Mariana Moretti¹; Emílio Silva¹

¹ University of São Paulo

doi:10.20906/CPS/CILAMCE2015-0690

Resumo

Recent developments in structure design for transient analysis based on TOM have covered the optimal distribution of piezoelectric material over a host structure to reduce its transient response. To this end, the system model accounts with an active control law provided by the designed piezo-ceramic layers for sensing and actuation purposes. Continuing on the dynamic applications mainstream, this work is devoted to the design of a piezoelectric vibrational structure optimized to amplify its absolute overshoot response in time under an applied load step. In this case, two piezo-ceramics regions, the sensor and actuator ones, are set in specific positions within the domain while the metallic structure layout is designed by using TOM and functionally graded material concept to maximize a measuring point displacement in peak time. The current amplifier definition is applied to measure the static charges generated in sensor ceramic and convert them into an isopotential input on the actuator's electrode by means of a specified feedback gain, what in terms of the dynamic governing equations will result in a constant gain velocity feedback. TOM is implemented based on the SIMP material model, which is employed for void and two metallic material properties to obtain a graded optimal structure where pseudo-densities are interpolated at each finite element. The sensitivity analysis is calculated by using the adjoint method. The discrete approximation of sensitivity is evaluated with a direct time integration method after the continuous function differentiation in time was taken, an approach denominated differentiate-than-discretize. Examples are restricted to two-dimensional models and one-dimensional material gradation constraint. The influence of the control gain over the correspondent optimal output displacement in peak time will be discussed.

Palavras-chave: Topology Optimization Method; Functionally Graded Material; Active Control Law; Piezoelectric Structure