Piezoelectric sensor location by the observability Gramian maximization using topology optimization

Abstract

This work presents an optimal design methodology for piezoelectric material positioning in structures aiming at vibration measurements. The main objective is to find the optimal location of piezoelectric sensors using a suitable topology optimization strategy. The sensors location is determined by an optimization formulation that defines where the material should have piezoelectric properties. The objective of the optimization is maximizing observability, measured by means of the trace of the Gramian matrix. The control strategy development is based on a truncated modal system model. A case study and its results are presented and discussed, showing that the optimal placement of the piezoelectric sensors in a cantilever beam can be suitably achieved through the proposed approach.

2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

“…Afterwards, other approaches including SIMP (Kögl and Silva 2005), BESO (de Almeida 2019) or level set method (Chen et al 2010) are also explored. By defining proper objective functions, TO methodology is applied to piezoelectric actuators (Moretti and Silva 2019;Gonċalves et al 2018), sensors (Menuzzi et al 2018) and energy harvesters (Homayouni-Amlashi et al 2020b;Homayouni-Amlashi 2019;Townsend et al 2019). The publications considered different types of system modeling including the static (Zheng et al 2009), dynamic (Noh and Yoon 2012;Wein et al 2009), modal (Wang et al 2017) and electrical circuit coupling (Salas et al 2018;Rupp et al 2009).…”

Multi Directional Piezoelectric Plate Energy Harvesters Designed By Topology Optimization Algorithm

“…By Substituting (19) in (13) and 14, the sensitivity of objective function with respect to density ratio can be calculated. In addition to what is mentioned in refs [20], [22], by employing the PEMAP-P [18], polarization is also a variable of optimization.…”

“…This methodology was interesting enough to be applied to piezoelectric structures. As such, after taking the first step of extending the SIMP scheme for the nonisotropic material [17], the application of TO to piezoelectric materials took different directions including the optimization of actuators [18], sensors [19] and energy harvesters [20], [21]. The application of TO to PEHs started by defining an energy-based objective function and sensitivity analysis [20].…”

Configuración óptima de transductores piezoeléctricos para control activo de vibraciones usando el método de optimización topológica

“…Por ejemplo, en [8] encuentran la posición óptima al obtener dos soluciones generalizadas de la ecuación de Riccati; en [9] desarrollan un método de posición óptima basada en gradientes, y en [10] proponen una optimización multiobjetivo con algoritmos genéticos. En los últimos 20 años se registran pocas publicaciones relacionadas al control activo de vibraciones con materiales piezoeléctricos usando le método de optimización topológica, entre ellos, se destacan los trabajos de [11]- [14] en los cuales se aborda el problema con diferentes formulaciones del modelado y optimización.…”