A Controllability-Based TO Approach for the Piezoelectric Actuator Design Considering Multimodal Vibration Control

Abstract

This paper addresses the design problem of piezoelectric actuators for multimodal active vibration control. The design process is carried out by a topology optimization procedure which aims at maximizing a control performance index written in terms of the controllability Gramian, which is a measure that describes the ability of the actuator to move the structure from an initial condition to a desired final state in a finite time interval. The main work contribution is that independent sets of design variables are associated with each modal controllability index, then the multi-objective problem can be split into independent single-objective problems. Thus, no weighting factors are required to be tuned to give each vibration mode a suitable relevance in the optimization problem. A material interpolation scheme based on the Solid Isotropic Material with Penalization (SIMP) and the Piezoelectric Material with Penalization (PEMAP) models is employed to consider the different sets of design variables and the sensitivity analysis is carried out analytically. Numerical examples are presented by considering the design and vibration control for a cantilever beam and a beam fixed at both ends to show the efficacy of the proposed formulation. The control performance of the optimized actuators is analyzed using a Linear-Quadratic Regulator (LQR) simulation.

A Systematic Review of Piezoelectric Materials and Energy Harvesters for Industrial Applications

“…The above Equation ( 31) is well known as the beam coupled FE governing equation for piezoelectric actuator modeling. Such an example was found in the case of a vibration analysis of structures by FE modeling of piezoelectric patches [55], active vibration control (AVC) [56][57][58][59][60][61][62][63], and dynamic structural control can also be found in many cases [64][65][66][67][68][69].…”

Simplification of Electrode Profiles for Piezoelectric Modal Sensors by Controlling Gap-Phase Length

“…Frequently, piezoelectric devices play a crucial role in providing both monitoring and actuation capabilities, such as damage sensing and self-healing [7,8]. In particular, piezoelectric materials serve as versatile components in the field of vibration monitoring.…”