Finite Element Charts and Active Vibration Suppression Schemes for Smart Structures Design

Abstract

This article employs a finite element method to introduce Displacement-Load-Sensor voltage-Actuator voltage (DLSA) Design Charts and associated vibration suppression schemes; namely, Constant Voltage (CV), Optimum Voltage (OV), Corresponding Voltage (COV), and Truncated Corresponding Voltage (TCOV), to develop actuator control voltages with amplitude and phase information for the design of smart structures with piezoelectric sensors and actuators for active vibration suppression. These techniques can be used to (a) design the location, size, and number of actuators without resorting to complex control strategies or formal optimization techniques, (b) investigate the actuation effectiveness of surface-mounted versus embedded piezoelectric patches in similar composite structures, and (c) determine actuator control voltages analogous to a feedforward open-loop control technique. Guidelines are presented for the development of DLSA Design Charts. In addition, closed form analytical equations that can replace DLSA Design Charts, are developed and presented due to their ease of use. An Active Composite Panel (ACP) with a surface-mounted piezoelectric patch actuator for lateral vibration suppression and an Active Composite Strut (ACS) with a piezoelectric stack actuator for axial vibration suppression are considered. The ACP and ACS are employed to demonstrate the applications of the introduced DLSA Design Charts and the vibration suppression schemes for vibration suppression and actuator placement optimization. The vibration suppression of both ACP and ACS is significant over a frequency range encompassing several resonances, and is indicated by the Suppressed Vibration Energy (SVE) index. This investigation shows that the optimum location of the actuator depends on the structural mode shape, based on the criteria of maximum SVE and minimum actuator power. In general, the actuator should be placed on the panel on a sub-area, where the sum of normal strains is maximum. However, a preferred location can be determined over a range of frequencies that encompass more than one natural frequency.