Improved active control of a functionally graded material beam with piezoelectric patches

Abstract

In this paper, the active vibration control tools are implemented for the vibration control of functionally graded material (FGM) beam with piezoelectric actuators and sensors. The properties of FGM are functionally graded in the thickness direction according to the volume fraction power law distribution. An analytical formulation, based on an efficient trigonometric shear deformation theory, is used to obtain a state space equation. The main steps to set up active control of FGM vibrations are considered in this work. The actuators' and sensors' locations are defined from two optimization problems using controllability and observability gramians. The linear quadratic regulator (LQR) control law, including a state observer is computed. Numerical examples show the influence of the volume fraction index on the observability and controllability properties of the system. The LQR leads to efficient active damping for several kinds of excitations. The study of the uncertainty in the volume fraction index shows the robustness of the control method, and also the possible induced defects.

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

“…Degree of controllability using the second optimal location for homogeneous beam: a 1 ¼ 0:3 m (%) In order to show the possible impact of the choice of actuator location to the efficiency of active control, the LQR method (Bruant and Proslier 2014;Kailath 1980), including a state observer, is developed from the state equations Eq. (33) considering the 4 first eigenmodes.…”

“…For examples, Bruant and Proslier (2014) and Gharib et al (2008) focused on active vibration control of FGM beams, Fakhari and Ohadi (2010), Fu et al (2013), He et al (2001), Kargarnovin et al (2007), Liew et al (2003), Mirzaeifar et al (2008), Yiqi and Yiming (2010) considered active control of FGM plates, and Kiani et al (2013), Narayanan and Balamurugan (2010), Sheng and Wang (2009) and Zheng et al (2009) the shells' one.…”

Finite element model based on an efficient layerwise theory for dynamics and active vibration control of smart functionally graded beams

“…Nguyen et al (2013) obtained the Navier solution for static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Bruant and Proslier (2015) carried out active vibration control of FGM beam based on state space formulation using trigonometric shear deformation theory. Ebrahimi and Hashemi (2017) carried out vibration analysis of non-uniform porous FGM beam under temperature gradient.…”

A numerical efficiency study on the active vibration control for a FGPM beam

“…Both electrodes are bounded at the top and bottom surfaces of the beam and have each a length of 0.1 L. Note that the sensor and actuator are not collocated. According to [23] this configuration is the optimal one for classical piezoelectric actuator and sensor on a cantilever beam, which ensures good observability and controllability of each eigenmodes. To study the influence of V k , T is fixed to 0.4.…”

“…Regarding the active vibration control using functionally graded material, we can find in literature papers dealing with active vibration control of FGM equipped with piezoelectric patches [14][15][16][17][18][19][20][21][22][23][24].…”