A wavelet approach for active-passive vibration control of laminated plates

Abstract

As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers. Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory, this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop, hence reducing the risk of residual coupling effects which are usually the source of spillover instability. Moreover, the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process. A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process. Numerical results demonstrate the efficiency of the proposed approach.

A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations

“…By solving algebraic equation (23), which has (2 + 1) equations, we can obtain the values of the unknown function , = 0, 1, 2, . .…”

“…As a newly developed powerful mathematical tool, which has been developed mostly over the last twenty years, the wavelet has become widely used in the development of numerical schemes for solving differential and integral equations [17][18][19][20], Laplace inversions [21], and active vibration control of piezoelectric smart structures [22,23]. In [11], Liang et al solved the second kind integral equations by applying Galerkin method with continuous orthogonal wavelets, and one can find that using the Daubechies wavelets to solve the integral equation has almost the same numerical results as those of noncontinuous multiwavelets [24].…”

Neuro-Fuzzy modal control of smart laminated composite structures modeled via mixed theory and high-order shear deformation theory

“…This technique utilizes secondary forces applied to the structure by a controller to minimize its vibrations (Zhang et al, 2015, Rahmani andShenas,2017). The semi-active techniques comprise the combination of the previous two (Wang et al, 2012). There has been an increasing number of works dedicated to the active control of vibrations in smart structures based upon the linear quadratic regulator (LQR) (Schulz et al, 2013;Koroishi et al, 2015, Mirghaffari andXu et al, 2017).…”

On the generalized wavelet-Galerkin method

“…Since the breakthrough in 1988 when Daubechies [1,2] constructed an orthogonal, compactly supported wavelet, there has been an increasing interest in wavelet-based methods for ordinary and partial differential equations. Briefly speaking, there exist three kinds of wavelet-based methods: the wavelet finite element method [3][4][5], the wavelet collocation method [6][7][8] and the wavelet-Galerkin method [9][10][11][12][13], whereas the wavelet-Galerkin method has gained the widest attention due to its good convergence and stability characteristics [14][15][16].…”