Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer

Abstract

In this paper, the nonlinear vibration control of the piezoelectric laminated cylindrical shell with point supported elastic boundary condition is analyzed, in which the geometric nonlinearity is considered by the first-order shear nonlinear shell theory. In the model, different boundary conditions are simulated by introducing a series of artificial springs. The elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained based on the Chebyshev polynomials and Lagrange equation, and decoupled by using the negative velocity feedback adjustment. Later, the Incremental Harmonic Balance Method (IHBM) is deduced, and the frequencyamplitude response of the piezoelectric laminated cylindrical shell is obtained by IHBM. Finally, the influence of the constant gain, size and position of the piezoelectric layer on frequency-amplitude response are investigated. The results show that the position, size and constant gain of the piezoelectric layer have a significant influence on its nonlinear vibration control.

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

“…Take Equations ( 16)- (24) into Equation (A1) and combine Equations ( 14) and ( 15) with Equations ( 26)- (30), then take the variational extremum and substitute the obtained back into Equation (24) to yield the specific expression of w(x, y) which can be seen in Appendix A (Equation (A2)):…”

“…Besides the dynamical modeling and dynamical properties of beam structures with complex boundary conditions [19], the dynamical modeling and dynamical properties of plate structures [20][21][22][23][24], shell structures [25][26][27][28][29][30][31], and other types of structures [32][33][34] with complex boundary conditions have also been investigated [35][36][37][38][39]. For example, Xue et al [20] developed and solved a dynamics model for medium-thick composite laminates with arbitrary boundary conditions based on Mindlin's theory, Hamilton's principle, a modified Fourier series method, and the spring technique, with parametric studies on the effects of several key parameters, such as thickness-to-width ratio, number of plies, and lay-up angle between two plies.…”