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

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 frequency-amplitude 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.

Nonlinear vibration control of nano-beam based on capacitive acoustic sensors

The nonlinear vibration control of the Euler–Bernoulli beam is studied based on capacitive micro-mechanical acoustic sensors The graphene film has the characteristics of high sensitivity and high accuracy which can be applied to sense the vibration signal. Capacitive micro-mechanical acoustic sensors can be used to detect the acoustic signal of the vibration of the nano-beam. The nonlinear vibration control equation of nano-beam can be established with the displacement and velocity voltage feedback controller based on capacitive micro-mechanical acoustic sensors. The amplitude-frequency response equation of the primary resonance of nano-beam can be gotten by using the multiple scales method. The relationship between the nonlinear vibration of nano-beam and system parameters is investigated. The influencing factors of how to weak system nonlinearity and enhance system stability are analyzed. The static bifurcation behavior of the system is discussed. The numerical results show that the nonlinearity of vibration can be reduced and the stability of the system can be improved by selecting the appropriate control gains and appropriately reducing the amplitude of DC and AC excitation voltages.

Operator-based nonlinear free vibration control of a flexible plate with sudden perturbations

In this paper, a new nonlinear vibration control scheme using piezoelectric actuator is proposed for a flexible plate with a free vibration and sudden perturbations. First, the effect of hysteresis nonlinearity from the piezoelectric actuator is considered by Prandtl-Ishlinskii (P-I) hysteresis model. Simultaneously, a dynamic model of the flexible plate with piezoelectric actuator is considered. Then, based on the dynamic model of the flexible plate, operator-based controllers are designed to guarantee the robust stability of the nonlinear control system. In addition, for ensuring the desired vibration control performance of the flexible plate with a free vibration and sudden perturbations, operator-based compensation method is given by the proposed design scheme. In the designed compensator, the desired compensation performances of tracking and of perturbations are obtained by increasing the number of designed n-times feedback loops. Finally, both of numerical simulation and experimental result are shown to verify the effectiveness of the proposed design scheme.