Nonlinear Vibration and Control of Piezoelectric Laminates

2009 ◽  
Author(s):  
Li-hua Chen ◽  
Chang-Liang Liu ◽  
Wei Zhang ◽  
Jin-hong Fan
Keyword(s):  
Differential Equations ◽  
Rectangular Plate ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Chaotic Motions ◽  
Nonlinear Dynamic Equations ◽  
Control Gain ◽  
Piezoelectric Layers ◽  
Nonlinear Relation ◽  
And Control

In this paper, the dynamic behavior of piezoelectric laminates is investigated. Thin piezoelectric layers are assumed to be embedded on the top and the bottom surfaces of the rectangular plate. The top and the bottom layers are taken as the actuator and sensor, respectively. Based on Von Karman theory, the geometrically nonlinear relation between strain and displacement is proposed and basic large deformation equations are established. Nonlinear dynamic equations of piezoelectric laminates are formulated using Hamilton’s principle. The Galerkin’s approach is applied to partial differential equations to obtain the ordinary differential equations. The numerical results show the existence of periodic, bifurcation and chaotic motions for the laminated piezoelectric rectangular plate with the changes of frequency and amplitude of forcing loads. Furthermore we can control the vibration of the piezoelectric laminates using a constant gain velocity minus control algorithm. Using the control gain, the free vibration of the plate is damped out more quickly, and the nonlinear dynamic behavior varies from the system without control. Finally, a numerical simulation example shows that the method suggested in this paper is effective and simply.

scholarly journals Nonlinear Dynamic Analysis of Macrofiber Composites Laminated Shells

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Xiangying Guo ◽  
Dameng Liu ◽  
Wei Zhang ◽  
Lin Sun ◽  
Shuping Chen
Keyword(s):  
Differential Equations ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Chaotic Motions ◽  
Laminated Shells ◽  
Laminated Shell

This work presents the nonlinear dynamical analysis of a multilayer d31 piezoelectric macrofiber composite (MFC) laminated shell. The effects of transverse excitations and piezoelectric properties on the dynamic stability of the structure are studied. Firstly, the nonlinear dynamic models of the MFC laminated shell are established. Based on known selected geometrical and material properties of its constituents, the electric field of MFC is presented. The vibration mode-shape functions are obtained according to the boundary conditions, and then the Galerkin method is employed to transform partial differential equations into two nonlinear ordinary differential equations. Next, the effects of the transverse excitations on the nonlinear vibration of MFC laminated shells are analyzed in numerical simulation and moderating effects of piezoelectric coefficients on the stability of the system are also presented here. Bifurcation diagram, two-dimensional and three-dimensional phase portraits, waveforms phases, and Poincare diagrams are shown to find different kinds of periodic and chaotic motions of MFC shells. The results indicate that piezoelectric parameters have strong effects on the vibration control of the MFC laminated shell.

scholarly journals Nonlinear Torsional Dynamics of Star Gearing Transmission System of GTF Gearbox

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Nonlinear Dynamic ◽  
Damping Ratio ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Transmission System ◽  
Dynamic Responses ◽  
Nonlinear Dynamic Model ◽  
Chaotic Motions ◽  
Meshing Stiffness ◽  
And Control

Considering time-varying meshing stiffness, comprehensive errors, and piecewise backlash nonlinearities of gear and spline, a torsional nonlinear dynamic model of star gear-rotor coupling transmission system of (Geared Turbofan Engine) GTF aeroengine is established. By using the Runge–Kutta numerical integration method, the dynamic responses are solved, analyzed, and illustrated with the bifurcation parameters including input rotational speed, gear backlash, damping ratio, and comprehensive meshing errors. The motions of the star gearing system and diverse nonlinear dynamic characteristics are identified through global bifurcation, FFT spectra, Poincaré map, and the phase diagram. The results reveal that the star gear-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, and mutation are demonstrated. These results provide an understanding of undesirable torsional dynamic motion for the GTF transmission system and provide a reference for the design and control of gear system.

Bifurcations and Chaos of Composite Laminated Piezoelectric Rectangular Plate With One-to-Three Internal Resonance

2008 ◽  
Author(s):  
Zhi-Gang Yao ◽  
Wei Zhang
Keyword(s):  
Rectangular Plate ◽  
Multiple Scales ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Third Order ◽  
Chaotic Motions ◽  
Piezoelectric Layers ◽  
Parametric And External Excitations ◽  
First Time

The bifurcations and chaotic motions of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are analyzed for the first time, which are forced by the transverse and in-plane excitations. It is assumed that different layers of symmetric cross-ply composite laminated piezoelectric rectangular plate are perfectly bonded to each other and with piezoelectric actuator layers embedded in the plate. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The excitation loaded by piezoelectric layers is considered. The Galerkin’s approach is employed to discretize partial differential governing equations to a two-degree-of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is utilized to obtain the four-dimensional averaged equation. Numerical method is used to find the periodic and chaotic motions of the composite laminated piezoelectric rectangular plate. The numerical results show the existence of the periodic and chaotic motions in the averaged equation. It is found that the chaotic responses are especially sensitive to the forcing and the parametric excitations. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.

Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators

2011 ◽  
Vol 22 (18) ◽  
pp. 2093-2102 ◽  
Author(s):  
Yiming Fu ◽  
Jianzhe Wang ◽  
Yiqi Mao
Keyword(s):  
Active Control ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Sensors And Actuators ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Layers

Employing higher order shear deformation theory, geometric nonlinear theory, and Hamilton’s principle, a set of nonlinear governing equations for the functionally graded beams with surface-bonded piezoelectric layers is derived. Then, the negative velocity feedback algorithm coupling the direct and inverse piezoelectric effect is used to control the piezoelectric functionally graded beams actively. Using the finite difference method and Newmark method synthetically, the numerical solutions for the nonlinear dynamic equations of functionally graded beams with piezoelectric patches are obtained iteratively. In the numerical examples, the effects of the volume fraction exponent on the nonlinear dynamic responses and amplitude–frequency curves are investigated, and the active control responses of the functionally graded beams with piezoelectric layers under different control gains and volume fraction exponents are analyzed. Some meaningful solutions have been presented.

Dynamic Model and Control Design for a Nonlinear Hydraulic Actuator

2018 ◽  
Author(s):  
Carlos Borrás Pinilla ◽  
José Luis Sarmiento ◽  
Juan Felipe Ortiz
Keyword(s):  
Optimal Control ◽  
Dynamic Behavior ◽  
Pid Control ◽  
Nonlinear Dynamic ◽  
Feedback Linearization ◽  
Position Control ◽  
Settling Time ◽  
Hydraulic Systems ◽  
Hydraulic Actuator ◽  
And Control

Industrial hydraulic systems are complex, and show nonlinear dynamic behavior because of their nature. When it is not easy to deal with the nonlinear models, hydraulic systems are usually described by linear or linearized models around operating points. In this work a nonlinear dynamic and mathematic model for the position control of a double rod hydraulic actuator was developed. Three control strategies were implemented: PID control, optimal control (LQR) and control by Feedback Linearization. For the PID control and optimal control (LQR) strategies a linearized model of the hydraulic actuator was developed around a specific operating point, contrary to the Feedback Linearization control that have a wide operation range and the nonlinear model was used. These mathematical models were represented on Simulink environment, in order to compare and analyze the response and dynamic behavior. The optimal control (LQR) shows better settling time than the PID control, both without overshoot; and the Feedback Linearization show the best dynamic performance in terms of settling time with a little overshoot and disturbance tolerance.

Nonlinear Vibration of a Cantilever FGM Rectangular Plate with Piezoelectric Layers Based on Third-Order Plate Theory

2011 ◽  
Vol 415-417 ◽  
pp. 2151-2155
Author(s):  
Ying Wang ◽  
Yu Xin Hao ◽  
Jian Hua Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Rectangular Plate ◽  
Initial Conditions ◽  
Plate Theory ◽  
Nonlinear Differential Equations ◽  
Nonlinear Dynamic Analysis ◽  
Control Voltage ◽  
Third Order ◽  
Piezoelectric Layers

This paper deals with nonlinear dynamic analysis of a cantilever FGM rectangular plate with piezoelectric layers subjected to the transversal excitation in thermo-electro-mechanical environment. The material properties of plate and piezoelectric layers are assumed to be temperature-dependent. The governing equations of the functionally graded plate are based on the Reddy’s third-order shear deformation plate theory that includes thermo-piezoelectric effects and Hamilton’s principle. The governing nonlinear partial differential equations are transformed into ordinary nonlinear differential equations using the Galerkin method and the nonlinear and linear frequencies obtained using the Runge–Kutta method. The effects played by control voltage and system initial conditions on the nonlinear vibration of the plate are studied.

scholarly journals Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

Vibration ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 805-821
Author(s):  
Ibrahim F. Gebrel ◽  
Samuel F. Asokanthan
Keyword(s):  
Differential Equations ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Electrostatic Force ◽  
Essential Element ◽  
Ring Structure ◽  
Dynamic Responses ◽  
Ongoing Research ◽  
Actuator Dynamics ◽  
External Forces

This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

scholarly journals Free Vibrations and Nonlinear Responses for a Cantilever Honeycomb Sandwich Plate

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Junhua Zhang ◽  
Xiaodong Yang ◽  
Wei Zhang
Keyword(s):  
Differential Equations ◽  
Nonlinear Dynamic ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Chaotic Motions ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate

Dynamics of a cantilever honeycomb sandwich plate are studied in this paper. The governing equations of the composite plate subjected to both in-plane and transverse excitations are derived by using Hamilton’s principle and Reddy’s third-order shear deformation theory. Based on the Rayleigh–Ritz method, some modes of natural frequencies for the cantilever honeycomb sandwich plate are obtained. The relations between the natural frequencies and the parameters of the plate are investigated. Further, the Galerkin method is used to transform the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Nonlinear dynamic responses of the cantilever honeycomb sandwich plate to such external and parametric excitations are discussed by using the numerical method. The results show that in-plane and transverse excitations have an important influence on nonlinear dynamic characteristics. Rich dynamics, such as periodic, multiperiodic, quasiperiodic, and chaotic motions, are located and studied by the bifurcation diagram for some specific parameters.

Sign in / Sign up

Export Citation Format

Share Document