scholarly journals Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. Sanbi ◽  
R. Saadani ◽  
K. Sbai ◽  
M. Rahmoune
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
High Performance ◽  
Structural Systems ◽  
Control Procedure ◽  
Finite Element Approximations ◽  
Active Structures ◽  
Piezoelectric Beam ◽  
Control Electronics ◽  
And Control

Smart structures with integrated sensors, actuators, and control electronics are of importance to the next generation high-performance structural systems. In this study, thermopiezoelastic characteristics of piezoelectric beam continua are studied and applications of the theory to active structures in sensing and optimal control are discussed. Using linear thermopiezoelastic theory and Timoshenko assumptions, a generic thermopiezoelastic theory for piezolaminated composite beam is derived. Finite element equations for the thermopiezoelastic media are obtained by using the linear constitutive equations in Hamilton's principle together with the finite element approximations. The structure consists of a modeling of cantilevered piezolaminated Timoshenko beam with integrated thermopiezoelectric elements between two aluminium layers. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG accompanied by the Kalman filter is applied. The effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. We show that the control procedure cannot be perturbed by applying a thermal gradient and the control can be applied at any time during the period of vibration of the beam.

scholarly journals Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
M. Sanbi ◽  
R. Saadani ◽  
K. Sbai ◽  
M. Rahmoune
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Thermal Effects ◽  
Thermal Gradient ◽  
Active Vibration Control ◽  
Control Procedure ◽  
Finite Element Approximations ◽  
Plate Vibrations ◽  
Active Vibration ◽  
And Control

Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton’s principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG-Kalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.

A Piezothermoelastic Thin Shell Theory Applied to Active Structures

1994 ◽  
Vol 116 (3) ◽  
pp. 295-302 ◽  
Author(s):  
H. S. Tzou ◽  
R. V. Howard
Keyword(s):  
High Performance ◽  
Shell Theory ◽  
Piezoelectric Materials ◽  
Electromechanical Properties ◽  
Mechanical Loads ◽  
Active Structures ◽  
Control Electronics ◽  
Principal Directions ◽  
And Control ◽  
Thin Shell Theory

“Smart” structures with integrated sensors, actuators, and control electronics are of importance to the next-generation high-performance structural systems. Piezoelectric materials possess unique electromechanical properties, the direct and converse effects, which, respectively, can be used in sensor and actuator applications. In this study, piezothermoelastic characteristics of piezoelectric shell continua are studied and applications of the theory to active structures in sensing and control are discussed. A generic piezothermoelastic shell theory for thin piezoelectric shells is derived, using the linear piezoelectric theory and Kirchhoff-Love assumptions. It shows that the piezothermoelastic equations, in three principal directions, include thermal induced loads, as well as conventional electric and mechanical loads. The electric membrane forces and moments induced by the converse effect can be used to control the thermal and mechanical loads. A simplification procedure, based on the Lame´ parameters and radii of curvatures, is proposed and applications of the theory to (1) a piezoelectric cylindrical shell, (2) a piezoelectric ring, and (3) a piezoelectric beam are demonstrated.

A morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints

2018 ◽  
Vol 24 (3) ◽  
pp. 1181-1206 ◽  
Author(s):  
Susanne C. Brenner ◽  
Thirupathi Gudi ◽  
Kamana Porwal ◽  
Li-yeng Sung
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Constraints ◽  
Distributed Optimal Control ◽  
And Control ◽  
State And Control Constraints ◽  
Element Method

We design and analyze a Morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints on convex polygonal domains. It is based on the formulation of the optimal control problem as a fourth order variational inequality. Numerical results that illustrate the performance of the method are also presented.

Sign in / Sign up

Export Citation Format

Share Document