scholarly journals Finite Element Model of Vibration Control for an Exponential Functionally Graded Timoshenko Beam with Distributed Piezoelectric Sensor/Actuator

Actuators ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 19 ◽  
Author(s):  
Khalid El Harti ◽  
Mohammed Rahmoune ◽  
Mustapha Sanbi ◽  
Rachid Saadani ◽  
Mouhcine Bentaleb ◽  
...  
Keyword(s):  
Finite Element ◽  
Active Control ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Piezoelectric Sensor ◽  
Functionally Graded ◽  
Flexible Beam ◽  
Linear Quadratic ◽  
Sensors And Actuators ◽  
Functionally Graded Beam

This paper presents a dynamic study of sandwich functionally graded beam with piezoelectric layers that are used as sensors and actuators. This study is exploited later in the formulation of the active control laws, while using the optimal control Linear Quadratic Gaussian (LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenko’s assumptions and the finite element method, which is applied to a flexible beam divided into a finite number of elements. By applying the Hamilton principle, the equations of motion are obtained. The vibration frequencies are found by solving the eigenvalue problem. The structure is analytically then numerically modeled and the results of the simulations are presented in order to visualize the states of their dynamics without and with active control.

scholarly journals Vibrations piezo-control of FGM beam in a thermal environment

2019 ◽  
Vol 286 ◽  
pp. 01001
Author(s):  
K. El Harti ◽  
MED. Rahmoune ◽  
M. Sanbi ◽  
R. Saadani ◽  
M. Bentaleb ◽  
...  
Keyword(s):  
Thermal Environment ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Functionally Graded ◽  
Flexible Beam ◽  
Sensors And Actuators ◽  
Functionally Graded Beam ◽  
Piezoelectric Sensors And Actuators ◽  
Active Vibration ◽  
Fgm Beam

An analytical method on the active vibration control of a functionally graded beam equipped with layers of piezoelectric sensors and actuators, in a thermal environment, is studied. The study based on Euler-Bernoulli theory and finite element method, applied to a flexible beam divided into a finite number of elements. The equations of motion are obtained by applying the principle of Hamilton. The structure is modeled analytically then numerically and the results of the simulations are presented to visualize the states of their dynamics.

Active Vibration Attenuation of Smart Shell Structure Instrumented With Piezoelectric Layers

2018 ◽  
pp. 22-49 ◽  
Author(s):  
Anshul Sharma
Keyword(s):  
Finite Element ◽  
Fuzzy Logic ◽  
Spherical Shell ◽  
Active Control ◽  
Degrees Of Freedom ◽  
Fuzzy Logic Controller ◽  
Equations Of Motion ◽  
Piezoelectric Sensor ◽  
Smart Structure ◽  
Fuzzy Logic Approach

The active control of vibration of piezoelectric flexible smart structure is an important issue in engineering. Reducing vibration may improve the user's comfort and safety. This chapter presents a fuzzy logic approach for active control of vibration of a smart composite laminated spherical shell. The spherical shell is in the form of a layered composite shell having collocated piezoelectric sensor/actuator pair. The vibratory response of the shell is modeled using finite element method. There are five mechanical degrees of freedom per node and the potential difference across the piezoelectric layer is introduced as an additional electrical degree of freedom on an element level. The mode superposition method has been used to transform the coupled finite element equations of motion in the physical coordinates into a set of reduced uncoupled equations in the modal coordinates. The simulation results illustrate that the superiority of designed nonconventional fuzzy logic controller over conventional controllers.

Performance Characteristics of a Smart Flexible Beam With Distributed ACLD Elements

2002 ◽  
Author(s):  
L. C. Hau ◽  
Eric H. K. Fung
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Element Model ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Optimal Output ◽  
Modes Of Vibration ◽  
Original Size

The finite element method, in conjunction with the Golla-Hughes-McTavish (GHM) viscoelastic model, is employed to model a clamped-free beam partially treated with active constrained layer damping (ACLD) elements. The governing equations of motion are converted to a state-space form for control system design. Prior to this, since the resultant finite element model has too many degrees of freedom due to the addition of dissipative coordinates, a model reduction is performed to revert the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different element configurations, with various spacing and locations, on the vibration control performance of a “smart” flexible ACLD treated beam. Results are presented for the damping ratios of the first two modes of vibration. It is found that improvement on the second mode damping can be achieved by splitting a single ACLD element into two and placing them at appropriate positions of the beam.

Analytical Investigation on Elastodynamic Vibration Suppression of a Flexible Four-Bar Mechanism System Featuring a Smart Coupler Link and Multivariable Optimal Regulator

1997 ◽  
Author(s):  
Muhammad Sannah ◽  
Ahmad Smaili
Keyword(s):  
Active Control ◽  
Smart Materials ◽  
Vibration Suppression ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Piezoelectric Sensor ◽  
Analytical Investigation ◽  
Vibration Modes ◽  
Linear Quadratic ◽  
Luenberger Observer

Abstract This paper presents an analytical investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and multivariable optimal control. The 4R mechanism consists of a flexible coupler link, relatively flexible follower link, and a relatively rigid crank. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. As the mechanism changes configuration, its modal characteristics are recalculated, and the controller is redesigned. The dynamic model used for the controller design includes the second and fourth vibration modes of the mechanism system. These modes are predominated by the first two bending modes of the mechanism’s coupler link. The results showed that while the proposed active control strategy is successful in reducing the amplitudes of vibrations about the quasistatic response, it has no effect on the quasistatic deflections due to steady state loading.

Active Control of Elastodynamic Vibrations of a Four-Bar Mechanism System With a Smart Coupler Link Using Optimal Multivariable Control: Experimental Implementation

1996 ◽  
Author(s):  
Muhammad Sannah ◽  
Ahmad Smaili
Keyword(s):  
Experimental Investigation ◽  
Active Control ◽  
Smart Materials ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Piezoelectric Sensor ◽  
High Mode ◽  
Multivariable Control ◽  
Linear Quadratic ◽  
Luenberger Observer

Abstract This paper presents an experimental investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and muitivariable optimal control. The experimental (4R) mechanism is made such that its coupler link is flexible, its follower link is slightly less flexible and its crank is relatively rigid. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at the high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. The results of the experimental investigation prove that in order to prevent high mode excitations, the controller design should be based on the modes representing vibrations of all components comprising the mechanism system rather than the modes corresponding to the link to which the S/A pairs are bonded. Response amplitude attenuation ratios up to 50 percent are achieved and high mode excitations are prevented.

Active Control of a Plate Using Segmented Distributed Sensors and Actuators: Finite Element Development and Analysis

1991 ◽  
Author(s):  
H. S. Tzou ◽  
H. Bahrami
Keyword(s):  
Finite Element ◽  
Active Control ◽  
Variational Equation ◽  
Flexible Structures ◽  
Monitoring And Control ◽  
Sensors And Actuators ◽  
Distributed Sensors ◽  
Computation Efficiency ◽  
Piezoelectric Structure ◽  
And Control

Abstract Distributed sensing and control of flexible structures have drawn much attention in recent years. Piezoelectric elements can be used with an elastic structure as sensors and actuators for structural monitoring and control applications. This paper presents a development of a thin piezoelectric finite element applied to active control of flexible structures. A piezoelectric finite element is derived using the variational equation and Hamilton’s principle. System equations of a piezoelectric structure are formulated accordingly. Guyan’s reduction technique is incorporated to improve the computation efficiency. Feedback control algorithms are also derived and implemented in the finite element code. Applications of the technique to a plate with segmented distributed sensora/actuators are studied and effectiveness evaluated.

A Comparison of Finite Element Beam Formulations for Thermoelastic Behavior of Functionally Graded Structures

Aerospace ◽  
2005 ◽  
Author(s):  
Thomas G. Eason ◽  
Simo´n A. Caraballo
Keyword(s):  
Finite Element ◽  
Shear Deformation Theory ◽  
Axial Direction ◽  
Beam Element ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Shell Elements ◽  
Static Condensation ◽  
Graded Structures ◽  
Structural Scale

Modeling at the structural scale most often requires the use of beam and shell elements. This paper compares two finite element formulations based on first-order shear deformation theory undergoing thermo-mechanical loading. One formulation is a two node beam element employing static condensation based on the work of Chakraborty et al. The second formulation follows a more traditional route using FSOD theory for a three node beam element. Both formulations are used to investigate the behavior of a functionally graded beam under axial and through-the-thickness temperature gradients. Both formulations work well for a constant uniform mechanical or temperature loading. However, for beam structures containing a thermal gradient in the axial direction, the two node beam element performs poorly as compared to the three node element in terms of transverse shearing stress calculated from the equilibrium equation.

Active Control of Elastodynamic Vibrations of a Four-Bar Mechanism System With a Smart Coupler Link Using Optimal Multivariable Control: Experimental Implementation

1998 ◽  
Vol 120 (2) ◽  
pp. 316-326 ◽  
Author(s):  
M. Sannah ◽  
A. Smaili
Keyword(s):  
Experimental Investigation ◽  
Active Control ◽  
Smart Materials ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Piezoelectric Sensor ◽  
High Mode ◽  
Multivariable Control ◽  
Linear Quadratic ◽  
Luenberger Observer

This paper presents an experimental investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and multivariable optimal control. The experimental 4R mechanism is made such that its coupler link is flexible, its follower link is slightly less flexible and its crank is relatively rigid. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at the high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. The results of the experimental investigation prove that in order to prevent high mode excitations, the controller design should be based on the modes representing vibrations of all components comprising the mechanism system rather than the modes corresponding to the link to which the S/A pairs are bonded. Response amplitude attenuation ratios up to 50 percent are achieved and high mode excitations are prevented.

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