A Computational Optimal Control Approach to the Design of a Flexible Rotating Beam With Active Constrained Layer Damping

Aerospace ◽  
2004 ◽  
Author(s):  
Y. C. E. Lee ◽  
E. H. K. Fung ◽  
J. Q. Zou ◽  
H. W. J. Lee
Keyword(s):  
Optimal Control ◽  
Coordinate System ◽  
Control Voltage ◽  
Constrained Layer Damping ◽  
Shape Functions ◽  
Control Parametrization ◽  
Highly Nonlinear ◽  
Active Constrained Layer Damping ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer

In this paper, a computational approach is adopted to solve the optimal control and optimal parameter selection problems of a rotating flexible beam fully covered with active constrained layer damping (ACLD) treatment. The beam rotates in a vertical plane under the gravitational effect with variable angular velocity and carries an end mass. Tangent coordinate system and the moving coordinate system are used in the system modeling. Due to the highly nonlinear and coupled characteristics of the system, a relative description method is used to represent the motion of the beam and the motion equations are set up by using relative motion variables. Finite element shape functions of a cantilever beam [1] are used as the displacement shape functions in this study. Lagrangian formulation and Raleigh-Ritz approach [2] are employed to derive the governing equations of motion of the nonlinear time-varying system. The problem is posed as a continuous-time optimal control problem. The control function parameters are the control gains. The two system parameters are the thickness of the constraining layer and the viscoelastic material layer. The software package MISER3.2, which is based on the Control Parametrization and the Control Parametrization Enhancing Transform (CPET) techniques is used to solve the combined problems. The optimal solution takes the end deflection, control voltage and the total weight into account. Results show that substantial improvements are obtained with ACLD as compared to the passive constrained layer damping (PCLD) treatment.

scholarly journals Performance Characteristics of Active Constrained Layer Damping

1995 ◽  
Vol 2 (1) ◽  
pp. 33-42 ◽  
Author(s):  
A. Baz ◽  
J. Ro
Keyword(s):  
Broad Band ◽  
Structural Response ◽  
Piezoelectric Sensor ◽  
Performance Characteristics ◽  
Constrained Layer Damping ◽  
New Class ◽  
Damping Characteristics ◽  
Active Constrained Layer Damping ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer

Theoretical and experimental performance characteristics of the new class of actively controlled constrained layer damping (ACLD) are presented. The ACLD consists of a viscoelastic damping layer sandwiched between two layers of piezoelectric sensor and actuator. The composite ACLD when bonded to a vibrating structure acts as a “smart” treatment whose shear deformation can be controlled and tuned to the structural response in order to enhance the energy dissipation mechanism and improve the vibration damping characteristics. Particular emphasis is placed on studying the performance of ACLD treatments that are provided with sensing layers of different spatial distributions. The effect of the modal weighting characteristics of these sensing layers on the broad band attenuation of the vibration of beams fully treated with the ACLD is presented theoretically and experimentally. The effect of varying the gains of a proportional and derivative controller and the operating temperature on the ACLD performance is determined for uniform and linearly varying sensors. Comparisons with the performance of conventional passive constrained layer damping are presented also. The results obtained emphasize the importance of modally shaping the sensor and demonstrate the excellent capabilities of the ACLD.

Optimum Design and Control of Active Constrained Layer Damping

1995 ◽  
Vol 117 (B) ◽  
pp. 135-144 ◽  
Author(s):  
A. Baz ◽  
J. Ro
Keyword(s):  
Rational Design ◽  
Broad Band ◽  
Design Parameters ◽  
Constrained Layer Damping ◽  
Wide Range ◽  
Active Constrained Layer Damping ◽  
Operating Temperatures ◽  
And Control ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer

Conventional Passive Constrained Layer Damping (PCLD) treatments with viscoelastic cores are provided with built-in sensing and actuation capabilities to actively control and enhance their vibration damping characteristics. The design parameters and control gains of the resulting Active Constrained Layer Damping (ACLD) treatments are optimally selected, in this paper, for fully-treated beams using rational design procedures. The optimal thickness and shear modulus of the passive visco-elastic core are determined first to maximize the modal damping ratios and minimize the total weight of the damping treatment. The control gains of the ACLD are then selected using optimal control theory to minimize a weighted sum of the vibrational and control energies. The theoretical performance of beams treated with the optimally selected ACLD treatment is determined at different excitation frequencies and operating temperatures. Comparisons are made with the performance of beams treated with optimal PCLD treatments and untreated beams which are controlled only by conventional Active Controllers (AC). The results obtained emphasize the potential of the optimally designed ACLD as an effective means for providing broad-band attenuation capabilities over wide range or operating temperatures as compared to PCLD treatments.

Dynamic Analysis of a Flexible Manipulator With Passive Constrained Layer Damping

2003 ◽  
Author(s):  
J. Q. Zou ◽  
E. H. K. Fung ◽  
H. W. J. Lee
Keyword(s):  
Degrees Of Freedom ◽  
Ritz Method ◽  
Vertical Plane ◽  
Flexible Manipulator ◽  
Constrained Layer Damping ◽  
Shape Functions ◽  
Lagrange’S Equation ◽  
Highly Nonlinear ◽  
The Time Domain ◽  
Passive Constrained Layer Damping

This paper studies the vibration behavior of a flexible manipulator with passive constrained layer damping (PCLD) treatment. The manipulator rotates in a vertical plane and carries an end mass. Due to the highly nonlinear and coupled characteristics of the beam with PCLD treatment, “relative description” method is used to define the motions of the manipulator system. Using Lagrange’s equation and Rayleigh-Ritz method, the dynamic model of the manipulator is obtained and its vibration response is analyzed in the time domain. By assuming finite element shape functions as the displacement shape functions and using the complex damping model for the visco-elastic material (VEM) layer, the number of degrees of freedom of the system or the model dimension is greatly reduced. Numerical simulations show that the VEM not only reduces the amplitude of the elastic deflection but also quickly attenuates the vibration to zero. Also, it is confirmed that the geometry and physical properties of the PCLD treatment have significant effects on the dynamic response of the manipulator.

scholarly journals Vibration Control of an Aero Pipeline System with Active Constraint Layer Damping Treatment

2019 ◽  
Vol 9 (10) ◽  
pp. 2094 ◽  
Author(s):  
Jingyu Zhai ◽  
Jiwu Li ◽  
Daitong Wei ◽  
Peixin Gao ◽  
Yangyang Yan ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Vibration Control ◽  
Element Model ◽  
Control Voltage ◽  
Pipeline System ◽  
Constrained Layer Damping ◽  
Active Constraint ◽  
Active Constrained Layer Damping ◽  
Active Constrained Layer

In this paper, vibration control of an aero pipeline system using active constrained layer damping treatment has been investigated in terms of the vibration and stress distribution. A three-dimensional finite element model of such a pipeline with active constrained layer damping (ACLD) patches is developed. The transfer of the driving force under harmonic voltage is analyzed based on the finite element model. The vibration control of the pipeline with active constrained layer damping treatment under different voltages is computed to analyze the influence of control parameters and structural parameters on the control effect. An experiment platform is developed to validate the above relations. Results show that the performance of the active constrained layer damping treatment is affected by the elastic modulus and thickness of the viscoelastic layer, control voltage and structure size. The performance increases significantly with the rising of the control voltage and cover area of ACLD patches among these parameters.

Boundary Control of Beams Using Active Constrained Layer Damping

1997 ◽  
Vol 119 (2) ◽  
pp. 166-172 ◽  
Author(s):  
A. Baz
Keyword(s):  
Boundary Control ◽  
Distributed Parameter ◽  
Constrained Layer Damping ◽  
Damping Characteristics ◽  
Distributed Parameter Model ◽  
Active Constrained Layer Damping ◽  
Cantilevered Beams ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer ◽  
Globally Stable

A variational mathematical model is developed using Hamilton’s principle to describe the dynamics of beams fully-treated with Active Constrained Layer Damping (ACLD) treatments. The resulting distributed-parameter model is utilized in devising a globally stable boundary control strategy which is compatible with the operating nature of the ACLD treatments. The effectiveness of the ACLD in damping out the vibration of cantilevered beams is determined for different control gains and compared with the performance of conventional Passive Constrained Layer Damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.

Optimum Design and Control of Active Constrained Layer Damping

1995 ◽  
Vol 117 (B) ◽  
pp. 135-144 ◽  
Author(s):  
A. Baz ◽  
J. Ro
Keyword(s):  
Rational Design ◽  
Broad Band ◽  
Design Parameters ◽  
Constrained Layer Damping ◽  
Wide Range ◽  
Active Constrained Layer Damping ◽  
Operating Temperatures ◽  
And Control ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer

Conventional Passive Constrained Layer Damping (PCLD) treatments with viscoelastic cores are provided with built-in sensing and actuation capabilities to actively control and enhance their vibration damping characteristics. The design parameters and control gains of the resulting Active Constrained Layer Damping (ACLD) treatments are optimally selected, in this paper, for fully-treated beams using rational design procedures. The optimal thickness and shear modulus of the passive visco-elastic core are determined first to maximize the modal damping ratios and minimize the total weight of the damping treatment. The control gains of the ACLD are then selected using optimal control theory to minimize a weighted sum of the vibrational and control energies. The theoretical performance of beams treated with the optimally selected ACLD treatment is determined at different excitation frequencies and operating temperatures. Comparisons are made with the performance of beams treated with optimal PCLD treatments and untreated beams which are controlled only by conventional Active Controllers (AC). The results obtained emphasize the potential of the optimally designed ACLD as an effective means for providing broad-band attenuation capabilities over wide range or operating temperatures as compared to PCLD treatments.

Active Control of Vibration and Noise Radiation from Fluid-Loaded Cylinder using Active Constrained Layer Damping

2002 ◽  
Vol 8 (6) ◽  
pp. 877-902 ◽  
Author(s):  
W. Laplante ◽  
T. Chen ◽  
A. Baz ◽  
W. Sheilds
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Acoustic Radiation ◽  
Sound Radiation ◽  
Element Model ◽  
Water Tank ◽  
Constrained Layer Damping ◽  
Active Constrained Layer Damping ◽  
Active Constrained Layer ◽  
Surrounding Fluid

Vibration and sound radiation from fluid-loaded cylindrical shells are controlled using patches of Active Constrained Layer Damping (ACLD). The performance and the enhanced damping characteristics via reduced vibrations and sound radiation in the surrounding fluid is demonstrated both theoretically and experimentally. A prime motivation for this work is the potential wide applications in submarines and torpedoes where acoustic stealth is critical to the effectiveness of missions. A finite element model is also developed to predict the vibration and the acoustic radiation in the surrounding fluid of the ACLD-treated cylinders. The developed model is used to study the effectiveness of the control and placement strategies of the ACLD in controlling the fluid-structure interactions. A water tank is constructed that incorporates test cylinders treated with two ACLD patches placed for targeting specific vibration modes. Using this arrangement, the effectiveness of different control strategies is studied when the submerged cylinders are subjected to internal excitation, and the radiated sound pressure level in the water is observed. Comparisons are made between the experimental results and the theoretical predictions to validate the finite element model.

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