Reduction of Noise Inside a Cavity by Piezoelectric Actuators

1999 ◽  
Author(s):  
Ichiro Hagiwara ◽  
Zhushi Rao ◽  
Qinzhong Shi
Keyword(s):  
Equations Of Motion ◽  
Piezoelectric Actuators ◽  
Control Case ◽  
Control Laws ◽  
Modal Coupling ◽  
Point Forces ◽  
Modal Amplitude ◽  
Flexible Panels ◽  
Global And Local ◽  
Rigid Walls

Abstract A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. The cavity is modeled with four rigid walls and two flexible panels, panel on the top is excited by disturbing point forces and thus radiating structure borne noise into the cavity, and the other panel which is on the bottom is bonded with actuators to control the noise inside the cavity. Modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating ‘global’ and ‘local’ optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. Numerical investigations into the effect of number of actuators, error sensors as well as disturbing point forces on SPL’s are presented. Based on the studies, it is found that the number of actuators has a significant influence on SPL’s for local control case, while for global control case, this influence is quite limited. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.

Reduction of Noise Inside a Cavity by Piezoelectric Actuators

2003 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
I. Hagiwara ◽  
D. W. Wang ◽  
Q. Z. Shi ◽  
R. S. Rao
Keyword(s):  
Sound Pressure ◽  
Control Mechanism ◽  
Equations Of Motion ◽  
Piezoelectric Actuators ◽  
Governing Equations ◽  
Control Laws ◽  
Modal Coupling ◽  
Modal Amplitude ◽  
Global And Local ◽  
Fully Coupled

A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. A modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating “global” and “local” optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.

Optimal Control of Nonlinear Parametrically Excited Beam Vibrations by Spatially Distributed Sensors and Actors

1997 ◽  
Author(s):  
Andreas Kugi ◽  
Kurt Schlacher ◽  
Hans Irschik
Keyword(s):  
Axial Strain ◽  
Equations Of Motion ◽  
Nonlinear Formulation ◽  
Control Laws ◽  
Distributed Sensors ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Piezoelectric Layers ◽  
Spatially Distributed ◽  
Support Motion

Abstract This contribution is focused on a straight composite beam with multiple piezoelectric layers under the action of an axial support motion. In the sense of v. Karman a nonlinear formulation for the axial strain is used and the equations of motion are derived by means of the Hamilton formalism. This system turns out to be a special class of infinite dimensional systems, the so called Hamilton AI-systems with external inputs. In order to suppress the excited vibrations two infinite control laws are proposed. The first one is an infinite PD-feedback law and the second one is based on the nonlinear H∞-design, where an exact solution of the corresponding Hamilton Jacobi Isaacs equation is presented. The necessary quantities for the control laws can be measured by appropriate space-wise shaped sensors and the asymptotic stability of the equilibrium point can be proved.

scholarly journals Control of Bending-Bending Coupled Vibrations of a Rotating Thin-Walled Composite Beam

2015 ◽  
Vol 39 (4) ◽  
pp. 605-613 ◽  
Author(s):  
Jarosław Latalski ◽  
Marcin Bocheński ◽  
Jerzy Warmiński
Keyword(s):  
Composite Beam ◽  
Dynamic Properties ◽  
Control Strategies ◽  
Fiber Composite ◽  
Bending Moment ◽  
Piezoelectric Actuators ◽  
Transversely Isotropic ◽  
Cross Sectional ◽  
Modal Coupling ◽  
The Impact

Abstract The paper presents a study of a possible application of structure embedded piezoelectric actuators to enhance the performance of a rotating composite beam exhibiting the coupled flexural-flexural vibrations. The discussed transversal and lateral bending modal coupling results from the directional properties of the beam's laminate and ply stacking distribution. The mathematical model of the beam is based on an assumption of cross-sectional non-deformability and it incorporates a number of non-classical effects. The final 1-D governing equations of an active composite beam include both orthotropic properties of the laminate and transversely isotropic properties of piezoelectric layers. The system's control capabilities resulting from embedded Macro Fiber Composite piezoelectric actuators are represented by the boundary bending moment. To enhance the dynamic properties of the composite specimen under consideration a combination of linear proportional control strategies has been used. Comparison studies have been performed, including the impact on modal coupling magnitude and cross-over frequency shift.

Modeling and Parameter Identification of an In-Tank Swimming Robot Performing Floor Inspection

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Imen Hbiri ◽  
Houssem Karkri ◽  
Fathi H. Ghorbel ◽  
Slim Choura
Keyword(s):  
Dynamic Model ◽  
Drag Force ◽  
Equations Of Motion ◽  
Experimental Tests ◽  
Force Model ◽  
Friction Drag ◽  
Control Laws ◽  
Low Speed ◽  
Advanced Control ◽  
Computational Fluid Dynamics Cfd

In this paper, we develop the equations of motion at low-speed of a swimming robot for tank floor inspection. The proposed dynamic model incorporates a new friction drag force model for low-speed streamlined swimming robots. Based on a boundary layer theory analysis, we prove that for low-speed maneuvering case (Re from 103 to 105), the friction drag force component is nonlinear and is not insignificant, as previously considered. The proposed drag viscous model is derived based on hydrodynamic laws, validated via computational fluid dynamics (CFD) simulations, and then experimental tests. The model hydrodynamic coefficients are estimated through CFD tools. The robot wheels friction LuGre model is experimentally identified. Extensive experimental tests were conducted on the swimming robot in a circular water pool to validate the complete dynamic model. The dynamic model developed in this paper may be useful to design model-based advanced control laws required for accurate maneuverability of floor inspection swimming robots.

Active Vibration Control for the Closed Loop Flexible Mechanisms Combined the Feedback and Feed-Forward Strategy: Part 2 — Control Design and Simulation

2000 ◽  
Author(s):  
Zhang Xianmin ◽  
Chao Changjian
Keyword(s):  
Equations Of Motion ◽  
Active Vibration Control ◽  
Elastic Vibration ◽  
Linkage Mechanism ◽  
Control Laws ◽  
Feed Forward ◽  
Feed Forward Control ◽  
Active Vibration ◽  
Four Bar Linkage ◽  
Flexible Mechanisms

Abstract On the basis of the complex mode theory and the equations of motion of the flexible mechanisms developed in part 1, a hybrid independent modal controller is presented, which is composed of state feedback and disturbance feed-forward control laws. As an illustrative example, the strategy is used to control the elastic vibration response of a four-bar linkage mechanism. The imitative computational result shows that the vibration is efficiently suppressed.

Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk System With the Eddy-Current Damper

2002 ◽  
Vol 124 (4) ◽  
pp. 519-526 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jung-Hung Sun ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Bilinear System ◽  
Optimal Feedback Control ◽  
Disk System ◽  
Control Laws ◽  
Assumed Mode Method ◽  
Eddy Current Damper ◽  
Flexible Disk

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by applying the assumed-mode method into the kinetic and strain energies, and the virtual work done by the eddy-current damper. From Lagrange’s equations, the resulting discretized equations of motion can be simplified as a bilinear system (BLS). Introducing the control laws, including the quadratic, nonlinear and optimal feedback control laws, into the BLS, it is found that the eddy-current damper can be used to suppress flexible and shear vibrations simultaneously, and the system is globally asymptotically stable. Numerical results are provided to validate the theoretical analysis.

Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections

2017 ◽  
Author(s):  
Kevin McHugh ◽  
Earl Dowell
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Large Deflections ◽  
Constraint Force ◽  
Nonlinear Responses ◽  
Nonlinear Motion ◽  
Resonant Modes ◽  
Cantilevered Beam ◽  
Point Forces ◽  
Free Beam

A theoretical and computational model has been developed for the nonlinear motion of an inextensible beam undergoing large deflections for cantilevered and free-free boundary conditions. The inextensibility condition was enforced through a Lagrange multiplier which acted as a constraint force. The Rayleigh-Ritz method was used by expanding the deflections and the constraint force in modal series. Lagrange’s Equations were used to derive the equations of motion of the system, and a 4th order Runge-Kutta solver was used to solve them. Comparisons for the cantilevered beam were drawn to experimental and computational results previously published and show good agreement for responses to both static and dynamic point forces. Some physical insights into the cantilevered beam response at the 1st and 2nd resonant modes were obtained. The free-free beam condition was investigated at the 1st and 3rd resonant modes and the nonlinearity (primarily inertia) was shown to shift the resonant frequency significantly from the linear natural frequency and lead to hysteresis in both modes.

Transient Vibration of Gyroscopic Systems With Unsteady Superposed Motion

1995 ◽  
Author(s):  
J. A. Wickert
Keyword(s):  
Equations Of Motion ◽  
Mathematical Structure ◽  
Time Dependent ◽  
Distributed Parameter ◽  
Rotating Shaft ◽  
Transient Vibration ◽  
Modal Amplitude ◽  
Technical Interest ◽  
Gyroscopic Systems ◽  
Two Degree Of Freedom

Abstract The equations of motion for a gyroscopic system with unsteady superposed motion are derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non-inertial frame. The resulting coefficient matrices are time-dependent, and skew-symmetric acceleration terms are present both as Coriolis acceleration and as a component of net stiffness. Such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems, including flexible media that translate with time-dependent speed. Following the asymptotic approach of Krylov, Bogoliubov and Mitropolsky, a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the natural periods of oscillation. First-order approximations for the modal amplitude and phase are obtained in closed form. The method is illustrated through two examples of technical interest: a two degree-of-freedom model of a rotating shaft, and a distributed parameter model of a moving tape.

Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

2012 ◽  
Vol 28 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A. A. Khdeir ◽  
E. Darraj ◽  
O. J. Aldraihem
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
Beam Model ◽  
Laminated Beams ◽  
State Space Approach ◽  
Laminated Beam ◽  
Beam Surface

ABSTRACTAnalytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Continuum of Motion Equations and Control Laws for the Inverted Pendulum Cart and Rotary Pendulum

2020 ◽  
Author(s):  
Constance Lare ◽  
Warren N. White
Keyword(s):  
Inverted Pendulum ◽  
Equations Of Motion ◽  
Control Law ◽  
Control Laws ◽  
Motion Equations ◽  
Base Radius ◽  
Limiting Condition ◽  
And Control ◽  
The Given ◽  
Insight Into

Abstract This paper questions whether the controller properties for a given rigid body mechanical system still apply as the given system is changed. As a first attempt in this investigation, the controller for the underactuated rotary pendulum is investigated as the system morphs into an underactuated inverted pendulum cart. As the limiting condition of the inverted pendulum cart is approached, the investigation allows the controller to also morph. The authors show that, as the pendulum base radius grows, the rotary pendulum equations of motion morph into the inverted pendulum cart dynamics. The paper presents necessary conditions for the successful morphing of the dynamic equations. The morphing process for the controller tests the idea whether the control law also satisfies the same continuum basis as the motion equations. The paper presents a framework for the class of controllers investigated for providing insight into when the controller morphing may be successful. This paper presents dimensionless quantities that render the equations of motion and controller for the inverted pendulum cart and rotary pendulum into dimensionless form. These dimensionless quantities allow comparison of controllers and systems that are not possible through simple inspection. This comparison ability is especially useful for quantifying the nonlinearities of a given system and controller compared to another system and controller having different parameter sizes, a comparison rarely seen in the control literature.

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