In this paper, a novel hybrid Rayleigh-Ritz/Boundary Element (RR/BE) solution method is proposed to model acoustic domains with flexible walls with piezoelectric patches. The RR approach is a simple, computationally inexpensive approach when compared to the finite element method for flexible walls with surface mounted piezoelectric patches. The RR method is then combined with the boundary element model of the interior acoustic domain and the coupled fluid-structure model is used for designing an active noise control system. This model also allows a designer to incorporate a passive absorber at the fluid-structure interface. The predicted sound pressure attenuation for three different thicknesses of passive absorber in the frequency range of 200 to 1200 Hz is calculated and an optimal thickness value of for the absorber for the smart panel is calculated. The attenuation in sound pressure levels due to an active control system in the presence of passive absorber is also computed. The system matrices resulting from this method are very smaller in size when compared to the FE models, which makes this approach most suitable for optimization studies. This new approach can be further extended to model the more complicated acoustic enclosures with complex interface.
KEYWORDS: Sensors, Acoustics, Actuators, Systems modeling, Motion models, Composites, Electrodes, Control systems, Control systems design, Finite element methods
This numerical study presents a detailed optimal control design based on the Rayleigh-Ritz approach for the smart plate-cavity system. Linear quadratic (LQ) theory with output feedback is considered on the basis of the state space model of the system. A vibroacoustic model, which includes a rectangular shaped cavity, enclosed with a five rigid walls and a flexible smart plate with discrete piezoelectric sensor/actuator pairs bonded to its surface. Classical laminated plate theory is used to model the composite plate and electroelastic theory is used model the discrete piezoelectric patches. Eigenfunctions of a clamped-clamped beam are used as the Ritz functions for the panel and the rigid walled cavity modes are used the model the acoustic cavity. The dynamic equations of motion for the coupled smart panel-cavity system are derived using Hamilton's principle. The forcing term due to the cavity acoustic pressure is determined by using virtual work considerations. For the present study, five collocated pairs of sensor/actuator pairs are attached to the plate at a predetermined placement scheme. The performance index considered for the design of the optimal controller includes both the displacement of the panel and the pressure inside the cavity. Numerical simulation is used to predict the reduction in the sound pressure level inside an enclosure radiated from this optimally controlled plate. The Rayleigh-Ritz approach is found to be faster and a more efficient method for designing control system for simple plate-cavity systems when compared to other numerical methods such as the finite element method.
KEYWORDS: Sensors, Actuators, Performance modeling, Smart structures, Finite element methods, Control systems, Matrices, Interference (communication), RGB color model, Feedback control
Smart structures incorporate sensors, actuators and control electronics that permit the structures to tailor their response to changes in the environment in an optimal fashion. The sensors and actuators are constructed from functional materials such as piezoelectric, electrostrictive, shape memory alloys and magnetostrictive materials and more recently using MEMS (Micro Electro Mechanical Systems) devices. All functional materials and devices therefrom involve coupled fields involving elastodynamic, viscoelastic, electric, magnetic and thermal fields. The materials are anisotropic and often nonlinear. Finite element modeling has been successfully used to model these complex structures. More recently, closed ioop numerical simulation of the tailored response of a smart structure has become possible by combining the finite element equations of the sensor response to applied dynamical and/or thermal loads to the input voltage or current to the actuators via a control algorithm. This hybrid approach permits us to simulate the response of the structure with feedback control. Simple feedback controllers have now been replaced by robust controllers that provide stability under a range of uncertainties and do not require a very accurate system model. The talk will present an overview of the approaches of various researchers and consider numerical applications and comparison with experiments for active vibration damping, noise control and shape modification.
Classical Plate Theory (CPT) has been applied successfully in the past to the plates with distributed piezoelectric patch bonded to the surface or embedded within the layers. In all earlier models the mass and stiffness' contributions from sensor and actuator patches were neglected for estimating the natural frequencies of the smart plate. Also the thickness direction electric fields and strain fields inside the patches are assumed to be constant over the entire area of the patch. The validity of these assumptions depends on the size and relative stiffnesses of the patches and is not investigated before. In this paper the CPT is used to estimate the natural frequencies of a plate structure with surface bonded piezoelectric patches without the above-mentioned assumptions. A detailed modeling of the patches is developed by expressing the electric potential inside the patch as a quadratic function of thickness coordinate. The equations of motion are derived for a generally isotropic plate with surface bonded segmented patches. Solution to the dynamic equation of motion are obtained using Fourier series method for a plate with collocated piezoelectric actuator/sensor patches. The effect of the passive and active stiffness' of the surface bonded actuator and sensor patches on the dynamic characteristics of host plate structure is investigated.
KEYWORDS: Acoustics, Sensors, Control systems, Actuators, Chemical elements, Feedback control, Control systems design, Interfaces, Foam, Systems modeling
This paper presents a finite element/boundary element (FE/BE) formulation for modeling and analysis of active-passive noise control system. Finite element method is proposed to model the smart plate with surface bonded piezoelectric patches and the enclosing walls and the dual reciprocity boundary element method is proposed for modeling the acoustic cavity. The use of FE/BE method facilitates us imposing the impedance boundary conditions at the fluid/passive absorber/structure interface. An output feedback optimal controller design procedure is given for the smart plate system with active patches for the low frequency regime.
KEYWORDS: Sensors, Actuators, Interfaces, 3D modeling, Composites, Electric field sensors, Ferroelectric materials, Vibration control, Chemical elements, Electrodes
The electrical and mechanical field distributions inside the layers of a piezolaminate beam are calculated when excited by a harmonic load or electric potential applied on the surface of the laminate. The Fourier series solution approach is used to solve the electroelasticity problem and the electrical and mechanical field distributions are estimated at frequencies away and close to the natural frequency of the laminate. Numerical results are computed for a single piezoelectric layer and a three layered piezoelectric laminate under cylindrical bending vibration. Our results indicate that the approximations made in many papers dealing with laminated piezoelectric beams are unjustified especially close to structural resonance frequencies at which control of vibration is most often desired.
In this paper the design of an optimal controller using discretely placed collocated sensor/actuator pairs to control the vibration of a plate structure is presented. Three- dimensional finite elements are used to model the smart structure containing discrete piezoelectric sensors and actuators by the use of a combination of solid, transition, and shell elements. Since several discrete piezoelectric patches are spatially distributed in the structure to effectively observe and control the vibration of a structure, the system model is thus utilized to design multi-input-multi- output (MIMO) controller. The output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from modal space model. An optimal controller design for the vibration suppression of a clamped plate is presented for the steady state excitation case. The reduction in the sound pressure level inside an enclosure radiated from this optimally controlled vibrating plate is also estimated.
Interior noise control in a cabin enclosure using active vibration control of the walls of the enclosure with discrete piezoelectric actuators and sensors is addressed. A hybrid approach using finite element formulation for the radiating walls of the enclosure. We use an exact 3D formulation without making the usual approximations for the electric field in the piezoelectric devices. The electrical boundary conditions and the charge on the electrodes are treated correctly. Computational time is optimized by using plate elements for the structure and 3D element for the devices with transition elements to connect them. A PD-controlled is used to relate the voltage output of the sensor in an open circuit conditions to the charge input to the actuator via appropriate gains to control vibrations. The acoustic part of the problem is modeled via a modal approach. The modal representation of the pressure is used as a mechanical force term on the structure which can be written in terms of a virtual mass. The driving team for the acoustic field is in turn the displacements on the surface of the radiating walls which is computed from the structural equations. This accounts for the acoustic field-structure interaction and the equations are solved simultaneously. By adjusting the feedback gain, significant noise reduction is achieved globally within the cavity for the dominant vibrational modes of the radiating panel.
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