MODELING OF PIEZOELECTRIC SMART STRUCTURES FOR ACTIVE VIBRATION AND NOISE CONTROL APPLICATIONS

Open Access
Author:
Gopinathan, Senthil Visagan
Graduate Program:
Engineering Science and Mechanics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 14, 2001
Committee Members:
  • Eduard Ventsel, Committee Member
  • Stephen A Hambric, Committee Member
  • Vasundara Varadan, Committee Chair
  • Sabih I Hayek, Committee Member
  • Vijay Krishna Varadan, Committee Chair
Keywords:
  • Smart Structres
  • Active vibration and noise control
  • BE/FE method
  • Fluid-structure interaction
Abstract:
Active vibration control and active structural acoustic control using piezoelectric sensors and actuators have recently emerged as a practical and promising technology. Efficient and accurate modeling of these structures bonded to or embedded with actuators and sensors is needed for efficient design of smart structures. This dissertation addresses the modeling of these structures and the associated control system design technique. Modeling of structures with both laminated and discrete type of actuators and sensors are addressed. For piezoelectric laminates the governing equations of motion are derived using First Order Shear Deformation Theory (FSDT) and for the first time the dynamic response fields inside the laminate are obtained and compared with full elasticity solutions. This comparison brought out the effect of assumptions made with respect to the electric and mechanical fields using FSDT and Classical Laminate Theory (CLT) in previous work. It is expected that this analysis and the interior field estimations would help designers to understand the shortcomings of FSDT in modeling piezoelectric laminates, and help them to adopt this theory properly for use in FE or other numerical models. For surface bonded discrete patch type actuators/sensors, the governing dynamic equation of motion for a plate is derived. The solution to this equation is obtained using a Fourier series method and the effect of passive stiffness and mass on the natural frequency is studied. The studies showed that ignoring the mass and the passive stiffness of actuators/sensors leads to large errors in estimating the vibration characteristics of the smart plate. A Rayleigh-Ritz (RR) approach is then presented for studying the active vibration and transmitted noise control of a smart plate with discrete piezoelectric patches. Classical laminated plate theory is used to model the composite plate and electro elastic theory is used model the piezoelectric patches. The dynamic equations of motion for the coupled smart panel-cavity system are derived using Hamilton’s principle. Close agreement between the present approach and the finite element and experimental results confirmed the validity of the approach. The RR approach is thus presented as a simple, computationally inexpensive approach when compared to the finite element method. The RR method also proved to be powerful method for modeling the adjacent acoustic medium and for the associated control system design. A finite element approach for the integrated design of a structure and its control system for suppressing vibration and the radiated noise are presented. A finite element model for a smart plate with surface bonded piezoelectric patches is developed using shell, brick and transition elements. The free and forced vibration characteristics of the plate are studied with and without closed loop feedback control. An optimal (multi-input multi-output) MIMO controller design for the vibration suppression of a clamped plate using the FE model is proposed. Numerical simulation showed that an optimal controller designed for controlling the smart plate vibration also reduces the transmitted noise to 20 dB for the first mode and to 40 dB for the second mode of plate. The RR approach accurately models rigid walled acoustic cavities, but flexible elastic boundaries or sound absorbing walls cannot be modeled using this approach. To model such acoustic domains, a novel hybrid Rayleigh-Ritz/Boundary Element solution method is proposed. This method would enable designers to model the panel with piezoelectric actuators and sensors and the adjacent acoustic medium with the presence of passive absorbers at the 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 conditions.