Controlling Deformation in Elastic and Viscoelastic Beams Due to Temperature and Moisture Changes Using Piezoelectric Actuator
Kuravi, Ramachandra Srinivasa Chaitanya
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This thesis analyzes the implementation of surface bonded piezoelectric actuators to control or minimize the deformation in elastic or viscoelastic cantilever beams due to simultaneous heat and moisture diffusion. The problem is addressed in the context of linearized elasticity and linearized viscoelasticity. The constitutive equations are derived from the balance laws for mass, linear and angular momenta, energy, entropy and the second law of thermodynamics. The constitutive equations for linearized elasticity are then obtained as a consequence of small deformation assumption. The temperature and moisture induced deformation is introduced through the coefficient of thermal expansion CTE and coefficient of moisture expansion CME. The constitutive equations for linearized viscoelasticity are obtained by correspondence principle. The coupled temperature and moisture diffusion equations are obtained as a consequence of Clausius-Duhem inequality. The extent of coupling between heat conduction and moisture diffusion phenomena is studied by varying the ratio of their diffusivities and a non-dimensional coupling parameter. The effect of coupled unsteady heat conduction and moisture diffusion phenomena on the short and long term response characteristics of the beam such as displacement, stress and strain fields is studied. Based on these response characteristics, the magnitude of external actuating voltage required to minimize deformation is predicted. This is followed by a comparative study of the field variables in cases of actuated and unactuated beams. Four materials are chosen for this study; aluminium, epoxy, carbon fiber reinforced polymer with fiber volume fraction of 60 percent, and an epoxy-like viscoelastic material. The viscoelastic material is assumed to be thermorheologically simple. The shift factor is assumed to be a linear function of temperature and moisture fields. To address this problem numerically, a finite difference formulation is presented for the field equations and boundary conditions. This numerical scheme is validated by solving the problem of uniformly loaded cantilever beam and comparing the results with the analytical solution known a priori. The results obtained numerically are validated by comparison with experimental results. It is observed that the under the effect of external actuation, the stress and displacement fields are largely minimized in all four cases chosen for study. The bending in the unactuated viscoelastic beam is more pronounced than bending in the unactuated elastic beam. This is due to the softening of the material with time due to evolving temperature and moisture fields. However, relatively lesser external actuating voltage is necessary to minimize bending in the former case compared to the latter. The magnitude of actuating electric field required in the piezoelectric layer suggests a need to address the problem with in a non-linear framework, no such attempt is made in this study.