Least-Squares Residual Solution for Displacement Control of a Composite Piezothermoelastic Cylinder

A least-squares method is employed for displacement control of a composite cylinder consisting of a thermoelastic inner layer in contact with a piezothermoelastic outer layer. The inside surface of the composite cylinder is subject to a prescribed axisymmetric ambient temperature. A solution is obtained for the uncontrolled thermally-induced elastic and electrostatic responses throughout the cylinder. Next the voltage applied to the cylinder's outer surface needed to suppress the radial displacement in a least-squares sense is found, and the resulting controlled responses are determined. Both stationary and transient situations are considered. Numerical results are calculated and compared with those obtained using a computer algebra system and Laplace transform analysis.