Control of thermally induced vibrations of rotating beams by using piezoelectric materials

Control of thermally induced vibrations of rotating isotropic and composite beams by using piezoelectric materials is studied in this thesis. First, thermally-induced vibrations of a stationary one-dimensional, bounded isotropic solid insulated on one side and subjected to various types of heat fluxes on the other side are studied by a series-based theoretical approach. The general temperature equation obtained via conduction heat transfer is used to derive equations for the thermal moment and thermally-induced vibrations, which are generated within the solid as a result. The resulting equations for the thermal moment and thermally-induced vibrations are general and can be applied to different types of heat fluxes. Three types of heat fluxes are used, namely constant, ramp and sinusoidal types. A thin aluminum beam with Simply-Supported (SS) and Cantilever (C) end conditions is used to analyze the thermally-induced vibrations resulting from these three types of heat fluxes. Finite element results are also obtained for the thermally-induced vibrations of the isotropic beam in order to compare them with the theoretical ones. Control of thermally induced vibrations for stationary or nonrotating thin isotropic beams is then carried out via the collocated piezoelectric sensor/actuator pair. The Linear Quadratic Regulator (LQR) effectively works as the control scheme. The above-mentioned 3 heat flux inputs, in so-called Cases 1 to 3, are applied to both the SS and C beams and the resulting vibrations are controlled in an effective manner by the LQR scheme. Modelling of rotating beams subjected to thermal heat fluxes lead to non-linear governing equations that require a suitable control theory other than the LQR approach and hence, the State Dependent Ricatti Equation (SDRE)-Based Sliding Mode Control (SMC) is employed in this case. This control theory is effectively utilized with the piezoelectric sensor/actuator pair to attenuate thermally induced vibrations of rotating thin beams. Thermally induced vibrations of thin composite beams with the same SS and C boundary conditions are studied next for the 3 types of heat fluxes belonging to Cases 1 to 3. Here, the well-known Classical Lamination Theory (CLT) is used together with the composite laminate equations to model the thermally-induced vibrational behavior of thin composite beams. Results are reported to demonstrate the presence of thermally-induced vibrations for the thin composite beams. Control of thermally induced vibrations for the stationary and rotating thin composite beams mounted with the piezoceramic sensor/actuator is finally considered using the LQR and SDRE-Based SMC theories, respectively. Studies of lateral vibrations both in time and frequency domains indicate succesful applications of these control schemes with the piezoelectric materials in the control of thermally induced vibrations.