Thermally-Induced Vibrations of One-Dimensional Bounded Solids Subject to Heat Fluxes in Various Forms

Thermally-induced vibrations of a one-dimensional, bounded isotropic and composite 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 in this work. 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 as case studies, namely constant, ramp and sinusoidal types. A thin isotropic and composite beam with various boundary 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.