Thermally induced vibration of a cantilever beam with periodically varying intensity of a heat source

In this paper an exact solution to the problem of the thermally induced vibration of a cantilever beam is presented. It is assumed that on a part of the beam the surface acts as a periodically time-varying heat source. The changing of the beam temperature produces thermal stresses, which cause displacements of the beam. The vibration of the beam is governed by the Bernoulli-Euler equation which includes the variable thermal moment. The heat equation and the vibration problem are solved by using the Green’s function method. The symbolic software Mathematica has been used to obtain the solution of the problem in an analytical form

Sensing and Control of Thermally Induced Vibrations of Stationary Blades Using Piezoelectric Materials

Vibration sensing and control of stationary blades (beam/plate-type structures) using piezoelectric materials subjected to thermal loads are considered in this work. Thermal effects are imposed on these blades, which are assumed to be mounted with piezoelectric patches for vibration sensing and control. Effects of the temperature field on the piezoelectric media are treated through the phenomenon of thermopiezoelectricity where electrical, mechanical, and thermal fields are all coupled. First, static blades are considered without control using the finite element method and analytical equations for verification of the finite element model. The finite element program ANSYS is utilized to implement the finite element method in all cases. Negative velocity feedback is then applied for the control of thermally induced vibrations of these stationary blades using the piezoelectric materials. It is concluded that the finite element model is accurate and that the use of the piezoelectric materials in the roots of stationary blades for the purpose of controlling thermally induced vibrations via a negative velocity feedback scheme is possible