ABSTRACT
In this chapter, the thermo-mechanical vibrational responses of sandwich beams will be derived for a beam consisting of an elastic core placed between two CNTR nanocomposite facesheets. The equivalent material properties of the nanocomposite facesheets will be developed using the modified form of the rule of the mixture. Via this method, the influences of the tiny dimensions of the CNTs will be covered, introducing size-dependent modifying coefficients. The kinematic relations of the beam will be derived based on the well-known Timoshenko beam hypothesis. Thereafter, the dynamic form of the principle of virtual work will be implemented to derive the governing equations of the beam for the case of thermal vibration problem. The set of the governing equations can be found by referring to Eqs. (2.112)–(2.114). The natural frequency of the system will be determined by employing the DTM considering various types of edge supports. Since FG materials like FG-CNTR nanocomposites are generally used in the cases of severe thermal gradients, the material properties of the core and the nanocomposite facesheets are assumed to be as functions of the local temperature to reach more reliable thermal results.
