Investigating thermal effects on vibration behavior of temperature-dependent FGM Timoshenko beams with porosities

In present investigation vibration analysis Timoshenko beams made of a functionally graded materials with porosities in thermal environment is considered by using semi analytical differential transform method (DTM) for the first time. The material properties of porous FG beams are assumed to be temperature-dependent. Two types of thermal loading, namely, uniform and linear temperature rises through thickness direction are considered. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). Hamilton’s principle is applied to obtain the governing differential equation of motion and boundary conditions. Several important parameters such as thermal effect, porosity volume fraction and boundary conditions which have impacts on natural frequencies of beams are investigated and discussed in detail