Analysis of the transverse vibration of a multistepped FGM beam resting on a Winkler foundation in a thermal environment and carrying concentrated masses

This paper examines a novel case study involving the free vibration of a stepped FGM beam-mass system resting on elastic foundations and subjected to a nonlinear or uniform thermal load. The present study examines the complex interaction of thermal effects on dynamic behaviour by varying the cross-section and length ratios, material parameters and mass magnitudes. After adopting Euler-Bernoulli's theory, the dynamic behaviour of non-uniform FGM beams was investigated using the generalized finite element method (GFEM) and the Rayleigh quotient finite element method (RQFEM). In line with the objective set, relevant results derived from parametric studies, showcasing accentuated variation in dimensional frequency curves and bending moments, have been highlighted and discussed.