Free vibration analysis of functionally graded beams resting on variable elastic foundations using a generalized power-law distribution and GDQ method

In this research work, based on the Euler–Bernoulli theory and by means of Generalized Differential Quadrature (GDQ) method, free vibration characteristics of functionally graded (FG) beams resting on two-parameter foundation are focused. The two-constituent functionally graded beam consists of ceramic and metal grading through the thickness. A generalized power-law distribution is considered for the ceramic volume fraction. A detailed parametric study is carried out to highlight the influences of different profiles of fiber volume fraction, four parameters of power-law distribution and two-parameter elastic foundation modulus on the vibration characteristics of the FG beams.