Computational modeling of an exponential functionally graded material (EFGM) beam

In this study, computational modelling of an exponential functionally graded material (EFGM) beam is proposed to demonstrate the vibration characteristics of exponential functionally graded material (EFGM) beams subjected to general end conditions. The mechanical parameters of the beam vary exponentially in a longitudinal direction. The width of the beam varies by an exponential expression in the longitudinal direction. The four end conditions are employed in this analysis, i.e., clamped–clamped, clamped-simply supported (CS), simply supported-simply supported and clamped-free (CF). The finite element software based on the finite element method is used to calculate the eigenfrequencies. The effect of exponent parameters, thickness-to-length ratio and end condition is analyzed. It can be stated from the results that natural frequency decreases when the exponent parameters lie in the range from  − 1 to 0. While it increases when the exponent parameters lie from 0 to 1 under the fixed end condition. The natural frequencies decrease for CS and CF end conditions when the exponent parameters lie from  − 1 to 1. In a simply supported end condition, the natural frequency increases when the exponent parameters lie from  − 1 to 0. While it decreases when the exponent parameters lie from 0 to 1 for the first mode. The natural frequency decreases for the second mode when the exponent parameters lie from  − 1 to 0. While it increases when the exponent parameters lie from 0 to 1.