Forced Vibration Analysis of Porous Beams Based on the Golla–Hughes–McTavish Viscoelastic Model

In this paper, the forced vibration of a porous beam is investigated considering the viscoelastic properties of the beam material. The porosity gradient of the beam is distributed through its thickness and the viscoelasticity property is modeled by the Golla–Hughes–McTavish (GHM) model. Applying the Hamilton principle and Euler–Bernoulli theory, the governing equation of motion is obtained for a simply supported beam. The Newmark method is employed to solve the time-dependent differential equation of the beam. The results are validated against given data in the literature and a commercial finite element software. In the results and discussion section of the paper, a parameter study is performed to investigate the effects of porosity and viscoelastic parameters on forced vibration of the beam under loads with variable input frequency. Finally, the results obtained by GHM model is compared with the Kelvin–Voigt model. According to the obtained results, while both models predict identical results for constant input frequency, the GHM model has the ability to predict accurate results for forced vibrations of a beam under variable input frequency in comparison with the Kelvin–Voigt model.