Dynamic behavior of micromorphic viscoelastic Euler–Bernoulli beams under viscoelastic boundary constraints

In this study, the free vibration analysis of viscoelastic nonlocal strain gradient Euler–Bernoulli beams under viscoelastic boundary conditions has been conducted. First, the equation of motion has been derived using the nonlocal strain gradient theory and Euler–Bernoulli beam theory, and the Kelvin-Voigt viscoelastic model has been incorporated into the problem to represent viscoelastic material behavior. Fourier series and Stokes’ transformations have been employed for the solution of the problem, and by integrating the boundary conditions into the solution, an eigenvalue problem has been obtained to determine the frequencies of viscoelastic nonlocal strain gradient Euler–Bernoulli beams. The results of the study revealed that the nonlocal scale parameter has a negative effect on damping, while the strain gradient scale parameter has a positive effect. The findings have been presented in detail with the help of tables and graphs and thoroughly evaluated.