Asymptotic approach for nonlinear vibrating beams with saturation type boundary condition

This article attempts to analyze the complicated vibrational behavior of the Euler–Bernoulli beam exposed to saturated nonlinear boundary condition through proposing an innovative precise equivalent function. In this direction, the beam vibrational response is attained by way of a new effective analytical method namely Hamiltonian approach. Despite all the procedures based on perturbation methods that deadzone or saturation dead-band parameter is omitted during integration, this study indicates that how using Hamiltonian approach, the impact of dead-band parameter is taken into account leading to higher accuracy of the approximated solution. Finally, the precision of the proposed equivalent function is evaluated in comparison with the numerical solutions, giving excellent results.