In this work, a nonlocal strain gradient beam model considering the thickness effect is developed to study the nonlinear vibration response of a functionally graded nanobeam. The governing equation of the functionally graded nanobeam is derived by using the Euler–Bernoulli beam theory with von Kármán’s nonlinear strain‐gradient relationship and the Hamilton principle. The expression of the nonlinear frequency for the functionally graded nanobeam with pinned‐pinned boundary conditions is obtained with the help of Galerkin technique and the Hamiltonian approach. The obtained results show that the effect of thickness is very important for the size‐dependent vibration response of the functionally graded nanobeam; the nonlinear vibration response of the nanobeam depends not only on the material length scale parameter and nonlocal parameter but also on the slenderness ratio. Effects of the slenderness ratio and the power‐law index on the vibration response of the functionally graded nanobeam are also investigated and discussed. The numerical results show that the nonlocal parameter reduces the nonlinear frequency of the functionally graded nanobeam, while the material length scale parameter increases the nonlinear frequency of the functionally graded nanobeam. The slenderness ratio leads to an increase in the nonlinear frequency of the functionally graded nanobeam, while the power‐law index leads to a decrease in the nonlinear frequency of the functionally graded nanobeam.

A closed-form solution for free vibration is constructed and used for obtaining explicit frequency equation and mode shapes of Timoshenko beams with arbitrary number of cracks. The cracks are represented by the rotational springs of stiffness calculated from the crack depth. Using the obtained frequency equation, the sensitivity of natural frequencies to crack of the beams is examined in comparison with the Euler-Bernoulli beams. Numerical results demonstrate that the Timoshenko beam theory is efficiently applicable not only for short or fat beams but also for the long or slender ones. Nevertheless, both the theories are equivalent in sensitivity analysis of fundamental frequency to cracks and they get to be different for higher frequencies.

This paper presents an experimental study to find out an effective parameter which is useful to enhance the progression rate of drifting vibro-impact systems excited by a harmonic force. It is assumed that the system performance would be better if the excitation force stays in a harmonious relationship with the natural motion of the impact mass. This hypothesis has been numerically analyzed and then experimentally verified. The phase lag between the excitation force and the motion of the impact mass is used to identify the best situation, where the system progression rate is maximal. It has been found that the highest progression rate of the system can be obtained when the phase lag is around one-eighth of the excitation period.