An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of t...

The solution of the Langevin equation describing the dynamics of a Brownian particle in a tilted periodic potential in the overdamped limit is obtained in terms of a matrix continued fraction, allowing us to evaluate statistical averages governing the nonlinear response to a strong ac force. Pronounced nonlinear effects are observed for large values of the ac force. For a weak ac force and low ...

In this study, the method of multiple scales is used to perform a nonlinear vibration analysis of a mechanical system in two cases; with dry and lubricated clearance joints. In the dry contact case, the Lankarani-Nikravesh model is used to represent the contact force between the joined bodies. The surface elasticity is modeled as a nonlinear spring-damper element. Primary resonance is discussed...

In this paper, accumulation of plastic deformation of AISI 1045 steel plates with circular cutouts under cyclic axial loading is studied. Loading was applied under force-control conditions. Experimental tests were performed using a Zwick/Roell servo hydraulic machine. Under force-control loading with nonzero mean force, plastic strain was accumulated in continuous cycles called ratcheting. Nume...

Internally-balanced Magnetic Unit (IB Magnet) has been developed as a fundamental technique of wall climbing robots. This unit comprises of a permanent magnet which generates a strong sticking force, and a spring unit which cancels the internal force so that the unit can provide easy sticking and releasing actions. In this paper, the authors aim to enlarge usefulness of IB Magnet by several app...

In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, whic...