The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method HAM . Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The...

Gravity time sequences collected at Etna volcano by continuously recording spring-based relative gravimeters showed significant variations in temporal correspondence with paroxysmal eruptions. Since the observed gravity variations can only be partially related to subsurface mass redistribution phenomena, we investigated the instrumental effects due to ground vibrations such as those that accomp...

A dynamic nonlinear model of rubber absorber in railway fastening is proposed in this paper based on a superposition principal demonstrating that the restoring force of rubber components consists of an elastic force and a damping force. In order to determine model parameters and verify the accuracy of this model, a dynamic experiment is designed. The obtained simulated results show good agreeme...

Nonlinear vibration and postbuckling behavior of a single layer graphene sheet (SLGS) embedded in a polymer matrix aroused by the nonlinear van der Waals (vdW) forces are investigated using the Kirchhoff plate theory. The interfacial vdW forces are described by a nonlinear function in terms of the graphene deflection. Through harmonic balance method, the nonlinear relation between deflection am...

In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...

Rolling bearing noise has become an aspect of increasing importance for the performance of rotating machinery, like electric motors and gearboxes. Generally, two aspects are important with regard to bearing noise, i.e. the transmission characteristics and the vibration generation characteristics. A potential source of vibrations are for example manufacturing imperfections of the di erent bearin...

The parametric resonance of the axial vibrations of a cantilever pipe conveying harmonically perturbed two-phase flow is investigated using the method of multiple scale perturbation. The nonlinear coupled and uncoupled planar dynamics of the pipe are examined for a scenario when the axial vibration is parametrically excited by the pulsating frequencies of the two phases conveyed by the pipe. Aw...

This paper applies a new variational approach proposed by Ji-Huan He for nonlinear oscillators. Two examples are given to illustrate the effectiveness and convenience of the method. The obtained results are valid for the whole solution domain with high accuracy. The method can be easily extended to other strongly nonlinear oscillations and it can be found widely applicable in engineering and sc...

this study presents a new approach to control the nonlinear dynamics of an adaptive absorber using shape memory alloy (sma) element. shape memory alloys are classified as smart materials that can remember their original shape after deformation. stress and temperature-induced phase transformations are two typical behaviors of shape memory alloys. changing the stiffness associated with phase tran...