Transverse vibrations of Timoshenko type beams carrying a concentrated mass have been investigated. Both ends of this mass-beam system have simply supports. Hamilton Principle has been used in order to derive equation of motion . For this coupled differential equations, approximately solutions have been searched by means of Method of Multiple Scales(a perturbation method). These solutions consi...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear componen...

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

in this paper, the effects of transverse cracks on rotating shaft were studied. according to earlier works, crack shaft failure decrease the critical speed of the shaft and also exhibit a nonlinear vibration behaviour leading to increases the amplitude of 1x and 2x harmonics (first and second order of rotational speed in torsional vibration). this suggests that the application of order analysis...

Vibration phenomena that might be modelled well using linear vibration theory include small amplitude vibrations of long, slender objects like long bridges, aeroplane wings, and helicopter blades; small rocking motions of ships in calm waters; the simplest whirling motions of flexible shafts, and so on. However, interactions between bridges and foundations, between wings/blades and air, between...

The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX) and adaptive neuro-fuzzy inference system (ANFIS), are used to model the behavior of an experimentally scaled three-story...

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with ...

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...