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...

In this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells subjected to radial harmonic excitation is investigated. The nonlinear formulation is based on a Donnell’s nonlinear shallow-shell theory, in which the geometric nonlinearity takes the form of von Karman strains. The Lagrange equations of motion were obtained by an energy approach. In order to reduce the syst...

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 ...

Nonlinear free vibration analysis of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium is studied in this paper based on classical (local) Euler-Bernoulli beam theory. Using the averaging method, the nonlinear free vibration responses of DWCNTs are obtained. The result is compared with the obtained results from the harmonic balance method for single-walled carbon nanotubes (...

recently, a large amount of studies have been related to nonlinear systems with multi-degrees of freedom as well as continuous systems. the purpose of this paper is to optimize passive vibration absorbers in linear and nonlinear states for an euler-bernoulli beam with a nonlinear vibratory behavior under concentrated moving load. the goal parameter in the optimization is maximum deflection of t...

in this paper, nonlinear vibration and instability response of an embedded pipe conveying viscose fluid is investigated. the pipe is considered as a timoshenko beam embedded on an elastic foundation which is simulated by spring constant of the winkler-model and the shear constant of the pasternak-model. the external flow force, acting on the beam in the direction of the flexural displacement is...

In this paper, research on transverse vibrations of axially moving strings and their control is thoroughly reviewed. In the last few decades, there have been extensive studies on analysis and control of transverse vibrations of axially moving strings because of the wide applications of many engineering devices that axially moving strings represent. In the investigations adopting linear models o...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

In this work, analytical solutions are provided to the nonlinear equations arising in thermal and flow-induced vibration in fluid-conveying structures using Galerkin-differential transformation method with cosine aftertreatment technique. From the analysis, it was established that increase of the length and aspect ratio of the fluid-conveying structures result in decrease the nonlinear vibratio...