Sharif Digital Repository

A distributed, nonlinear dynamic vibration neutralizer is presented to improve vibration suppression characteristics of harmonically excited structures. The absorber subsection consists of a double-ended cantilever beam carrying intermediate lumped masses. The positions of the moving masses are adjustable along the beam in order to comply with the desired optimal performance. The absorber is assumed to be linearly elastic but with the inextensibility along the neutral axis of the beam. Due to the existence of parametric resonance, nonlinearities of the system begin to affect the motion and hence parametric instability occurs. The necessary and sufficient conditions for the existence of... 

This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special... 

In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is... 

In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is... 

In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled... 

Parametric resonance is a phenomenon caused by time-varying changes in the parameters of a system which may result in undesirable motion responses and instability. Floating bodies like ships and spar-buoys are prone to Mathieu instability mainly due to the instantaneous change of the metacentric height. With the fast-growing developments in Ocean Renewable Energy systems, spar-buoys are commonly used for wave energy convertors and floating wind turbines. Undesirable, unstable motions as a result of the parametric resonance can be problematic as it may cause inefficiency in operations and structural risk integrity. In this research, a new approach has been developed to investigate these...