Sharif Digital Repository

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations. © 2009 Elsevier Ltd. All rights reserved  

An array of N weakly coupled oscillators is investigated in two major configurations. The locking bandwidth for linear and circular arrays is assessed through an array coupling matrix, in a worst-case free-running frequency distribution of oscillators. The superior locking bandwidth for circular arrays is demonstrated  

In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of more than one oscillator to see how the frequencies of small oscillations change when non-linear terms are added to a linear system and observe an interesting beat phenomenon in degenerate coupled... 

Self-excited and forced vibrations are important topics in machining processes because their occurrence results in poor surface finish, increase in tool wear and hampers productivity. In this paper, turning process is modeled as a SDOF dynamic system including quadratic and cubic structural nonlinearities. The effect of tool flank wear, as a contact force between the work-piece and tool, is addressed vigorously. Multiple scale method is used to find the solution of the nonlinear dynamic equation including regenerative chatter, forced excitation and tool wear. It is shown that, width of cut can be considered as the bifurcation parameter of the system. Primary, super-harmonic and sub-harmonic... 

Self-excited and forced vibrations are important topics in machining processes because their occurrence results in poor surface finish, increase in tool wear and hampers productivity. In this paper, turning process is modeled as a SDOF dynamic system including quadratic and cubic structural nonlinearities. The effect of tool flank wear, as a contact force between the work-piece and tool, is addressed vigorously. Multiple scale method is used to find the solution of the nonlinear dynamic equation including regenerative chatter, forced excitation and tool wear. It is shown that, width of cut can be considered as the bifurcation parameter of the system. Primary, super-harmonic and sub-harmonic... 

This paper is a proposal for the generation of a many-body entangled state in atomic and mechanical systems. Here the detailed feasibility study shows that application of a strong Rydberg dressing interaction and a fast bifurcation scheme in a Bose-Einstein condensate of Rb atoms, results in the formation of large cat states. By detailed study of the decoherence effects using the quantum jump Monte Carlo approach and taking into account the obstacles like collective decoherence and level mixing, this proposal predicts the formation of a 700-atom cat state. Subsequent transfer of the generated superposition to far separated mechanical oscillators is proposed, using dipole coupling between... 

Extensive experimental tests have been conducted to examine the roughness effects on the aerodynamic performance of a model in an oscillatory motion. All tests were carried out in a 0.8×0.8 m 2 low-speed wind tunnel. The model had 0.25m chord and was pitched about its quarter-chord. Data were acquired at various Reynolds number and reduced frequencies. Surface roughness was applied at two different locations of the model upper surface, leading edge and the point of maximum thickness. Furthermore, tunnel turbulent was varied and all tests were repeated. The results indicate that the width of the hysteresis loop, position of the figure eight shape, slope of the normal force coefficient curve,... 

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased.... 

This paper investigates the secondary Bjerknes force for two oscillating bubbles in various pressure amplitudes in a concentration of 95% sulfuric acid. The equilibrium radii of the bubbles are assumed to be smaller than 10 μm at a frequency of 37 kHz in various strong driving acoustical fields around 2.0 bars (1 bar=10 5 Pa). The secondary Bjerknes force is investigated in uncoupled and coupled states between the bubbles, with regard to the quasi-adiabatic model for the bubble interior. It finds that the value of the secondary Bjerknes force depends on the driven pressure of sulfuric acid and its amount would be increased by liquid pressure amplitude enhancement. The results show that the... 

In this work, a powerful analytical method, called Liao's homotopy analysis method is used to study the limit cycle of a two-dimensional nonlinear dynamical system, namely the van der Pol oscillator with delayed amplitude limiting. It is shown that the solutions are valid for a wide range of variation of the system parameters. Comparison of the obtained solutions with those achieved by numerical solutions and by other perturbation techniques shows that the utilized method is effective and convenient to solve this type of problems with the desired order of approximation  

In this paper we introduce a new low phase noise cascode Cross-coupled oscillator by use of the general topology of Cross-coupled oscillator and cascode amplifier. By simulation a comparison between the conventional Cross-coupled oscillator and the new cascode Cross-coupled oscillator is also presented, which shows that the latter improves the phase noise by 2dB under the same conditions. The figure of merit (FOM) of -186.4 dBc/Hz is achieved for the new oscillator by simulation  

in this paper the phase distribution in an array of coupled oscillators arranged on a circular surface is discussed. Coupling is considered to be weak and each oscillator is coupled to its four nearest neighbours. In a continuum limit where the number of oscillators goes to infinity a theoretical formulation in polar coordinates is proposed to describe the dynamic behaviour of phases of the array elements. A Green's function for phase distribution of the array is proposed in terms of its normalized eigenfunctions. Beam steering can be done via detuning the edge oscillators. © 2009 EuMA  

Coupled oscillator arrays (COAs) can be used to control the phase distribution across the aperture of an array antenna in such a manner as to affect steering of the beam without the use of phase shifters. Given the various possible planar configurations of COAs, a systematic design approach is necessary. In this study, the authors present a comprehensive comparison of various configurations of planar COAs based on their sensitivity to random errors in their free running frequencies. The parameters considered are (a) the beam pointing error of the array, (b) the locking probability, (c) the side lobe level, and (d) the beam width of the radiation pattern. These results can serve as a design... 

This paper deals with investigating the maximum number of frequencies generated by an oscillator in the case that a half number of integrators in the conventional dynamic structure of this oscillator are replaced by fractional integrators with an identical order. First, an upper bound for the maximum number of frequencies, which can exist in a steady state response of the oscillator, with respect to the number of integrators, is obtained. Then, on the basis of the recent advances in the field of determinant-based representations of bivariate polynomials, a lower bound is found for the maximum number of sinusoidal components in the steady state oscillations generated by the oscillator. A... 

In this study a synchronization method is developed to prevent the blocking arrhythmias which are caused by lack of synchronization between the two major heart pacemakers called the Sino-Atrial (SA) node and Atrio-Ventricullar (AV) node. Such pacemakers can be modeled by the Van der Pol oscillators. Feedback linearization method is used in synchronization. Since all states are not always available, they are estimated by a new observer in this research. To design the observer, first we introduce a robust observer for a unique Van der Pol oscillator. The robustness of proposed observer is obtained using gain and phase margins test. The observer variables are such that the error dynamical... 

This paper presents a digital hardware implementation of a frequency adaptive Hopf oscillator along with investigation on systematic behavior when they are coupled in a population. The mathematical models of the oscillator are introduced and compared in sense of dynamical behavior by using system-level simulations based on which a piecewise-linear model is developed. It is shown that the model is capable to be implemented digitally with high efficiency. Behavior of the oscillators in different network structures to be used for dynamic Fourier analysis is studied and a structure with more precise operation which is also more efficient for FPGA-based implementation is implemented. Conceptual... 

This paper presents the dynamic response of a delaminated composite beam under the action of a moving oscillating mass. In this analysis the Poisson's effect is considered for the first time. Moreover, the effects of rotary inertia and shear deformation are incorporated. In our modeling linear springs are used between delaminated surfaces to simulate the dynamic interaction between sub-beams. To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. The obtained results for the free and forced vibrations of beams are... 

The dynamic response of a delaminated composite beam under the motion of an oscillatory mass moving with a constant velocity has been studied. The delaminated composite beam is modeled as four interconnected sub-beams using the delamination limits as their boundaries. The constrained model is used to model the delamination region. The continuity and equilibrium conditions are forced to be satisfied between the adjoining beams. A set of derived governing differential equations along with those obtained by imposing boundary conditions are simultaneously solved in a closed form manner. The results for the response of the delaminated beam were compared with those of the intact beam. Furthermore,... 

Due to international competition and strict limitations of standards regarding the noise level, investigation of gear vibration is of great importance. In this paper, nonlinear oscillations of spur gear pairs including the backlash nonlinearity is studied. Dynamic system is described through the classical single degree of freedom (SDOF) model in terms of dynamic transmission error (DTE). Using multiple scale method, forced vibration responses of the gear system including primary, super-harmonic and sub-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system... 

This paper presents dynamic response of a delaminated composite beam under the action of moving oscillatory mass. The Poisson's effect, shear deformation and rotary inertia have been considered in this analysis. We have used the constrained mode model to simulate the behavior between the delaminated surfaces. Based on this model, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes for the delaminated beam. Then, the forced response is determined by employing the modal series expansion technique. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literature. Moreover, the...