Sharif Digital Repository

Periodic solutions and their existence are one of the most important subjects in dynamical systems. Fractional order systems like integer ones are no exception to this rule. Tavazoei and Haeri (2009) have shown that a time-invariant fractional order system does not have any periodic solution. In this article, this claim has been investigated and it is shown that although in any finite interval of time the solutions do not show any periodic behavior, when the steady state responses of fractional order systems are considered, periodic orbits can be detected  

A model-based algorithm is proposed and tested using the simulator and operation data of a plastic pipeline prototype to locate multiple non-simultaneous leaks in the pipeline. A combination of an extended Kalman filter and obtained relations from the steady state response is used in order to tackle the problem of multi-leak localization. To achieve the mentioned relations, a real pipe with two leaks is equated to a virtual pipe with a single virtual equivalent leak  

A comprehensive mathematical model has been developed for the simulation of simultaneous chemical absorption of carbon dioxide and hydrogen sulfide by means of Monoethanolamine (MEA) aqueous solution in hollow fiber membrane reactors is described. In this regard, a perfect model considering the entrance regions of momentum, energy, and mass transfers was developed. Computational Fluid Dynamics (CFD) techniques were applied to solve governing equations, and the model predictions were validated against experimental data reported in the literature and excellent agreement was found. Effects of different disturbances on the dynamic behavior of the reactor were investigated. Moreover, effects of... 

This paper presents a method to determine the denominator and numerator polynomials of a closed-loop transfer function in order to obtain desired transient and steady-state responses in terms of the overshoot, speed (time needed for the relative error to become less than a specific amount) and the steady-state error when the desired output is a ramp signal. Meanwhile, a controller is designed with the same characteristic equation for the closed-loop system to eliminate step and ramp disturbances  

With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and... 

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... 

Recently, a class of fractional multi-frequency oscillators, constructed based on using n integrators and n half-order ones, has been introduced, whose steady-state responses contain sinusoidal components with 0.5 (3 n- 1 ) number of selectable frequencies. In this paper, the structure of the introduced multi-frequency oscillator is modified such that, notwithstanding the frequency content preservation, the number of its involved integrators is reduced. With no effect on the frequency content of the generated oscillations, this modification causes that the circuitry implementation of the considered class of multi-frequency oscillators can be done with a less number of energy storage... 

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two... 

This paper analytically studies the effect of functionally graded materials (FGMs) on the primary resonances of large amplitude flexural vibration of in-extensional rotating shafts with nonlinear curvature as well as nonlinear inertia. The constituent material is assumed to vary along the radial direction according to a power-law gradation. The governing differential equations and the corresponding boundary conditions are derived employing the variational approach. Then, the Galerkin method and the multiple scales perturbation method are utilized to obtain the frequency–response equation. In a numerical case study, the effects of the power-law index on the steady-state responses and locus of... 

Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite... 

In many medical applications, it is necessary to precisely control a robot to achieve exact positioning. In such cases, some components of robot which had been considered rigid should be modeled with visco-elastic elements to present more exact model of robot, and hence controllers designed under the assumption of rigidity may not accurately control them, especially when time-delay and disturbances have been appeared in the closed-loop system. In this study, we present a new control approach to force such robots to have rigid and exact motions, while they have visco-elastic components. Time-delay in the feedback path defects transient state response, while disturbances change the steady... 

In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are... 

Overwhelming number of control laws has been studied for control of robot manipulators with rigid links and joints. However controllers designed under this assumption may not accurately control the manipulator link due to visco-elastic properties that appear in the link behavior. In this study, a novel approach for robust control of a single-link manipulator is presented to force the link to have rigid motions, while it has visco-elastic behavior. In this regard, initially robot dynamics is extracted, followed by the design of four appropriate controllers through the loop-shaping approach. The obtained model is first represented in state space, however later converted to transfer function...