Sharif Digital Repository

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 investigate the dynamic analysis of a strongly nonlinear microrobot using a three-term harmonic balance method. The employed locomotion concept, namely "friction drive principle," is based on the superposition of a horizontal vibration at the interface between the robot and work floor and an active variation of friction force, obtained by the vertical vibration of the base at the same interface. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity for which the elastic force term is proportional to a signum function. The obtained periodic solution not only is of high accuracy, but also can predict the contribution of the... 

Among the locomotion concepts employed in the microrobotics, friction-based locomotion principles are of considerable importance. In this study, the dynamic modelling of friction drive microrobots subjected to the tangential and normal excitations is investigated, which have the same frequency, but are shifted in phase. The motion equation of the microrobot reveals a strongly non-linear differential equation with discontinuity for which the elastic force term is proportional to a signum function. Using the homotopy perturbation method, simple expressions are derived for predicting average velocity of the slider. The obtained results are in good agreement with those achieved from numerical... 

This paper presents a novel, sliding, A-shaped microrobot with nanometric resolution for precision positioning applications. The microrobot is actuated near its natural frequency using a piezoelectric stack actuator to produce translational motion. The dynamic modeling of the mechanism is based on the assumptions of the linear piezoelectric behavior and the Coulomb friction model. Using this model the required condition for generating net motion is found. The suitability of three simple, friction-based locomotion modes for implementation on the proposed device is addressed. Influences of some important configuration parameters on the behavior of the microrobot, based on defined criteria, are... 

In this paper, we analytically investigate the dynamic modeling of a nonlinear microrobot based on the "friction drive principle". The superposition of a horizontal vibration at the interface between the robot and work floor and an active variation of friction force, obtained by the vertical vibration of the base, makes the robot to move on the substrate. Periodic solutions obtained from the harmonic balance method can predict the contribution of the friction coefficient on the average velocity of the slider. Unlike traditional analytical techniques and in agreement with both numerical simulations and experiments reported in the literature, results show that the maximum average velocity... 

The nonlinear equation of motion for pre-stretched EulerBernoulli beams is derived. The effect of pre-tension and pre-compression in EulerBernoulli beams is studied. It is shown that compressive strain affects the bending stiffness much more than tensile strain. Based on the derived equation, the dynamic model of bimorph piezo-actuated beams, which is accurate, yet simple, is then developed. Afterwards, the critical voltage, which makes the piezo-actuated microbeam unstable, is numerically investigated. It is shown that the strain of the centerline is proportional to the beam's aspect ratio squared. Results show that the more the aspect ratio, the less the critical voltage. In addition, it... 

In this paper, a novel, A-shaped microrobot with nanometric resolution for precision positioning applications is addressed. The locomotion concept of the mechanism is founded on the "friction drive principle". To achieve the translational motion, a stack piezoelectric actuates the microrobot near its natural frequency. The dynamic modeling of the mechanism is based on the assumptions of linear behavior of piezo stack actuator and Coulomb friction model at contact points. The suitability of three simple, friction-based locomotion modes for implementation on the proposed device is presented. Influences of different friction coefficients on the behavior of the microrobot, with respect to... 

The friction drive principle, which is based on the superposition of two synchronized perpendicular vibrations at the interface of the robot and the work floor, plays a fundamental role in the locomotion of miniaturized robots. In this paper, the iteration perturbation method proposed by He is used to generate a periodic solution for this type of friction drive microrobot. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity, the elastic force term for which is proportional to a signum function. The obtained solutions are in excellent agreement with those achieved from numerical integration and experiments reported in the literature. Results... 

In this paper, we investigate the influence of nonideal boundary conditions on the nonlinear vibration of damped Euler-Bernoulli beams subjected to harmonic loads. These nonidealities allow for small deflections and/or moments at the supports of the beam. Using the iteration perturbation method, analytical expressions for the case of simply supported beams with immovable end conditions are provided. The results reveal that the first order of approximation obtained by the proposed method is more accurate than the perturbation solutions. Moreover, compared with the previous studies, some interesting phenomenon is predicted. We have shown that in some special combinations of the nonidealities... 

The motion of a stick-slip microrobot propelled by its piezoelectric unimorph legs is mathematically modeled. Using a continuously distributed mass model for the robot's body, the working equation of the mechanism is derived based on the assumption of linear Euler-Bernoulli beam theory and linear piezoelectric behavior. Moreover, the required condition for generating net motion is calculated in terms of physical characteristics of the microrobot. It is demonstrated that the higher the friction constant, then a lower average speed is obtained. Also, it is shown that a microrobot with heavier legs can move in a rougher environment. Regardless of the mass proportion between robot's main body... 

Al-Zn-Mg-Cu alloys (7xxx series Al alloys) are extensively used for their superior mechanical and corrosion performance. These properties are microstructure-sensitive and highly dependent on the formation, growth and coarsening of precipitates. To date, a wide variety of ageing procedures have been developed to tailor the evolved microstructures so as to yield a good combination of mechanical capacity and corrosion resistance of 7xxx series Al alloys. Among these methods, isothermal ageing, multi-stage ageing, non-isothermal ageing, retrogression and re-ageing (RRA), and stress ageing (i.e. creep ageing) are the most significant. In the present review, all of these approaches are... 

Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the... 

This article presents a novel identification approach which can deal with nonlinear and time-varying characteristics of complex dynamic systems, especially an aerial vehicle in the entire flight envelope. A set of local sub-models are first developed at different operating points of the system, and subsequently a self-organizing multi-model ensemble is introduced to aggregate the outputs of the local models as a single model. The number of employed local models in the proposed multi-model ensemble is optimized using a novel self-organizing approach. Also, wavelet neural networks, which combine both the universal approximation property of neural networks and the wavelet decomposition... 

In order to optimize the aging treatment of Mg-1.8Zn-0.7Si-0.4Ca alloy, different times and temperatures of solid solution and age hardening were applied to the alloy specimens. Microstructures and mechanical properties of the specimens were investigated using the optical microscopy, field emission scanning electron microscopy equipped with an energy dispersive x-ray spectrometer, x-ray diffraction, hardness, and shear punch tests. The lowest hardness and strength were achieved by solution treating of the alloy at 500 °C for 8 h, presenting the optimal condition for solution treatment of the alloy. The microstructural examinations revealed three different precipitates consisting of CaMgSi,... 

Redistribution of alloying elements in the transient liquid phase (TLP) bonding zone of IN738LC/ BNi-3/IN738LC was studied to investigate microstructural evolution in this area. Wavelength dispersive spectrometry and electron probe microanalysis revealed that, during non-isothermal solidification in the TLP bonding zone, enrichment of residual liquid phase with the positive segregating elements caused formation of intermetallic in the bonding zone. Scanning electron microscopy observation Indicated that the redistribution of alloying elements, between TLP bonding zone and base alloy, resulted In formation of a γ′ boundary layer, containing high density of fine γ′, around the bonding zone.... 

Transient-liquid-phase (TLP) bonding of the IN-738LC base alloy with BNi-3 interlayer was investigated in this article. Effects of the TLP bonding thermal cycle on the base alloy were studied microstructurally and macrostructurally. Microscopic investigation revealed that the microstructural evolution in the TLP bonding area was affected substantially by the bonding temperature. Therefore, a critical bonding temperature (Tcr) was defined for TLP bonding of IN-738LC/ BNi-3/IN-738LC samples. Unlike bonding below Tcr, TLP bonding at temperatures higher than Tcr resulted in formation of individual γ-γ' colonies in the adjacent base alloy to TLP bonding zone and caused significant reduction in... 

The effects of the mold preheating and the silicon content of ductile iron on the percentage of carbides, graphite nodule counts and shrinkage volume were investigated. The results showed that the percentage of carbides and the shrinkage volume decreased when the mold preheating increased. The ductile iron with the carbon equivalent of 4.45% and the silicon content of 2.5% without any porosity defects was achieved when the mold preheating was 450 °C. Increasing the silicon content in the range of 2.1%-3.3% led to the increase in graphite nodule count and graphite size and the decrease in percentage of carbides. It is due to the increase in induced expansion pressure during the graphite... 

We propose an analytical circuit model for accurate analysis of one-dimensional periodic array of metallic strips. The proposed model is valid not only in subwavelength regime, but also for wavelengths shorter than the period of structure. The working frequency can reach the visible range and thus electromagnetic properties of periodic arrays of nano-slits can be analyzed by the proposed model. The proposed model remains valid for arbitrary incident angles even when nonspecular diffracted orders become propagating. Analytical expressions are derived explicitly in order to describe the parameters of the proposed circuit model. The circuit model is derived by assuming that only one guided mode... 

In this paper, combined effects of material degradation, p-delta, and foundation uplift are incorporated in a soil-structure-interaction (SSI) framework to assess seismic response of a single-degree-of-freedom system. The considered phenomenological systems represent a column with a lumped mass on top is placed on a rigid foundation. The foundation is mounted on Winkler springs and dashpots to take account of soil-foundation compliance and material/radiation damping. The springs are tensionless to guarantee that uplift is properly modelled. The model is verified for two specific limit cases with the code and literature to make sure that the model is capable of capturing SSI and foundation...