Sharif Digital Repository

In this paper, a novel approach is proposed for solving the nonlinear problems based on the collocation and energy balance methods (EBMs). Rational approximation is employed as an initial guess and then it is combined with EBM and collocation method for solving nonlinear oscillators with cubic term. Obtained frequency amplitude relationship is compared with exact numerical solution and subsequently, a very excellent accuracy will be revealed. According to the numerical comparisons, this method provides high accuracy with 0.03% relative error for Duffing equation with strong nonlinearity in the second-order of approximation. Furthermore, achieved results are compared with other types of... 

The aim of this paper is to use higher-order energy balance method as a novel solution procedure for investigation the nonlinear oscillation of various systems. The method is associated with collocation method and employed for a group of nonlinear problems including pure cubic nonlinearity, fractional elastic force and duffing harmonic terms. Obtained results are evaluated by comparing with the classical balance method and also the exact solutions computed numerically. It is shown our solution procedure achieves more accurate results versus the classical solution and higher agreement are observed between the newer solutions and the exact ones for the systems. Effect of initial conditions in... 

Nonlinear free/forced vibration of a functionally graded graphene nanoplatelet (GNP) reinforced microbeam having geometrical imperfection which is rested on a non-linear elastic substrate have been studied in the present research. Graphene Platelets have been uniformly and non-uniformly scattered in the cross section area of the microbeam. Non-uniform distribution of GNPs is considered to be linear or non-linear type. Geometric imperfection is considered similar to the first vibration mode of microbeam. Size effects due to micro-rotations are captured in this study by means of modified couple stress elasticity. In the case of forced vibration, a uniform harmonic load is exerted to the top... 

Balancing a rotating machine is a vital step towards ensuring it will operate reliably and safely. To achieve this condition monitoring is an important aspect for early faulty detection and it can also result in the improvement of the operational continuity and equipment safety. Imbalance itself, is a common problem in rotating machinery and it can lead to poor or even dangerous vibration levels. And, for example, it is also well known that misalignment can lead to bearing defects. So, in order to overcome these problems many balancing techniques have been developed that are largely based on measured vibration data using accelerometers attached to the faulty device. The three-point method is... 

The objective of this study is to calibrate Priestley-Taylor (PT) model for estimating open water evaporation from an arid region reservoir called Chahnimeh. Chahnimeh Reservoir which is situated in the Sistan area in the southeast of Iran is being affected by regional energy advection during May to October. Therefore, common models of open water evaporation estimation such as PT require calibration. PT method was calibrated for Chahnimeh Reservoir using a volume balance method. Results showed that PT coefficient, αPT, as a constant over the year varies between 2.47±0.09 and 1.20±0.03 for two different hydrologic conditions of dry and wet. It means that there is also an intra-annular... 

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... 

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... 

In fractured reservoirs, a large variation of permeability due to the presence of fractures leads to changes in the production mechanism compared to conventional reservoirs. Hence, an appropriate model with the ability to describe the reservoir properly can provide a more confident prediction of its future performance. One of the features of a representative model is the number and height of the matrix blocks. The determination of these two parameters is one of the decisive steps in the calculation of an accurate amount of oil production from these reservoirs. In fact, matrix height shows its effect as a gravity force, which is one of the driving mechanisms. If the matrix height is less than... 

Superconducting materials are known to exhibit nonlinear effects and to produce harmonic generation and intermodulation distortion in superconductive circuits. In planar structures, these nonlinearities depend on the current distribution on the strip which is mainly determined by the structure of the device. This paper investigates the current distribution at the step-in-width discontinuity in superconducting microstrip transmission lines, which is computed by a numerical approach based on a 3-D finite-element method. This current distribution is used to obtain the parameters of the nonlinear circuit model for the superconducting microstrip step-in-width discontinuity. The proposed... 

In this paper the problem of chaos control in single mode lateral oscillations of spinning disks is studied. At first, using the harmonic balance method, one of the periodic orbits of system is evaluated. Then proposing a nonlinear feedback strategy a control law is presented for chaos elimination by tracking the mentioned periodic solution. It is shown that although the system is not input-state feedback linearizable, by defining an output signal and using the input-output linearization method, the objective of complete periodic orbit tracking is achieved. The sufficient condition for this purpose is presented, and the performance of proposed method is examined by numerical simulation. ©... 

Remote sensing is an effective tool for capturing spatial and temporal variations of water surface temperature (WST) in large lakes. The WST of Urmia Lake in northwestern Iran was examined from 2007 to 2010, using MODIS land surface temperature (LST) products. Spatial and temporal (diurnal, monthly, seasonal and inter-annual) variations of Urmia Lake WST were also investigated. Results indicate that the MODIS-derived WSTs are in a good agreement with the in situ data (R2=0.92 and bias=-0.27). Spatial analysis of WST revealed that there are three thermal zones along the lake: the shallow region in barriers of the causeway, islands and the shoreline; the south part; and the deep north parts.... 

Using a simple nonlinear model based on rate equations, and by employing a harmonic balance method, we develop a theory of optimal mixing in directly modulated semiconductor laser diodes. We perform a consistent numerical solution to the mixing in laser diodes to the arbitrary accuracy and intermodulation index (m, n). Through numerical computations we demonstrate that there is an optimal bias in mixing, corresponding to a relaxation frequency, fr, coinciding with the subcarrier frequency, f1, at which the mixing power is maximized nearly simultaneously for all intermodulation products, fmn. In terms of increasing the signal's current amplitude, it will be shown that it would result in a...