Search for: nonlinear-differential-equation
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    Oscillation of solutions of second-order nonlinear differential equations of Euler type

    , Article Journal of Mathematical Analysis and Applications ; Volume 326, Issue 2 , 2007 , Pages 1076-1089 ; 0022247X (ISSN) Aghajani, A ; Moradifam, A ; Sharif University of Technology
    We consider the nonlinear Euler differential equation t2 x″ + g (x) = 0. Here g (x) satisfies x g (x) > 0 for x ≠ 0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t2 x″ + a (t) g (x) = 0. © 2006 Elsevier Inc. All rights reserved  

    Solution of nonlinear fractional differential equations using homotopy analysis method

    , Article Applied Mathematical Modelling ; Volume 34, Issue 6 , 2010 , Pages 1634-1641 ; 0307904X (ISSN) Ganjiani, M ; Sharif University of Technology
    In this article, the homotopy analysis method has been applied to solve nonlinear differential equations of fractional order. The validity of this method has successfully been accomplished by applying it to find the solution of two nonlinear fractional equations. The results obtained by homotopy analysis method have been compared with those exact solutions. The results show that the solution of homotopy analysis method is good agreement with the exact solution. Crown  

    Application of homotopy-Padé technique to the Volterra's prey and predator problem

    , Article Applied and Computational Mathematics ; Volume 10, Issue 2 , 2011 , Pages 262-270 ; 16833511 (ISSN) Faghidian, S. A ; Moghimi Zand, M ; Farjami, Y ; Farrahi, G. H ; Sharif University of Technology
    In this study, the Volterra's prey and predator problem is investigated. Homotopy-Pade technique is utilized to find analytic solutions to the problem. Results show the accuracy of the method comparing with other methods. It is illustrated that homotopy-Pade technique can greatly enlarge the convergence region of the solution series  

    Nonlinear initial value ordinary differential equations

    , Article Nonlinear Approaches in Engineering Applications: Applied Mechanics, Vibration Control, and Numerical Analysis ; October , 2015 , Pages 117-136 ; 9783319094625 (ISBN) ; 9783319094618 (ISBN) Aghdam, M. M ; Haghi, P ; Fallah, A ; Sharif University of Technology
    Springer International Publishing  2015
    Ordinary frequently occur as mathematical models in many fields of science, engineering, differential equations (ODEs) and economy. It is rarely that ODEs have closed form analytical solutions, so it is common to seek approximate solutions by means of numerical methods. One of the most useful methods for the solution of ODEs is multi-step methods. Although the existing multi-step methods such as Adams—Moulton are accurate and useful, they also have their own limitations such as instability at large step sizes or weak performance in the case of stiff ODEs. Thus, multi-step methods that show better behavior compared to the existing methods are preferred, because they decrease the computational... 

    Analytical solutions for generalized duffing equation

    , Article Nonlinear Approaches in Engineering Applications: Advanced Analysis of Vehicle Related Technologies ; 2016 , Pages 263-278 ; 9783319270555 (ISBN) Aghdam, M. M ; Fallah, A ; Sharif University of Technology
    Springer International Publishing  2016
    Structures like beams, plates, shells, and sectors have a key role in different fields of science and engineering. Reliable design of structures requires detailed understanding of their behavior in different service conditions including statics, dynamics, and vibration. For instance, dynamics and vibration characteristics of structures such as natural frequencies, mode shapes, and damping ratios are among interesting properties. Furthermore, in most severe conditions, linear theories are not enough to accurately capture real structural behavior. Thus, investigation of nonlinear and/or large amplitude vibration of structures which is normally governed by system of nonlinear differential... 

    Free chattering synchronization of two Lur'e differential inclusions with sector input nonlinearity

    , Article 2014 IEEE Conference on Control Applications ; 2014 , PP. 1035-1040 ; ISBN: 9781479974092 Abooee, A ; Haeri, M ; Sharif University of Technology
    This paper deals with the synchronization of two Lur'e differential inclusions containing sector nonlinearity. Lyapunov stability theorem is employed to design the control inputs. The controllers are designed considering three important practical features in physical systems. First, differential equation part of the Lur'e differential inclusion is assumed to be convex. Second, it is presumed that parameters of the Lur'e differential inclusion are not completely known. Third, sector nonlinearities are considered on control inputs applied to the Lur'e differential inclusions. To assess performance and effectiveness of the proposed controllers, synchronization of two rotor dynamic systems is... 

    Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams

    , Article Microsystem Technologies ; Vol. 21, Issue 2 , 2014 , pp. 457-464 ; Online ISSN: 1432-1858 Miandoab, E. M ; Yousefi-Koma, A ; Pishkenari, H. N ; Sharif University of Technology
    Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss–Seidel iteration methods are used. Both clamped-free and clamped–clamped micro- and nano-beams under electrostatical actuation are considered where... 

    Nonlinear dynamic modeling and simulation of an insect-like flapping wing

    , Article Applied Mechanics and Materials ; Vol. 555, issue , 2014 , p. 3-10 Banazadeh, A ; Taymourtash, N ; Sharif University of Technology
    The main objective of this paper is to present the modeling and simulation of open loop dynamics of a rigid body insect-like flapping wing. The most important aerodynamic mechanisms that explain the nature of the flapping flight, including added mass, rotational lift and delayed stall, are modeled. Wing flapping kinematics is described using appropriate reference frames and three degree of freedom for each wing with respect to the insect body. In order to simulate nonlinear differential equations of motion, 6DOF model of the insect-like flapping wing is developed, followed by an evaluation of the simulation results in hover condition  

    MHD flow in a channel using new combination of order of magnitude technique and HPM [MHD tok u kanalu uporabom novih kombinacija tehnika grubog opisa vrijednosti i HPM]

    , Article Tehnicki Vjesnik ; Volume 21, Issue 2 , April , 2014 , Pages 317-321 ; ISSN: 13303651 Abbasi, M ; Ganji, D. D ; Rahni, M. T ; Sharif University of Technology
    The present work is concerned with the steady incompressible flow through a parallel plate channel with stretching walls under an externally applied magnetic field. The governing continuity and Navier-Stokes equations are reduced to a fourth order nonlinear differential equation by using vorticity definition and similarity solution transformation. The obtained equations are solved by applying the analytical homotopy perturbation method (HPM). The method is called order of magnitude suggested for simplifying series solution to finite expression that is useful in engineering problems. The results are verified by comparing with numerical solutions and demonstrate a good accuracy of the obtained... 

    Stabilisation of commensurate fractional-order polytopic non-linear differential inclusion subject to input non-linearity and unknown disturbances

    , Article IET Control Theory and Applications ; Volume 7, Issue 12 , 2013 , Pages 1624-1633 ; 17518644 (ISSN) Abooee, A ; Haeri, M ; Sharif University of Technology
    In this study, a fractional-order adaptive-sliding mode control (SMC) scheme is proposed to stabilise commensurate fractional-order polytopic non-linear differential inclusion systems containing sector and dead-zone nonlinearities in the control inputs and unknown bounded disturbances. The suggested control method is composed of fractional-order sliding surfaces, adaptive-SMC inputs and adaptation laws for unknown bounds of disturbances. The Lyapunov stability theorem is used to prove the stability of the closed-loop system. A practical system and two numerical examples are simulated to show the effectiveness and performance of the proposed control technique  

    Static and dynamic analysis of a clamp-clamp nano-beam under electrostatic actuation and detection considering intermolecular forces

    , Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) ; Volume 10 , 2013 ; 9780791856390 (ISBN) Mojahedi, M ; Barari, A ; Firoozbakhsh, K ; Ahmadian, M. T ; ASME ; Sharif University of Technology
    American Society of Mechanical Engineers (ASME)  2013
    Micro/nano gyroscopes which can measure angular rate or angle are types of merging gyroscope technology with MEMS/NEMS technology. They have extensively used in many fields of engineering, such as automotive, aerospace, robotics and consumer electronics. There are many studies of a variety of gyroscopes with various drive and detect methods and different resonator structures in last years. In case of electrostatically actuated and detected beam micro/nano-gyroscopes, DC voltages are applied in driving and sensing directions and AC voltage is utilized in driving direction in order to excite drive oscillation. The intermolecular surface forces are especially significant when the gyroscopes are... 

    Nonlinear analysis of pull-in voltage for a fully clamped microplate with movable base

    , Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) ; Volume 10 , 2012 , Pages 71-75 ; 9780791845264 (ISBN) Karimzade, A ; Moeenfard, H ; Ahmadian, M. T ; Sharif University of Technology
    Micro-electro-mechanical systems (MEMS) such as sensors and actuators are rapidly gaining popularity in a variety of industrial applications. Usually these systems are constructed by a cantilever beam or plate along with a fixed substrate. The movable beam or plate deflects due to applied voltage between the plates. Pull-in voltage and contact time are the most important characteristic of these systems. Allowing the substrate to be movable in vertical direction pull-in voltage in comparison with the fixed substrate is expected to be much smaller. In this paper the pull-in voltage and the point at which pull-in takes place for a fully clamped microplate is evaluated. The nonlinear... 

    Nonlinear vibration analysis of a micro beam exposed to an external flow

    , Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011 ; Volume 7, Issue PARTS A AND B , 2011 , Pages 643-646 ; 9780791854938 (ISBN) Mazaheri, H ; Hosseinzadeh, A ; Ahmadian, M. T ; Barari, A ; Sharif University of Technology
    In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity  

    A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory

    , Article Nonlinear Dynamics ; Volume 81, Issue 4 , 2015 , Pages 2127-2140 ; 0924090X (ISSN) Safa, A. T ; Alasty, A ; Naraghi, M ; Sharif University of Technology
    Kluwer Academic Publishers  2015
    Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different... 

    On the energy extraction from large amplitude vibrations of MEMS-based piezoelectric harvesters

    , Article Acta Mechanica ; Volume 228, Issue 10 , 2017 , Pages 3445-3468 ; 00015970 (ISSN) Pasharavesh, A ; Ahmadian, M. T ; Zohoor, H ; Sharif University of Technology
    As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and... 

    Nonlinear optimal control of planar musculoskeletal arm model with minimum muscles stress criterion

    , Article Journal of Computational and Nonlinear Dynamics ; Volume 12, Issue 1 , 2017 ; 15551415 (ISSN) Sharifi, M ; Salarieh, H ; Behzadipour, S ; Sharif University of Technology
    American Society of Mechanical Engineers (ASME)  2017
    In this paper, the optimal performance of a planar humanlike musculoskeletal arm is investigated during reaching movements employing an optimal control policy. The initial and final states (position and velocity) are the only known data of the response trajectory. Two biomechanical objective functions are taken into account to be minimized as the central nervous system (CNS) strategy: (1) a quadratic function of muscle stresses (or forces), (2) total time of movement plus a quadratic function of muscle stresses. A two-degress of freedom (DOF) nonlinear musculoskeletal arm model (for planar movements) with six muscle actuators and four state variables is used in order to evaluate the proposed... 

    Solution of the falkner-skan equation for wedge by adomian decomposition method

    , Article Communications in Nonlinear Science and Numerical Simulation ; Volume 14, Issue 3 , 2009 , Pages 724-733 ; 10075704 (ISSN) Alizadeh, E ; Farhadi, M ; Sedighi, K ; Ebrahimi Kebria, H. R ; Ghafourian, A ; Sharif University of Technology
    The Adomian Decomposition Method is employed in the solution of the two dimensional laminar boundary layer of Falkner-Skan equation for wedge. This work aims at the solution of momentum equation in the case of accelerated flow and decelerated flow with separation. The Adomian Decomposition Method is provided an analytical solution in the form of an infinite power series. The effect of Adomian polynomials terms is considered on accuracy of the results. The velocity profiles in boundary layer are obtained. Results show a good accuracy compared to the exact solution. © 2007 Elsevier B.V. All rights reserved  

    Closed-form approximation and numerical validation of the influence of van der Waals force on electrostatic cantilevers at nano-scale separations

    , Article Nanotechnology ; Volume 19, Issue 1 , 2008 ; 09574484 (ISSN) Ramezani, A ; Alasty, A ; Akbari, J ; Sharif University of Technology
    In this paper the two-point boundary value problem (BVP) of the cantilever deflection at nano-scale separations subjected to van der Waals and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. In the numerical method, the BVP is solved with the MATLAB BVP solver, which implements a collocation method for... 

    Estimation of power system frequency using an adaptive notch filter

    , Article IEEE Transactions on Instrumentation and Measurement ; Volume 56, Issue 6 , December , 2007 , Pages 2470-2477 ; 00189456 (ISSN) Mojiri, M ; Karimi Ghartemani, M ; Bakhshai, A ; Sharif University of Technology
    An algorithm based on the concept of adaptive notch filter (ANF) is proposed for estimation of power system frequency. The ANF is a second-order notch filter that is further furnished with a nonlinear differential equation to update the frequency. The method permits direct estimation of frequency and its rate of change for a power system signal. The performance of the algorithm is compared with that of a newly introduced algorithm, which is based on using an enhanced phase-locked loop (PLL) system. Unlike the PLL-based frequency estimator, the proposed algorithm does not employ a voltage-controlled oscillator. This makes its structure much simpler for implementation. The transient response... 

    Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces

    , Article International Journal of Solids and Structures ; Volume 44, Issue 14-15 , 2007 , Pages 4925-4941 ; 00207683 (ISSN) Ramezani, A ; Alasty, A ; Akbari, J ; Sharif University of Technology
    In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under...