parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity in this paper the parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity are analyzed the two dimensional lindstedt poincare perturbation technique applied for finding an approximate solution of linear parametrically excited systems is extended for analyzing a strong nonlinear oscillator based on the solution of a nonlinear differential equation with constant coefficients an approximative solution is introduced the transition curves and transient surfaces along which periodic solutions exist are obtained their strong dependence on the initial conditions is evident to prove the analytical solution the numerical experiment is done for certain values initial conditions and parameter values the time history diagrams for the oscillator are plotted

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

a note on optimal homotopy asymptotic method for the solutions of fractional order heat and wave like partial differential equations optimal homotopy asymptotic method oham is prolifically implemented to find the optimal solutions of fractional order heat and wave like equations we inspect the competence of the method by examining fractional order time dependent partial differential equations it is observed that oham is a prevailing and convergent method for the solutions of linear and nonlinear fractional order time dependent partial differential problems the numerical results rendering that the applied method is explicit effective and easy to use for handling more general fractional order heat and wave like models

convergence of a relaxation scheme for hyperbolic systems of conservation laws this paper concerns the study of a relaxation scheme for n times n hyperbolic systems of conservation laws in particular with the compensated compactness techniques we prove a rigorous result of convergence of the approximate solutions toward an entropy solution of the equilibrium system as the relaxation time and the mesh size tend to zero

a domain decomposition method for semilinear hyperbolic systems with two scale relaxations we present a domain decomposition method on a semilinear hyperbolic system with multiple relaxation times in the region where the relaxation time is small an asymptotic equilibrium equation can be used for computational efficiency an interface condition is provided to couple the two systems in a domain decomposition setting a rigorous analysis based on the laplace transform on the l2 error estimate is presented for the linear case which shows how the error of the domain decomposition method depends on the smaller relaxation time and the boundary and interface layer effects the given convergence rate is optimal we present a numerical implementation of this domain decomposition method and present some numerical results in order to study the performance of this method

materials with internal variables and relaxation to conservation laws the theory of materials with internal state variables of coleman gurtin cg provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics after reviewing the requirements imposed on constitutive theories by the principle of consistency with the clausius duhem inequality we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy they each lead to a relaxation framework for the theory of thermoelastic non conductors of heat equipped with globally defined entropy functions for the associated relaxation process next we consider a semilinear model problem of stress relaxation we discuss uniform stability and compactness for solutions of the relaxation system in the zero relaxation limit and establish convergence to the system of isothermal elastodynamics by using compensated compactness finally we prove a strong dissipation estimate for the relaxation approximations proposed in jin xin jx when the limit system is equipped with a strictly convex entropy

global bv solutions to a p system with relaxation in this paper we study the global existence of bv solutions to a p system with a relaxation source term using the glimm s scheme the pressure p is given by a law with 1 by a suitable choice of the measure for the strength of the shock waves we show that the total strength of the waves and the total variation of the solutions are uniformly bounded with respect to the relaxation parameter furthermore when the relaxation parameter tends to zero we show that the sequence of bv solutions eventually converges to a weak solution to the equilibrium equation 2000 academic press

non linear dynamics of gear pair systems with periodic stiffness and backlash the present work investigates dynamics of a gear pair system involving backlash and time dependent mesh stiffness in addition the system is under the action of external excitation caused by torsional moments and gear geometry errors first the equation of motion is established in a strongly non linear form then the emphasis is laid on a specific forcing frequency range corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance for these conditions several types of periodic steady state response are identified and determined by employing suitable methodologies including techniques applicable to piecewise linear systems and to oscillators with time periodic coefficients moreover these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions in the second part of the work numerical results are presented these results verify the validity and effectiveness of the new analytical methodology and provide information on the gear pair dynamics first series of typical response diagrams are obtained illustrating the effect of the mesh stiffness variation the damping and the forcing parameters on the gear pair periodic response these response diagrams are accompanied by results obtained with direct integration of the equation of motion in this way it is demonstrated that for some parameter combinations the dynamical system examined can exhibit more complicated and irregular response including crises and intermittent chaos

the dynamics of a vibromachine with parametric excitation the dynamics of a vibration machine with piecewise linear elastic ties under parametric harmonic excitation is investigated different designs of elastic elements with periodically time varying elasticity are described specific non linear features of parametric oscillations in the system under study are revealed the invariance of parametric vibration regime to possible disturbance of phase co ordinates conditions of limitedness of amplitude of parametric vibrations spectral features of non linear parametric regimes etc by the utilization of these non linear effects a procedure for the design of the main parameters of a parametric vibromachine is proposed

free boundary problems and the set valued mappings we have pointed out that many free boundary problems may be reduced to find the fixed points of certain set valued mappings and have solved the free boundary problem arising in the plasma physics 7 and the free boundary problem of the water cone in an oil reservoir with bottom water 111 as examples it is the purpose of this paper to develop the idea more extensively in this paper some typical free boundary problems such as the obstacle problem the seepage surface problem the stefan problem the elenbaas equation etc are all picked up into our scheme although most of them have been attacked by other methods there are still some new things in our approach especially the multiplicity of the solutions of the elenbaas equation is interesting we prove that there are l 1 and two distinct positive solutions of the equation

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

stability and bifurcations of hysteretic systems subjected to principal parametric excitation dynamic behavior of smooth hysteretic systems subjected to harmonic parametric excitation is investigated wen s differential equation model for hysteresis which can describe a large class of hysteretic systems is used employing the piecewise power series expression for hysteresis proposed in the previous paper the method of multiple scales is applied for the case of principal parametric resonance to obtain the second order approximate solutions and their stability it is shown that the hysteretic systems are unstable inside the principal resonance region but the responses are bounded having symmetric periodic solutions it is also shown that the systems are stable outside the region even if viscous damping does not exist because of hopf bifurcation numerical integrations are also performed to illustrate the nonlinear resonant characteristics of the systems and confirmed that trivial stationary solutions and stable symmetric periodic solutions in principal resonance region bifurcate to produce a pair of non symmetric periodic solutions stability regions with regard to excitation parameters are also illustrated the theoretical and numerical results are compared to examine the validity of the present analysis

stiff well posedness and asymptotic convergence for a class of linear relaxation systems in a quarter plane abstract in this paper we study the asymptotic equivalence of a general linear system of 1 dimensional conservation laws and the corresponding relaxation model proposed by s jin and z xin 1995 comm pure appl math 48 235 277 in the limit of small relaxation rate the main interest is this asymptotic equivalence in the presence of physical boundaries we identify and rigorously justify a necessary and sufficient condition which we call the stiff kreiss condition or skc in short on the boundary condition to guarantee the uniform well posedness of the initial boundary value problem for the relaxation system independent of the rate of relaxation the skc is derived and simplified by using a normal mode analysis and a conformal mapping theorem the asymptotic convergence and boundary layer behavior are studied by the laplace transform and a matched asymptotic analysis an optimal rate of convergence is obtained

heat equations with discontinuous nonlinearities on convex and nonconvex constraints in this paper we use a variational method for solving some semilinear parabolic equations with a discontinuous nonlinearity possibly on either some convex or nonconvex constraints the approach is based on the fact that the solutions of the above mentioned problems can be viewed as steepest descent curves in a suitable sense to be specified for some lower semicontinuous functionals possibly restricted to suitable constraints this abstract framework which is presented in section 1 seems interesting to us in that it provides a unifying tool for treating various kinds of constrained problems including cases in which the constraint is not convex see section 4 moreover the existence theorem that we get holds under reasonably weak assumptions all these ideas in great part originated from the paper lo where a general framework for variational evolution was proposed and are also related to the theory of maximal monotone operators see 4 and some of its extensions see 5 6 9 11 15 17 19 241 for some applications the main difference being in the fact that using compactness we find existence theorems without uniqueness the applications presented can be described roughly speaking as follows given an open set sz c rn and g q x r r possibly discontinuous we search for u 0 t t2 sz which solve wf e g q u t a t v t in i and a e in i

amplitude decay of damped non linear oscillators studied with jacobian elliptic functions approximate bounded solutions of the equation x bx c 1 x c 3 x 3 0 with b 0 c 1 0 and c 3 0 are developed in terms of the jacobian elliptic functions cn cd and dn the solutions are found by following the method developed by christopher in 1973 for the case with c 1 0 and c 3 0 formulas for the amplitude decay are given in two different approximations the solutions are compared with runge kutta numerical integration results and shown to be accurate for a wide range of b c 1 c 3 and initial conditions

relaxation limit for piecewise smooth solutions to systems of conservation laws abstract in this paper we study the asymptotic equivalence of a general system of 1 d conservation laws and the corresponding relaxation model proposed by s jin and z xin 1995 comm pure appl math 48 235 277 in the limit of small relaxation rate it is shown that if the relaxation system satisfies the subcharacteristic condition and the solution of the hyperbolic conservation laws is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition then there exist solutions of the relaxation systems that converge to the solution of the original conservation laws equilibrium system at a rate of order e as the rate of relaxation e goes to zero the proof uses a matched asymptotic analysis and an energy estimate related to the nonlinear stability theory for viscous shock profiles

application of optimal homotopy asymptotic method for the analytic solution of singular lane emden type equation abstract in this study optimal homotopy asymptotic method is applied on singular initial value lane emden type problems to check the effectiveness and performance of the method it is observed that the method is easy to implement quite valuable to handle singular phenomena and yield excellent results at minimum computational cost computational results of some of the test problems are presented to demonstrate the viability and practical usefulness of the method

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

melnikov s criteria and chaos in systems with fractional order deflection in this paper a qualitative analysis of the dynamic systems described with the second order differential equation with fractional order deflection function is considered the existence of fixed points closed orbits and the unions of fixed points and the trajectories connecting them is shown the homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form melnikov s procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function the critical parameter values for chaos are obtained analytically and proved numerically using the lyapunov exponents the bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown the phase plane diagrams and the poincare maps for certain fractional orders are obtained the control of chaos and the transformation to periodic motion is considered

nonlinear dynamic analysis of an electrical machine rotor bearing system by the optimal homotopy perturbation method in this paper an analytical technique called the optimal homotopy perturbation method ohpm is employed to study the nonlinear behaviour of an electrical machine modelled as a rotor supported by two journal bearings with nonlinear suspension the dynamics of the rotor centre and bearing centre are studied and the spatial displacements in the horizontal and vertical directions are obtained it is shown that the main strength of the ohpm is its fast convergence since after only one iteration we obtain very accurate results for a complicated nonlinear problem which proves that this method is very efficient in practice

analyses of oscillators with non polynomial damping terms in this paper the properties of the oscillatory motion of the system with non polynomial damping is investigated the two limits for damping are the dry friction and linear viscous damping the mathematical model of the system is a strong nonlinear differential equation with fraction order velocity terms using the modified version of he s homotopy perturbation method the approximate analytic solution is obtained the generating solution is assumed in the form which corresponds to the system with linear viscous damping two special cases are considered first when the coefficient of the damping force is small and second when the damping force is close to dry friction the obtained analytical solutions are compared with numerical ones they show good agreement

entropy satisfying relaxation method with large time steps for euler ibvps this paper could have been given the title how to positively and implicitly solve euler equations using only linear scalar advections the new relaxation method we propose is able to solve euler like systems as well as initial and boundary value problems with real state laws at very low cost using a hybrid explicit implicit time integration associated with the arbitrary lagrangian eulerian formalism furthermore it possesses many attractive properties such as i the preservation of positivity for densities ii the guarantee of min max principle for mass fractions iii the satisfaction of entropy inequality under an expressible bound on the cfl ratio the main feature that will be emphasized is the design of this optimal time step which takes into account data not only from the inner domain but also from the boundary conditions

weakly nonlinear limit for the relaxation approximation of conservation laws in several space dimensions abstract in this paper the weakly nonlinear limit for the relaxation approximation of conservation laws in several space dimensions is derived through asymptotic expansions and justified by employing the energy estimates compared with the work of g q chen c d levermore and t p liu 1994 comm pure appl math 47 787 830 the main difficulty we confront in our analyzes lies in the fact that the problem of the existence of an convex entropy which was essential in the proof of their estimate 5 29 for the system under our consideration is still an open problem since their theorem 3 2 was proved only for the 2 2 case

periodic solutions for some strongly nonlinear oscillations by he s variational iteration method in this paper we implement a new analytical technique he s variational iteration method for some strongly nonlinear oscillations a correction functional is constructed by using a general lagrange multiplier which can be identified via the variational theory the obtained approximate solutions and periods are compared with exact or numerical results to verify the effectiveness and accuracy of the method

chaotic motion of van der pol mathieu duffing system under bounded noise parametric excitation abstract the chaotic behavior of van der pol mathieu duffing oscillator under bounded noise is investigated by using random melnikov technique a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases which is further verified by the maximal lyapunov exponents of the system the effect of bounded noise on poincare map is also investigated in addition the numerical simulation of the maximal lyapunov exponents

a viability theorem for set valued states in a hilbert space abstract applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact possibly non convex sets rather than vectors this leads to evolutions in a basic set which can be supplied with a metric like the well established pompeiu hausdorff distance but it does not have an obvious linear structure this article extends differential inclusions with state constraints to compact valued states in a separable hilbert space h the focus is on sufficient conditions such that a given constraint set of compact subsets is viable a k a weakly invariant our main result extends the tangential criterion in the well known viability theorem usually for differential inclusions in a vector space to the metric space of non empty compact subsets of h

principal response of duffing oscillator to combined deterministic and narrow band random parametric excitation abstract the principal resonance of a duffing oscillator to combined deterministic and narrow band random parametric excitations is investigated in particular the case in which the parametric terms share close frequencies is examined the method of multiple scales is used to determine the equations of modulation of amplitude and phase the behavior stability and bifurcation of steady state response are studied by means of qualitative analyses jumps are shown to occur if the random excitation is small the effects of damping detuning and magnitudes of deterministic and narrow band parametric excitations are analyzed the theoretical analyses are verified by numerical results

stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws we propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models we consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and when the compensated compactness theory is applicable do converge to a weak solution of the hyperbolic system the schemes use piecewise polynomials of arbitrary degree and their consistency error is of high order we also prove that the rate of convergence of the relaxation system to a smooth solution of the conservation laws is of order o eps

global solutions and zero relaxation limit for a traffic flow model we construct global solutions and study their relaxation limit for a system of nonlinear hyperbolic conservation laws with relaxation arising in traffic flows the system of nonlinear hyperbolic conservation laws with relaxation was derived as a nonequilibrium continuum model of traffic flows the purpose of the new model is to address the anisotropic feature of traffic flows the resulting hyperbolic system with relaxation is marginally stable thus there is no diffusion in the process of relaxation our analysis is vastly different from existing theory for hyperbolic conservation laws with relaxation which relies on the dissipative nature of the relaxation process our analysis is based on a generalized glimm scheme for initial data with bounded total variation we prove that the total variation of the solutions is bounded for all time and the bound is independent of the relaxation parameter thus we obtain the zero relaxation limit finally we make a comparison between our results and data measured on

chaotic motion in the resonant separatrix bands of a mathieu duffing oscillator with a twin well potential the m 1 resonant bands in the left and right potential wells are skew symmetric and the 2m 1 resonant bands of the large orbit motion are symmetric the analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach the numerical predictions of such onset and destruction are also completed by the energy increment spectrum method the sub resonance interaction occurs for strong excitations which needs to be further investigated these results are applicable to the small and large orbit motions of post buckled structure under a parametric excitation

a multigrid homotopy method for nonlinear inverse problems abstract in the present contribution we develop a novel method combining the multigrid idea and the homotopy technique for nonlinear inverse problems in which the forward problems are modeled by some forms of partial differential equations the method first attempts to use the multigrid method to decompose the original inverse problem into a sequence of sub inverse problems which depend on the grid variables and are solved in proper order according to the grid size from the coarsest to the finest and then carries out the inversion on the coarsest grid by the homotopy method the strategy may give a rapidly and globally convergent method as a practical application this method is used to solve the nonlinear inverse problem of a nonlinear convection diffusion equation which is the saturation equation within the two phase porous media flow we demonstrate the effectiveness and merits of the multigrid homotopy method on two actual model problems

period one motions of a mechanical oscillator with periodically time varying piecewise nonlinear stiffness the dynamic behavior of a piecewise nonlinear mechanical oscillator with parametric and external excitations is investigated the viscously damped single degree of freedom oscillator is subjected to a periodically time varying piecewise nonlinear restoring function defined by a clearance surrounded by continuously nonlinear quadratic and cubic regions typical applications represented by this oscillator are highlighted a multi term harmonic balance formulation is used in conjunction with discrete fourier transforms and a parametric continuation scheme to determine steady state period 1 motions of the system due to both parametric and external excitations the accuracy of the analytical solutions is demonstrated by comparing them to direct numerical integration solutions floquet theory is applied to determine the stability of the steady state harmonic balance solutions at the end detailed parametric studies are presented to quantify the combined influence of clearance quadratic and cubic nonlinearities within reasonable ranges of all other system parameters a comparison between time varying and time invariant systems is also provided to demonstrate the influence of the parametric and external excitations on a piecewise nonlinear system

averaging method using generalized harmonic functions for strongly non linear oscillators abstract an averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non linear oscillators g x e x and g x ef x t where g x is an arbitrary non linear function the method gives the approximate solutions in terms of generalized harmonic functions these functions are also periodic and are exact solutions of strongly non linear differential equations some phenomena considered include limit cycles of strongly non linear autonomous oscillators and steady state response of strongly non linear oscillators subject to weak harmonic excitation the procedure is simple and easy to apply

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

impulse capture basins of sets under impulse control systems given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions that are hybrids of continuous and discrete evolutions this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set it is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time it also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints

on the barenblatt model for non equilibrium two phase flow in porous media we prove global existence and uniqueness of solutions to a quasilinear goursat problem which was proposed by g i barenblatt to describe non equilibrium two phase fluid flow in permeable porous media when the equilibrium relaxation time tends to zero the solution is shown to converge to the entropy solution of the corresponding initial boundary value problem for the classical buckley leverett equation

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

dichotomous noise induced chaos in a generalized duffing type oscillator with fractional order deflection abstract the chaotic behavior of a generalized duffing type oscillator with fractional order deflection under dichotomous noise excitation is discussed in detail using the melnikov method together with mean square criterion necessary conditions for the onsets of chaos are derived it is shown that with the increase of noise transition rate the threshold of noise amplitude for chaos firstly decreases to a minimum and then increases the effects of dichotomous noise on the duffing type oscillator are also obtained by vanishing the mean largest lyapunov exponent of the oscillator this is further verified by phase portraits and time histories with numerical simulations

maximal lyapunov exponent and almost sure stability for stochastic mathieu duffing systems abstract the principal resonance of a mathieu duffing oscillator to random excitation is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning cubic term and magnitudes of random excitation are analyzed the explicit asymptotic formulas for the maximal lyapunov exponent is obtained the almost sure stability or instability of the stochastic mathieu duffing system depends on the sign of the maximal lyapunov exponent in the last part of the work the numerical results are obtained

characteristic properties of subharmonic oscillations and their application in vibration engineering the results of a theoretical and experimental study of subharmonic vibrations in nonlinear mechanical systems of different structural complexity are presented specific nonlinear properties of subharmonic regimes complex vibration spectrum essential asymmetry of time response predominance of low frequency harmonic components in vibration spectrum etc are studied it is shown that utilizing these nonlinear effects ensures more effective operation of vibromachines for different technological purposes vibrocompaction vibroforming vibration emptying etc the original procedure of program simulated actuation of subharmonic vibromachine is proposed

an equivalent direct modeling of a rotary shaft with hot fit components using contact element modal analysis results one key factor in designing a motor built in high speed motor spindle is to assemble the motor rotor and shaft by means of hot fit in a previous study the optimization approach was recommended by introducing an equivalent local young s modulus characterizing the effects on the local stiffness of the shaft at the location of hot fit this approach being based on the modal testing results is a posterior improvement in this paper contact pressure between the rotor and the shaft is firstly calculated through contact theory the stress state is thus determined the contact element modal analysis then follows with the stress state as a pre stressed condition the effects of pre stress are then adopted for subsequent contact element modal analysis the accuracy and the validity of the finite element results are verified by modal testing finally an equivalent direct modeling is suggested as an efficient alternative this equivalent model is constructed with line elements and the model is created based on the results obtained from the contact element modal analysis the results obtained from this study indicate that the equivalent direct model with line elements is accurate and efficient in analyzing the dynamic behavior of a rotary shaft system with hot fit components

comparison of some approaches to stability of a sdof system under random parametric excitation we give a rigorous comparison of the asymptotic stochastic averaging method and the moment lyapunov exponent approach in assessing the mean square stability through an example of a single degree of freedom system under small periodic parametric excitation with random phase modulation the comparison is based on an efficient numerical procedure to determine the regions of mean square stability

generalized parametric resonance in electrostatically actuated microelectromechanical oscillators this paper investigates the dynamic response of a class of electrostatically driven microelectromechanical mem oscillators the particular systems of interest are those which feature parametric excitation that arises from forces produced by fluctuating voltages applied across comb drives these systems are known to exhibit a wide range of behaviors some of which have escaped explanation or prediction in this paper we examine a general governing equation of motion for these systems and use it to provide a complete description of the dynamic response and its dependence on the system parameters the defining feature of this equation is that both the linear and cubic terms feature parametric excitation which in comparison to the case of purely linear parametric excitation e g the mathieu equation significantly complicates the system s dynamics one consequence is that an effective nonlinearity for the overall system cannot be defined instead the system features separate effective nonlinearities for each branch of its nontrivial response as such it can exhibit not only hardening and softening nonlinearities but also mixed nonlinearities wherein the response branches in the system s frequency response bend toward or away from one another near resonance this paper includes some brief background information on the equation of motion under consideration an outline of the analytical techniques used to reach the aforementioned results stability results for the responses in question a numerical example explored using simulation of a mem oscillator which features this nonlinear behavior and preliminary experimental results taken from an actual mem device which show evidence of the analytically predicted behavior practical issues pertaining to the design of parametrically excited mem devices are also considered

improvement of a krylov bogoliubov method that uses jacobi elliptic functions abstract an improved version of a krylov bogoliubov method that gives the approximate solution of the non linear cubic oscillator x c 1 x c 3 x 3 ef x x dot 0 in terms of jacobi elliptic functions is described compact general expressions are given for the time derivatives of the amplitude and phase similar to those obtained by the usual krylov bogoliubov method which gives the approximate solution in terms of circular functions these expressions are especially simple for quasilinear c3 0 and quasi pure cubic c1 0 oscillators two types of cubic oscillators have been used as examples the linear damped oscillator f x x dot x dot and the van der pol oscillator f x x dot x 2 x dot the approximate solutions of these quasilinear and quasi pure cubic oscillators are simple and accurate the influence of the non linearity on the rate of variation of the amplitude of these two types of cubic oscillators was also studied

determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method this paper deals with the nonlinear oscillations of a particle which moves on a rotating parabola an analytic approximate technique namely optimal homotopy asymptotic method oham is employed to propose an analytic approach to solve nonlinear oscillations the validity of the oham is independent on whether or not there exist small or large parameters in the considered nonlinear equations our procedure provides us with a convenient way to optimally control the convergence of the approximate solutions an example is given and the results reveal that this procedure is very effective simple and accurate this paper demonstrates the general validity and the great potential of the oham

optimal homotopy asymptotic method for solving nonlinear fredholm integral equations of second kind abstract the aim of this communication is to present the effectiveness of optimal homotopy asymptotic method oham for solving nonlinear fredholm integral equations of second kind here we consider the first second and third order fredholm integral equations of second kind comparisons are made with adomian decomposition method discrete adomian decomposition method homotopy perturbation method quasi interpolation method triangular functions method trapezoidal rule and simpson rule the results reveal that the oham is very effective simple and has close agreement with exact solutions

convergence rates for relaxation schemes approximating conservation laws in this paper we prove a global error estimate for a relaxation scheme approximating scalar conservation laws to this end we decompose the error into a relaxation error and a discretization error including an initial error omega ep we obtain the rate of convergence of sqrt ep in l1 for the relaxation step the estimate here is independent of the type of nonlinearity in the discretization step a convergence rate of sqrt del x in l1 is obtained these rates are independent of the choice of initial error omega ep thereby we obtain the order 1 2 for the total error

cauchy problem for hyperbolic conservation laws with a relaxation term this paper considers the cauchy problem for hyperbolic conservation laws arising in chromatography

convergence of relaxation schemes to the equations of elastodynamics we study the effect of approximation matrices to semi discrete relaxation schemes for the equations of one dimensional elastodynamics we consider a semi discrete relaxation scheme and establish convergence using the l p theory of compensated compactness then we study the convergence of an associated relaxation diffusion system inspired by the scheme numerical comparisons of fully discrete schemes are carried out

space localization and well balanced schemes for discrete kinetic models in diffusive regimes we derive and study well balanced schemes for quasi monotone discrete kinetic models by means of a rigorous localization procedure we reformulate the collision terms as nonconservative products and solve the resulting riemann problem whose solution is self similar the construction of an asymptotic preserving ap godunov scheme is straightforward and various compactness properties are established within different scalings finally some computational results are supplied to show that this approach is realizable and efficient on concrete 2 2 models

improved lindstedt poincare method for the solution of nonlinear problems abstract we apply the linear delta expansion lde to the lindstedt poincare distorted time method to find improved approximate solutions to nonlinear problems we find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator duffing equation of the non linear pendulum and of more general anharmonic potentials the approximate solutions found with this method converge more rapidly to the exact ones than in the simple lindstedt poincare method

numerical solutions of weakly singular volterra integral equations using the optimal homotopy asymptotic method the purpose of this paper is to apply a numerical technique namely the optimal homotopy asymptotic method oham for finding the approximate solutions of a class of volterra integral equations with weakly singular kernels this method uses simple computations with quite acceptable approximate solutions which has close agreement with exact solutions illustrative examples are included to demonstrate the validity and applicability of the present method and a comparison has been made with existing results

a relaxation scheme for conservation laws with a discontinuous coefficient lwe study a relaxation scheme of the jin and xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient k x if k e bv we show that the relaxation scheme produces a sequence of approximate solutions that converge to a weak solution the murat tartar compensated compactness method is used to establish convergence we present numerical experiments with the relaxation scheme and comparisons are made with a front tracking scheme based on an exact 2 x 2 riemann solver

construction of approximate analytical solutions to a new class of non linear oscillator equation the principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire by assuming that harmonic balance will hold solutions are devised for a steady state limit cycle and or limit point motion a method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective fourier expansions the latter technique is actually a generalization of the method proposed by kryloff and bogoliuboff 1943

tuneable non degenerated nonlinear parametrically excited amplifier abstract the proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator parametric amplifiers had been studied extensively although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier s natural frequency these amplifiers are confined to amplifying predetermined frequencies the proposed parametric amplifier s bandwidth is indeed tuneable to nearly any input frequency not bound to be an integer multiple of a natural frequency in order to tune the stiffness and induce a variable frequency parametric excitation a digitally controlled electromechanical element must be incorporated in the realization we introduce a novel parametric amplifier with nonlinearity duffing type hardening that bounds the otherwise unlimited amplitude moreover we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system and thus to transform external excitations to a frequency band where signal levels are considerably higher using the method of multiple scales analytical expressions for the responses have been retrieved and verified numerically parametric studies of the amplifiers gain sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically the results demonstrate the advantage of the proposed approach over existing schemes practical applications envisaged for the proposed method will be outlined

the modified homotopy perturbation method for solving strongly nonlinear oscillators in this paper we propose a reliable algorithm for the solution of nonlinear oscillators our algorithm is based upon the homotopy perturbation method hpm laplace transforms and pade approximants this modified homotopy perturbation method mhpm utilizes an alternative framework to capture the periodic behavior of the solution which is characteristic of oscillator equations and to give a good approximation to the true solution in a very large region the current results are compared with those derived from the established runge kutta method in order to verify the accuracy of the mhpm it is shown that there is excellent agreement between the two sets of results results also show that the numerical scheme is very effective and convenient for solving strongly nonlinear oscillators

nagumo type condition for partial differential inclusions on etudie un probleme de la forme x t ax t g xc h x o x 0 k t o t x t k ou a est un operateur elliptique et k n est pas necessairement compact on trouve des conditions tangentielles de type nagumo

vibrations in a parametrically excited system abstract this paper deals with vibrations of parametrically excited non linear systems with one degree of freedom the non linearity is cubic and is of the same order as the linear terms the parametric vibrations are excited by a periodical force of jacobi elliptic type the mathematical model of the system is a special type of non linear hill s equation the analytical approximate solution of the equation is obtained applying the elliptic krylov bogolubov method method of variable phase and amplitude developed for strong non linear differential equation of duffing type it enables the regions of unbounded solution to be defined approximately the parameters of a dynamic absorber which transforms the motion to regular are calculated in this paper

convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws we prove the convergence of flux vector splitting schemes associated to hyperbolic systems of conservation laws with a single compatible entropy c we prove estimate on the l2 norm of the gradient of the numerical approximation in the inverse square root of the space increment x this estimate is related to the notion of strictly c dissipativity on f f and id f f where f f is the flux decomposition the second tool of the proof is a kinetic formulation of the flux splitting scheme with three velocities then we get a control for all entropies and apply the compensated compactness theory

viability theorems for a class of differential operator inclusions abstract this paper discusses the following viability problem of a differential inclusion x t ax t f x t x 0 x0 k t 0 x t k where k is a compact subset of a banach space x a is the infinitesimal generator of a compact differentiable semigroup of bounded linear operators on x and f k x is upper semicontinuous with compact convex values we show that a natural tanegential condition is necessary and sufficient for the existence of a global solution to this problem

stability analysis of the non linear mathieu equation abstract the non linear mathieu equation is analyzed within the framework of the method of normal forms analytical conditions for explosive instability are obtained and expressions for the period as well as the amplitude of the stable response are derived

the optimal homotopy asymptotic method for solving blasius equation starting from the reality that many known methods fail in the attempt to obtain analytic solutions of blasius type equations in this work a new procedure namely optimal homotopy asymptotic method oham is proposed to obtain an explicit analytical solution of the blasius problem comparison with howarth s numerical solution as well as the obtained residual reveals that the proposed method is highly accurate this proves the validity and great potential of the proposed procedure oham as a new kind of powerful analytical tool for nonlinear problems

an analytical approach to the dynamic analysis of a rotating electric machine this study presents an analytical approach to the dynamic problem encountered by a rotating electric machine supported by nonlinear bearings with damping properties subjected to a forcing excitation caused by an unbalanced force and a parametric excitation caused by an axial thrust the method employed in this analytical study is the optimal variational iteration method ovim which proves to be very effective and accurate in solving nonlinear problems the results are presented in the form of a time displacement response the results obtained from numerical simulations are in very good agreement with the approximate analytical results obtained through the proposed method

an artificial parameter linstedt poincare method for the periodic solutions of nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable abstract an artificial parameter linstedt poincare method is presented and used to determine the periodic solution of a nonlinear singular oscillator for small and large amplitudes comparisons with the results of harmonic balance two level iterative linearized harmonic balance and parameter perturbation methods are presented

accurate analytical solutions to oscillators with discontinuities and fractional power restoring force by means of the optimal homotopy asymptotic method in this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to sign x a very fast convergence to the exact solution was proved since the second order approximation lead to very accurate results comparisons with numerical results are presented to show the effectiveness of this method four numerical applications prove the accuracy of the method which works very well for the whole range of initial amplitudes the obtained results prove the validity and efficiency of the method which can be easily extended to other strongly nonlinear problems

on the relaxation approximation of boundary control of the isothermal euler equations we consider the isothermal euler equations without friction that simulate gas flow through a pipe we consider the problem of boundary stabilisation of this system locally around a given stationary state we present a feedback law that is linear in the physical variables and yields exponential decay of the system state for the numerical solution of hyperbolic systems of conservation laws the jin xin relaxation scheme can be used therefore we also consider the boundary stabilisation of the relaxation system by the linear riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system

the cauchy problem for hyperbolic conservation laws with three equations where a b t are nonnegative constants when b s 0 system 1 1 can be w x used to model the adiabatic gas flow through porous media 5 where is specific volume u denotes velocity s stands for entropy and s denotes pressure its form in euler coordinates is also a model of isothermal w x unsteady two phase flow in pipelines 1 in this paper we study the global generalized solution for this case the case b 0 when written in euler

transition curves in a parametrically excited pendulum with a force of elliptic type this article investigates the equilibria and stability of a pendulum when the support has a prescribed motion defined by an elliptic function stability charts are generated in the parameter plane for different values of the elliptic function modulus numerical integration and floquet theory are used to generate stability charts that are later obtained through harmonic balance analysis it is shown that the size and location of the instability tongues is directly linked to the elliptic function modulus comparisons are also made between the stability charts of mathieu s equation and those of the pendulum when the prescribed motion is defined by an elliptic function

the energy in one dimensional rate type semilinear viscoelasticity abstract the existence and properties of a free energy function compatible with the second law of thermodynamics in one dimensional rate type semilinear viscoelasticity is analysed necessary and sufficient conditions are given such that a free energy as a function of strain and stress exists and is unique that it is a non negative function and possesses a monotony property with respect to the equilibrium curve a bound in energy for the smooth solutions of certain initial and boundary value problems with respect to the input data is established when the equilibrium curve is a nonmonotonic curve i e the free energy function is a non convex one thus iron like behaviour for instance is also included an l 2 approach to equilibrium is also discussed