Influence Of Nonlinear Terms Research Articles

STABILITY OF THE FLYWHEEL ENGINE IN A CARDAN SUSPENSION

A mathematical model of a flywheel engine in a cardan suspension and also its motion stability research is offered. A mechanical system with an ecologically clean energy source in the form of a flywheel in a gimbal mounted on a vibrating base is under consideration. Such a model of mechanical systems occupies, in some sense, an intermediate place between a gyroscope and a flywheel that rotates in rigidly fixed supports. Currently, we have extensive experience in researching the stability and oscillations of nonlinear systems described by nonlinear differential equations. However, the use of the mathematical theory of stability for specific problems continues to be a relevant task. The problem of stability of the proposed mechanical system is considered using the second Lyapunov method, which is applied to definitly positive functions characterizing the slow evolution of the process. The equations of motion were formulated and the influence of nonlinear terms in the equations of motion on stability was investigated. The study of the stability of the mechanical system under initial disturbances is presented, as well as the conclusions of the system movement behavior are made.

Rotation Angle Control Strategy for Telescopic Flexible Manipulator Based on a Combination of Fuzzy Adjustment and RBF Neural Network

The length of flexible manipulators with a telescopic arm alters during movement. The dynamic parameters of telescopic flexible manipulators exhibit significant time-varying characteristics owing to variations in length. With an increase in the manipulators’ length, the nonlinear terms caused by flexibility in the manipulators’ dynamic equations cannot be ignored. The time-varying characteristics and nonlinear terms of telescopic flexible manipulators cause fluctuations in rotation angles, which affect the operation accuracy of end-effectors. In this study, a control strategy based on a combination of fuzzy adjustment and an RBF neural network is utilized to improve the control accuracy of flexible telescopic manipulators. First, the dynamic equation of the manipulators is established using the assumed mode method and Lagrange’s principle, and the influence of nonlinear terms is analyzed. Subsequently, a combined control strategy is proposed to suppress the fluctuation of the rotation angle in telescopic flexible manipulators. The variation ranges of the feedforward PD controller parameters are determined by the pole placement strategy and length of the manipulators. Fuzzy rules are utilized to adjust the controller parameters in real-time. The RBF neural network is utilized to identify and compensate the uncertain part of the dynamic model of the flexible manipulators. The uncertain part comprises time-varying parameters and nonlinear terms. Finally, numerical simulations and prototype experiments prove the effectiveness of the combined control strategy. The results prove that the proposed control strategy has a smaller standard deviation of errors. Therefore, the combined control strategy is more suitable for telescopic flexible manipulators, which can effectively improve the control accuracy of rotation angles.

Influence of Nonlinear Terms on Orbital Stability of Solitary Wave Solutions to the Generalized Symmetric Regularized-Long-Wave Equation

The influence of two nonlinear terms on the orbital stability of solitary wave solutions to the generalized symmetric regularized-long-wave(gsrlw) equation is investigated in this paper. Based on the general conclusion to judge the orbit stability of solitary wave solution to the equation, the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with two low order nonlinear terms are given. By appropriate transformation and scaling, the complexity caused by two high-order nonlinear terms is overcome, and the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with high-order nonlinear terms are also obtained. Last, the influences of the coefficients and the order of the nonlinear terms on the stability of solitary wave solutions are studied.

Influence of nonlinear terms on dynamical behavior of graphene reinforced laminated composite plates

This research is focused on the effects of nonlinear terms on the dynamical behavior of graphene reinforced laminated composite plates. Firstly, the governing equations of the graphene reinforced composite thin plate subjected to transverse excitations are derived by using the Hamilton's principle and the von Karman deformation theory. Then numerical method is applied to investigate the nonlinear behaviors of graphene reinforced composite plates. Bifurcation diagram, waveform and phase portrait are demonstrated to analyze the nonlinear dynamics of the graphene reinforced laminated composite plates. Furthermore, the effects of nonlinear terms on the dynamical behavior are discussed in detail, where both the stronger and weaker nonlinear characteristics of lower modes of the plate are presented. Moreover, some interesting phenomena are obtained in numerical simulation.

Nonlinear sound propagation on acoustic phased array

This paper presents the numerical result of sound propagation on an acoustic phased array in water environment using the approach based on the Navier–Stokes equation. The numerical calculation is carried out on the axisymmetric sound propagation of phase-shifted signals emitted from two transducers with and without nonlinear terms in the governing equations. The result shows that the influence of nonlinear terms is found on the sound pressure field, especially in out-of-phase emission. The nonlinear effect appears for the sound amplitude larger than 0.01MPa and it increases abruptly with an increase in the source pressure amplitude.

Vacancy-driven stress relaxation in layers

The role of vacancies together with their generally non-ideal sources and sinks has been investigated previously in the context of multi-component diffusion. This concept is applied to a thin layer on a substrate subjected to an initial eigenstress state. The surface of the layer is assumed to act as an ideal source and sink for vacancies. The interface may act either as an ideal or as no source and sink for vacancies. Non-ideal sources and sinks are supposed in the bulk. The formation of a vacancy site fraction profile across the layer due to active sources and sinks and due to diffusion is studied, provoking a relaxation of the residual eigenstress state. A set of two nonlinear partial differential equations for both the vacancy site fraction and the eigenstress distributions is developed. The problem is reformulated in dimension-free quantities. The relation between the diffusivity and the activity of sources and sinks for vacancies in the bulk is characterized by a vacancy intensity parameter k. Numerical solutions are presented, and the influence of nonlinear terms in the evolution equations is evaluated. The simulations provide the evolution of the vacancy site fraction and of the hydrostatic stress profiles in the layer. The development of a film of newly deposited or removed atoms at the layer surface and of the total thickness of the layer is also calculated. The results of simulations are discussed.

Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth

Abstract. We analyze coupled Alfvén and slow magnetosonic eigenmodes in a dipole geomagnetic field with different ionospheric conductivities in the framework of ideal magnetic hydrodynamics (MHD) with finite pressure. We use numerical and, if possible, analytical methods to describe eigenmode frequencies, growth rates and eigenfunctions. The spectrum of Alfvén and slow magnetosonic modes is discrete and equidistant. The frequencies of the first Alfvén and slow magnetosonic eigenmodes are estimated as ~1 Hz and ~1 mHz, respectively. In the case of finite conductivity, periodic and aperiodic modes are separated and their interaction analyzed. It was shown that periodic and aperiodic perturbations can mutually transform into each other. A new flute stability criterion is derived (α~4.25), which is stricter than the Gold criterion (α=20/3). Here, as usual, α=−L/p dp/dL. For flute perturbations, the deviations of transversal displacement from a constant are calculated. An approximation for longitudinal displacement is derived. We determined the position of the main longitudinal peak, which can be responsible for nonlinear structures observed by Freja. An influence of nonlinear terms in pressure is estimated as well.

A systematic solution methodology for inferential multivariate modelling of industrial grinding process

Abstract The need for precision components and parts in manufacturing industries has bought an increase in the need for finishing operations that can satisfy this demand. In addition, there is a continuous demand for hard and tough materials that can withstand varying stress conditions to ensure prolonged service life of components and parts. The need to process these materials economically so as to meet stringent product quality requirements (generally expressed as composite of a family of properties, so-called multiple response characteristics) has become a real challenge for researchers and practitioners in manufacturing industries. Grinding has the potential to meet these critical needs for accurate and economic means of finishing parts, and generate the required surface topography. Despite this importance and popularity, grinding still remains one of the most difficult and least-understood processes due to lack of adequate inferential mechanistic and analytical multivariate models, for varied industrial situations. In this context, data-driven inferential linear or nonlinear multiple statistical regression, and artificial neural network modelling have become increasingly popular techniques for complex industrial grinding processes. Unfortunately, these techniques are either proposed and implemented in isolation or presented as a comparative evaluation grinding case study. A systematic solution methodology for inferential multivariate modelling, which addresses the different phases, starting from preliminary linear random x -case multivariate regression model, hypothesis testing of influence of addition of higher-order nonlinear terms to the adequate linear model (or presence of nonlinearity), and subsequent selection of a suitable nonlinear artificial neural network-based multivariate model, is lacking. In view of the above-mentioned conditional requirements, this paper attempts to provide a systematic methodology to develop a multivariate linear regression model, hypothesis testing for the influence of nonlinear terms to linear model, and accordingly selection of a suitable artificial neural network-based inferential model with improved prediction accuracy and control of grinding behaviour. The methodology suggests the use of various statistical techniques, such as Q–Q (quantile–quantile) plotting, data transformation, data standardization, outlier detection test, model adequacy test, model cross-validation and generalization. The suitability of the recommended methodology is illustrated with the help of an engine cylinder liner grinding (honing) case example, in a leading automotive manufacturing unit in India.

The influence of nonlinear terms in mechanical systems having two degrees of freedom

For many years the higher order stochastic averaging method has been widely used for investigating nonlinear systems subject to white and coloured noises to predict approximately the response of the systems. In the paper the method is further developed for two-degree-of-freedom systems subjected to white noise excitation. Application to Duffing oscillator is considered.

Stability analysis of ships undergoing strong roll amplifications in head seas

A new mathematical model with nonlinearities defined up to the third order in terms of the heave, roll and pitch couplings is introduced, in order to simulate strong roll parametric amplifications in head seas. The influence of hull stern shape is discussed. A theoretical analysis discloses some essential dynamical characteristics associated with the proposed coupled third order mathematical model The influence of nonlinear terms on the dynamics of roll parametric resonance appears to be relevant for low metacentric conditions and extreme waves in the head seas condition.

On the non-linear geodetic boundary value problem for a fixed boundary surface

The fixed gravimetric boundary value problem of Physical Geodesy is a nonlinear, oblique derivative problem. Expanding the non-linear boundary condition into a Taylor series—based upon some reference potential field approximating the geopotential—it is shown that the numerical convergence of this series is very rapid; only the quadratic term may have some practical impact on the solution. The secondorder solution term can be described by a spherical integral formula involving the deflections of the vertical with respect to the reference field. The influence of nonlinear terms on the figure of the level surfaces (e.g. the geoid) is roughly estimated to have an order of magnitude of some few centimetres, based upon a Somigliana-Pizzetti reference field; if on the other hand some high-degree geopotential model is used as reference then the effects by non-linearity are negligible from a practical point of view.

Nonlinear interactions of gravity-capillary waves: Lagrangian theory and effects on the spectrum

A weakly nonlinear inviscid theory describing the interactions within a continuous spectrum of gravity-capillary waves is developed. The theory is based on the principle of least action and uses a Lagrangian in wavenumber-time space. Advantages of this approach compared to the method of Valenzuela & Laing (1972) are much simplified mathematics and final equations and validity on a longer timescale. It is shown that much of the development of the spectrum under the influence of nonlinear terms can be understood without actually having to integrate the equations. To this end multiwave space, a new concept comparable with phase space, is introduced. Using multiwave space the magnitude of the nonlinear transfer is estimated and it is shown how the energy goes through the spectrum. Also it is predicted that at fixed wavenumbers, the smallest being 520 m −1 , finite peaks will arise in the spectrum. This is confirmed by numerical integrations. From the integrations it is also deduced that nonlinear interactions are at least as important to the development of the spectrum as wind growth. Finally it is shown numerically that the near-Gaussian statistics of the sea surface are unaffected by nonlinear interactions.

Influence of dissipation on the propagation of a spherical explosion shock wave

The problem of the propagation of an explosion shock wave in a weakly compressible viscous medium at low Reynolds numbers is solved by the method of asymptotic expansions. The influence of non-linear terms in the principal approximation is studied, and the law of wave amplitude damping and its profile are found.

Influence of non-linear terms in the flux equation on the particle growth

physica status solidi (a)Volume 82, Issue 1 p. K21-K25 Structure Influence of non-linear terms in the flux equation on the particle growth O. Simmich, O. Simmich Sektion Mathematik/Physik der Pädgogischen Hochschule N.K. Krupskaja, Halle Search for more papers by this author O. Simmich, O. Simmich Sektion Mathematik/Physik der Pädgogischen Hochschule N.K. Krupskaja, Halle Search for more papers by this author First published: 16 March 1984 https://doi.org/10.1002/pssa.2210820146 Kröllwitzer Str. 44, DDR-4020 Halle (Saale), GDR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume82, Issue116 March 1984Pages K21-K25 RelatedInformation