Home HomeW S Gan, Acoustical Services Pte Ltd (Singapore)
Nonlinear Vibration Signals are more well-defined and established that nonlinear noise signals which most works are dealing with electronic noise and the unwanted noise in signals. In this paper, we will consider nonlinear industrial and machinery noise. In particular non-Gaussian noise and chaotic signals and nonlinear vibration signals. First we consider chaotic signals. Here two types of fractal functions are used to represent them: the Weierstrass function and the radial basis function. These functions have to be subjected to computation of their fractal dimension. The Hausdorff definition of fractal dimension is used. Next the technique of higher order statistics is used to process nonlinear noise and vibration signals. The bispectrum is used which is a nonlinear generalisation of the spectral approach to linear time-series analysis. Here we review the method of estimation of bispectrum and study possible applications to non-Gaussian signals, such as chaos. We find that the estimated bispectrum could be used to distinguish between nonlinear deterministic stable systems and nonlinear deterministic chaotic systems. We also consider the properties of one nonlinear model, called bilinear model and study their application to nonlinear noise and vibration signals processing.
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A.J. Clark, VIPAC Engineers and Scientists Ltd (Australia)
L.J. Schmid, VIPAC Engineers and Scientists Ltd (Australia)
David C. Rennison, VIPAC Engineers and Scientists Ltd (Australia)
As part of the introduction of the J version of thc C-130 Hercules Aircraft it was decided to redesign the aluminium centre and outer wing flaps in composite in order to improve their sonic fatigue durability. Inherent in the process was the need to predict the response of the composite flaps to the acoustic environment: the response was found to be highly non-linear due primarily to the combined action of bending and membrane effects. The paper presents the numerical and analytical methods used to predict vibration levels and provides a comparison with measured responses. It is shown that effects can greatly reduce the maximum response and to ignore them results in highly overestimated strain levels with an associated reduction of associated fatigue life.
sv970496.pdf (Scanned) TOPShamil U. Galiyev, University of Auckland (New Zealand)
Nonlinear, dispersive and viscous terms in the Boussinesq type equation, written for displacement u, are considered as second order values. Media fixed at x=0 (u=0) and excited at x =L (u= lcos wt) are studied. Periodical solutions of the Boussinesq equation are sought by the perturbation method. As a first approximation u = f(r) f(s), where f(r) and f(s) are right- and left-hand side traveling waves. Far from a resonance u is a smooth standing wave. Nonsmooth traveling waves appear in the solutions within a frequency band around some resonant frequencies. The solutions display on the one hand generation and interaction of kink-, solitary-and cnoidal- type waves and on the other hand weak nonlinear (quadratic) interaction left- and right-hand side traveling waves. The solutions describe well the resonant sloshing of water [ 1], and nonlinear waves in porous [2], bubbly [3,4] and granular [5] media.
sv970428.pdf (Scanned) TOPA.K. Abramian, Institute for Problems in Mechanical Engineering (Russia)
The aim of this paper is to describe some new physical effects which (as it has been shown in preliminary investigations) could appear in the interaction between elastic solid of a complicated form and flows of fluid. These basic effects can be described as follows: a) a possibility of existence of localized in space time periodical modes (quasimodes) (in linear models); b) a weak delocalization of these modes ( as a result of resonances in non-linear models); c) a possibilityy of existence of coherent chaotic and quasiperiodic interaction of these modes; In connection with c), we developed the theory of control of these coherent structures. By adjusting the elastic system parameters one can control the properties of localized modes and their time behaviour. The existence of localized modes leads to sharp gradients of additional vibration fluid pressure which acts on the elastic solid (construction), In turn, it could lead to the significant radiation of the construction. The other aim is to know where maxima of this pressure are localized, in order to reinforce the construction. A mathematical analysis shows that there are possible effects a,b and c for potentials V(i) of a singular form. We are going to use different methods to resolve problems. First we will find localized modes and quasimodes for linear equation. The second step is an investigation of the dynamics in nonlinear models. It allows to consider the points b,c and it can be done by two ways: by traditional perturbation theory and by methods of infinite-dimensional KAM theory. As for point c, for dissipative, authors developed mathematically rigorous analytic theory for dissipative systems where the existence of coherent chaotic structures consisting of localized modes has been proved and also it has shown that one can control the inertial form (and thus attractor of system). Developed approaches can be applied also to conservative systems. It should solve problem c and create an algorithm control of coherent structures and their time behaviour in systems. We suppose that one can obtain all type of hamiltonian chaos and that one can control the chaos form adjusting the system parameters.
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S.A. Safi, University of New South Wales (Australia)
D.W. Kelly, University of New South Wales (Australia)
R. Mohajeri, Sydney University (Australia)
This paper investigates the aeroelastic response of a wing-aileron system subject to incompressible flow. A three degree of freedom wing-aileron model is derived and free-play non-linearity is introduced in the aileron control circuit stiffness. The resulting equations of motion for the system are integrated numerically to give the time history of the wing-aileron motion. It is found that the aileron demonstrate a sustained oscillation well below the linear flutter speed. The effects of the amount of free-play on the aeroelastic response of the system is examined. The amplitude of the sustained oscillation is strongly dependent on the amount of free-play in the aileron stiffness and could provide a catastrophic feedback accelerating the wear which leads to free-play.
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Valery G. Andreev, Moscow State University (Russia)
N.B. Brandt, Moscow State University (Russia)
O.V. Rudenko, Moscow State University (Russia)
Nonlinear wave physics deals basically with effects connected with evolution of disturbances of finite amplitude. A slow distortion of time-spatial and spectral characteristics is observed with wave propagation. But nonlinear effects may be already pronounced at small wave distances from a radiator and they can have a significant influence on the process of radiation of itself. In this paper a radiation of a flat piston vibrating with high amplitude is studied theoretically. At a first step a solution for a piston motion driven by external force is determined. It is shown that a piston subjected to the harmonic force of large amplitude can radiate not only the fundamental frequency but high order harmonics as well. A form of particle vibration near a piston face is disturbed. A nonlinear reaction to radiation is arisen also .
sv970334.pdf (Scanned) TOPStefan Kaczmarczyk, University of Natal (South Africa)
Longitudinal and lateral oscillations in a catenary-vertical hoisting cable system are investigated. The main sources of external excitation in the system are taken into consideration, namely a load due to the winding cycle acceleration/deceleration profile, and a periodic excitation due to the coiling mechanism applied at the winder drum surface. Due to the time-varying length of the vertical cable the natural frequencies and mode shapes of the system vary slowly with time. The system is therefore nonstationary, and its response is qualitatively different from the response of the corresponding stationary parameter system. A mathematical model describing the lateral response of the catenary, and the coupled longitudinal response of the vertical rope, is derived. The non-linear partial-differential equations of motion are discretised by writing the deflections in terms of the linear, free-vibration modes. A non-linear set of ordinary-differential equations with slowly varying coefficients results. The dynamic response of a model example is simulated numerically. The simulation predicts strong modal interactions during a passage through the primary and internal resonances of the system.
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Gyu-Sang Choe, LG Electronics Inc. (Korea)
Kwang-Joon Kim, Korea Advanced Institute of Science and Technology (Korea)
The force acting on the reciprocating piston during a compression cycle shows typically non-linear dynamic behavior in electrodynamic piston compressors. In order to increase the efficiency in design, in this paper, the compression cycle is modeled as a linear spring and a hysteretic damper by 4 different methods. Hysteretic damping coefficient is obtained in all of the 4 methods based on the dissipation energy equivalency corresponding to the area of pressure-volume diagram. Regarding the stiffness, the simplest method is to use the slope of two extreme points in the diagram. Another simple method is to derive the stiffness coefficient by applying piecewise equivalency of the potential energy. The other two methods are to apply describing function approach to the compression cycle alone and a single degree of freedom system comprising the reciprocating compressor cycle. Characteristics of the 4 linearized dynamic models are compared with the full nonlinear model, which are obtained by numerical integration for various parameters.
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