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1.
A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is
constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via
an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is
derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid
bodies subject to accelerative damping is developed. The double phase–frequency resonance of a two-mass system is studied 相似文献
2.
In this paper, the nonlinear free vibration of a stringer shell is studied. The mathematical model of the string shell, which is the most convenient for frequency analysis, is considered. Due to the geometrical properties of the vibrating shell, strong nonlinearities are evident. Approximate analytical expressions for the nonlinear vibration are provided by introducing the extended version of the Hamiltonian approach. The method suggested in the paper gives the approximate solution for the differential equation with dissipative term for which the Lagrangian exists. The aim of this study is to provide engineers and designers with an easy method for determining the shell nonlinear vibration frequency and nonlinear behavior. The effects of different parameters on the ratio of nonlinear to linear natural frequency of shells are studied. This analytical representation gives excellent approximations to the numerical solutions for the whole range of the oscillation amplitude, reducing the respective error of the angular frequency in comparison with the Hamiltonian approach. This study shows that a first-order approximation of the Hamiltonian approach leads to highly accurate solutions that are valid for a wide range of vibration amplitudes. 相似文献
3.
We pose the problem of self-excitation of elastic wave torsional vibrations of a rotating drill string, which arise as a result
of frictional interaction of the drill bit with the rock at the bottom of the deep hole. We use d’Alembert’s solution of the
wave equation to construct a mathematical model of the wave torsion pendulum in the form of a nonlinear ordinary differential
equation with retarded argument. We show that there exists a range of variation in the angular velocity of the drill string
rotation, where, along with the unstable stationary solution characterized by the absence of vibrations, there are oscillatory
solutions in the form of a stable limit cycle (attractor). The self-excitation of these vibrations is soft, and the self-oscillations
themselves belong to the class of relaxation vibrations, because their period can be divided into several separated intervals
corresponding to slow and fast variations in the state of the system. The velocities of the drill bit elastic motions on each
of these time intervals remain constant, and the durations of all of them are the same and equal to the time interval (quantum)
of the twist mode propagation from the drill bit to the drill string top and conversely. 相似文献
4.
Experimental studies of a plane jet impinging upon a small circular cylinder are conducted by hot-wire measurements. The
cylinder is located on the jet centerline within the potential-core region. The jet–cylinder interactions on the instability
shear layer frequency, the cylinder wake shedding frequency, and the induced self-sustained oscillation phenomenon are carefully
investigated. Test data indicate that the self-sustained flow oscillation is mainly generated by the resonant effect of the
flow between the jet exit and the cylinder. Its resonant frequency is found to vary linearly and exhibits jump-stage pattern
as a function of the distance between the jet exit and the cylinder. The feedback mechanism and the hydrodynamic instability
theorem are proposed to predict correctly the frequency jump position, wave number and the convection speed of the self-sustained
oscillating flow for different jet exit velocities.
Received: 15 July 1998/Accepted: 9 December 1998 相似文献
5.
Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision 总被引:1,自引:0,他引:1
This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing
and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with
the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination
oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical
speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance
ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Balance Method (HBM). As
the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically
by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these
oscillation are also clarified. 相似文献
6.
For an absorber with the magnetic action and the delayed feedback, the equivalent strongly nonlinear model of the magnet force is proposed. We develop an identification algorithm with correcting distorted output measurement to identify and estimate the relevant parameters of the equivalently nonlinear model and the time delay in the feedback loop. The detailed steps of the algorithm are given analytically. We configure an experimental device of a delayed electromechanical absorber with action of the nonlinear magnetic force. The new algorithm is employed to identify the relative parameters of the device, such as time delay, damping and nonlinear stiffness, based on data of the output measurement with distortion. The results show that it is reasonable that the magnet action may be equivalent to the cubic nonlinear force. One may also see that the new algorithm may treat the experimental distorting measurement and correct it as long as the measurement still keeps periodicity. As an important result, values of the identified parameters with the correcting distortion are closer to those of the original measurement than those without the no correcting distortion for some excitation frequencies. It means that the algorithm may correct the polluted measurement, so that the quality of the identification is greatly improved. The new algorithm may be useful for design of nonlinear electromechanical absorber with time-delayed feedback. 相似文献
7.
N. V. Gavrilov E. V. Ermanyuk 《Journal of Applied Mechanics and Technical Physics》1999,40(2):258-262
Propagation of internal waves over a circular cylinder under the conditions of a continuous stratification characterized by
the presence of a high-gradient density layer (the pycnocline) of finite thickness is studied. The dependences of the coefficent
of wave propagation on the wavelength of the first-mode incident wave for various thicknesses of the pycnocline are obtained.
In the diffraction of internal waves, substantial nonlinear effects are shown to occur, which result in the appearance of
waves of double oscillation frequency compared to the frequency of the incident waves. The generation coefficient for these
waves is found.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 79–85, March–April, 1999. 相似文献
8.
M. A. Abdou 《Nonlinear dynamics》2008,52(1-2):1-9
In this paper, the Exp-function method with the aid of the symbolic computational system Maple is used to obtain the generalized
solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, (2+1)-dimensional
Konopelchenko–Dubrovsky equations, the (3+1)-dimensional Jimbo–Miwa equation, the Kadomtsev–Petviashvili (KP) equation, and
the (2+1)-dimensional sine-Gordon equation. It is shown that the Exp-function method, with the help of symbolic computation,
provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics. 相似文献
9.
C. W. Lim S. K. Lai B. S. Wu W. P. Sun Y. Yang C. Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):411-431
An analytical approach is developed for the nonlinear oscillation of a conservative, two-degree-of-freedom (TDOF) mass-spring
system with serial combined linear–nonlinear stiffness excited by a constant external force. The main idea of the proposed
approach lies in two categories, the first one is the transformation of two nonlinear differential equations of a two-mass
system using suitable intermediate variables into a single nonlinear differential equation. Another is the treatment a quadratic
nonlinear oscillator (QNO) by the modified Lindstedt–Poincaré (L-P) method presented recently by the authors. The first-order
and second-order analytical approximations for the modified L-P method are established for the QNOs with satisfactory results.
After solving the nonlinear differential equation, the displacements of two-mass system can be obtained directly from the
governing linear second-order differential equation. Unlike the common perturbation method, the modified L-P method is valid
for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical
expressions valid for small as well as large amplitudes of oscillation. In short, this new approach yields extended scope
of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to
the previous approaches such as the perturbation and classical harmonic balance methods. Two examples of nonlinear TDOF mass-spring
systems excited by a constant external force are selected and the approximate solutions are verified with the exact solutions
derived from the Jacobi elliptic function and also the numerical fourth-order Runge–Kutta solutions. 相似文献
10.
Banavara N. Shashikanth Artan Sheshmani Scott David Kelly Jerrold E. Marsden 《Theoretical and Computational Fluid Dynamics》2008,22(1):37-64
We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid
body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled
without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart
law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving
rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity
and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings
model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure
when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the
Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian
function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure
is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization,
provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency
conditions.
相似文献
11.
Mergen H. Ghayesh Niloofar Moradian 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(6):781-799
The dynamical response of axially moving, partially supported, stretched viscoelastic belts is investigated analytically in
this paper. The Kelvin–Voigt viscoelastic material model is considered and material, not partial, time derivative is employed
in the viscoelastic constitutive relation. The string is considered as a three part system: one part resting on a nonlinear
foundation and two that are free to vibrate. The tension in the belt span is assumed to vary periodically over a mean value
(as it occurs in real mechanisms), and the corresponding equation of motion is derived by applying Newton’s second law of
motion for an infinitesimal element of the string. The method of multiple scales is applied to the governing equation of motion,
and nonlinear natural frequencies and complex eigenfunctions of the system are obtained analytically. Regarding the resonance
case, the limit-cycle of response is formulated analytically. Finally, the effects of system parameters such as axial speed,
excitation characteristics, viscousity and foundation modulus on the dynamical response, natural frequencies and bifurcation
points of system are presented. 相似文献
12.
N. V. Nikitin 《Fluid Dynamics》2000,35(2):185-190
The attenuation of turbulent pulsations in near-wall flows by means of spanwise periodic surface oscillation is examined.
A direct numerical simulation of the flow in a circular pipe with imposed rotational oscillations has shown that for Re=4000
and the optimal oscillation frequency, the degree of turbulence attenuation increases with increase in the oscillation amplitude
until the flow relaminarizes. The estimated optimal frequency ω+=0.06. The results of applying the theory of the development of near-wall coherent structures agree qualitatively with those
of numerical simulation. It is concluded that the intensity of the pulsations is reduced because the spanwise movements weaken
the longitudinal vortices which cause turbulent bursts in near-wall flows.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 37–44, March–April, 2000.
The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-01095). 相似文献
13.
V. B. Larin 《International Applied Mechanics》2008,44(10):1148-1160
The optimization of the parameters of a controller of given structure for a controlled unstable scalar system with delay is
studied. First, the original system with delay is approximated by a system without delay. To this end, the exponent is approximated
by a fractional rational function. Since the structure of the controller is fixed, the quality of the approximation is assessed
by comparing the stability domains of the original and approximating systems (in the space of controller coefficients). Next,
the coefficients of the controller for the reduced system are optimized. The performance of the controller thus synthesized
can be assessed by mathematically modeling the original system (with delay) whose feedback is determined by the controller
coefficients found. The approach is exemplified by stabilizing an inverted mathematical pendulum with a PD controller. This
example is used to examine the issue of synthesis of a robust controller
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 86–100, October 2008. 相似文献
14.
A linear and nonlinear analysis of the distributed oscillations of an elastic tube with a fluid flowing in it is developed.
The critical flow velocity and the wavelength and oscillation frequency in the tube-flow system at loss of stability are found.
The geometrical and physical nonlinearities, the latter related to increase in the Young’s modulus of the tube wall material
with increasing strain, are considered. It is shown that four characteristic regimes of change of tube shape are possible:
local dilatation, collapse, flexure, and distributed auto-oscillations. The tube oscillations are analyzed numerically for
the nonaxisymmetric case. The conditions of existence of these effects in blood vessels are examined.
Nizhni Novgorod, e-mail: klochkov@appl.sci-nnov.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti
i Gaza, No. 4, pp. 46–55, July–August, 2000.
The work was supported by the Russian Foundation for Basic Research (project No. 97-02-18612). 相似文献
15.
There is evidence from balloon measurements that atmospheric buoyancy–frequency profiles, apart from a sharp increase (roughly
by a factor of two) at the tropopause, often feature appreciable oscillations (typical wavelength 1–2 km) with altitude. It
is argued here that such short-scale oscillatory variations of the background buoyancy frequency, which usually are ignored
in theoretical models, can have a profound effect on the generation of mountain waves owing to a resonance mechanism that
comes into play at certain wind speeds depending on the dominant oscillation wavelength. A simple linear model assuming small
sinusoidal buoyancy–frequency oscillations suggests, and numerical solutions of the Euler equations for more realistic flow
conditions confirm, that under resonant conditions the induced gravity-wave activity is significantly increased above and
upstream of the mountain, similarly to resonant flow of finite depth over topography.
相似文献
16.
We give sufficient conditions for the global stability of the zero solution of a functional differential equation with pulse
action and with nonlinear function satisfying the conditions of negative feedback and sublinear growth.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 258–269, April–June, 2007. 相似文献
17.
Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom 总被引:1,自引:0,他引:1
In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external
excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam
coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations
with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric
resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze
the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of
phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical
simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase
portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear
vibrations of the string-beam coupled system under certain conditions.
An erratum to this article is available at . 相似文献
18.
A. V. Demidov A. G. Makarov A. M. Stalevich 《Journal of Applied Mechanics and Technical Physics》2007,48(6):897-904
A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation
processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation
processes with alternative loading and unloading.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007. 相似文献
19.
Near-resonance highly nonlinear ideal perfect gas oscillations in tubes are studied numerically for boundary conditions of
various types. The oscillations are initiated by weak periodic perturbations at one end of the tube. As distinct from earlier
studies [1–10], the oscillation amplitudes were not assumed to be small and the entropy increase at the shock waves formed
was taken into account. Periodic flow regimes result as a limit of the solution of a Cauchy problem for one-dimensional time-dependent
gasdynamic equations. The frequency responses of the oscillations under consideration are determined for boundary conditions
of various types. It is shown that in specific cases the attainment of a periodic regime is accompanied by the appearance
of long-wave modulations. The “repeated resonance” effect is revealed. This is due to the change in the tube's natural acoustic
frequency, which takes place during the heating of the gas in the tube by the shock waves traveling in it.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 150–157, July–August, 1994. 相似文献
20.
Two differential constitutive equations, i.e. Giesekus model and Johnson–Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson– Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the melt at high shear rate.The project was supported by the National Natural Science Foundation of China (10402024, 50335010).The English text was polished by Yunming Chen. 相似文献