Isolation performance of a quasi-zero stiffness isolator in vibration isolation of a multi-span continuous beam bridge under pier base vibrating excitation

Nonlinear Dynamics - This paper considers a vibration control problem for a multi-span beam bridge under pier base vibrating excitation by using nonlinear quasi-zero stiffness (QZS) vibration...     

Vehicle response statistics to nonstationary track excitation - a direct formulation

The track unevenness is a nonhomogenous random process and as such moving vehicles have nonstationary excitation induced by the ground. A simple formulation for response statistics differential equation has been obtained for multi-mass multi-wheeled vehicle system with general ground velocity. Results are presented for a linearised model with some typical track profiles and ground motions.     

Non-linear response of a string to random excitation

The mean square deflection of a non-linear string subjected to nonplanar Gaussian white noise excitation is determined by the perturbation method. It is shown that increase in tension due to stretching, and transverse transverse mode coupling tend to reduce the mean square deflection; while longitudinal-transverse mode coupling tends to counter this effect to some extent. These results are in conformity with the trend observed in the case of periodic excitation.     

Radial electroelastic nonstationary vibration of a hollow piezoceramic cylinder subject to electric excitation

The paper studies the radial nonstationary vibration of a piezoceramic cylinder polarized throughout the thickness and subjected to a dynamic electric load. A numerical algorithm for solving an initial–boundary-value problem using mesh-based approximations and difference schemes is developed. The dynamic electroelastic state of the cylinder subjected to a constant potential difference applied instantaneously is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 30–35, February 2009.     

Equivalent linearization for systems subjected to non-stationary random excitation

The method of eauivalent linearization is applied to the general problem of the response of non-linear discrete systems to non-stationary random excitation. Conditions for minimum equation difference are determined which do not depend explicitly on lime but only on the instantaneous statistics of the response process. Using the equivalent linear parameters, a deterministic non-linear ordinary differential equation for the covariance matrix is derived. An example is given of a damped Duffing oscillator subjected to modulated white noise.     

Response statistics of two-degree-of-freedom non-linear system to narrow-band random excitation

The principal resonance of two-degree-of-freedom non-linear system to narrow-band random external excitation is investigated. 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 analysis. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions, saturation and jumps may exist.     

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated. The analysis is based on a special Zhuravlev transformation, which reduces the system to the one without impacts or velocity jumps, and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses. The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset. The effects of damping, detuning, and bandwidth and magnitudes of the random excitations are analyzed. The theoretical analyses are verified by the numerical results. The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.     

Parametric random excitation of nonlinear coupled oscillators

The stochastic bifurcation and response statistics of nonlinear modal interaction under parametric random excitation are studied analytically, numerically and experimentally. Two basic definitions of stochastic bifurcation are first introduced. These are bifurcation in distribution and bifurcation in moments. bifurcation in moments is examined for the case of a coupled oscillator subjected to parametric filtered white noise. The center frequency of the excitation is selected to be close to either twice the first mode or second mode natural frequencies or the sum of the two. The stochastic bifurcation in moments is predicted using the Fokker-Planck equation together with gaussian and non-Gaussian closures and numerically using the Monte Carlo simulation. When one mode is parametrically excited it transfers energy to the other mode due to nonlinear modal interaction. The Gaussian closure solution gives close results to those predicted numerically only in regions well remote from bifurcation points. However, bifurcation points predicted by the non-Gaussian closure are in good agreement with those estimated by numerical simulation. Depending on the excitation level, the probability density of the excited mode is strongly non-Gaussian and exhibits multi-maxima as predicted by Monte Carlo simulation. Experimental tests are carried out at relatively low excitation levels. In the neighborhood of stochastic bifurcation in mean square the measured results exhibit different regimes of response characteristics including zero motion and occasional small random motion regimes. These two regimes are characterized by the phenomenon of on-off intermittency. Both regimes overlap and thus it is difficult to locate experimentally the bifurcation point.     

Seismic behaviour of industrial masonry chimneys

This paper deals with the seismic behaviour of an unreinforced masonry chimney representative of the large number of chimneys currently in existence in many European areas which were built during the period of the industrial revolution. Maximum seismic intensity value that can be resisted in terms of peak ground acceleration and failure mode are the main goals. A 3D finite element model capable of reproducing cracking and crushing phenomena have been used in a non-linear analysis in order to obtain lateral displacements, crack pattern and failure mode for this type of construction. Earthquakes artificially generated for a low to moderate seismic intensity area from the response spectrum proposed by the codes have been tested on the structure obtaining failure mode, maximum stresses and displacements. Subsequently, the accelerograms generated were scaled until non-failure earthquakes were obtained.     

Response statistic of strongly non-linear oscillator to combined deterministic and random excitation

The principal resonance of a van der Pol-Duffing oscillator to the combined excitation of a deterministic harmonic component and a random component has been investigated. By introducing a new expansion parameter , the method of multiple scales is adapted for the strongly non-linear system. Then the method of multiple scales is used to determine the equations of modulation of response amplitude and phase. The behavior and the stability of steady-state response are studied by means of qualitative analysis. The effects of damping, detuning, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the non-trivial steady-state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady-state solutions. Random jump may be observed under some conditions. The results obtained in the paper are adapted for a strongly non-linear oscillator that complement previous results in the literature for the weakly non-linear case.     

Narrowband random excitation of a limit cycle system

Summary The response of the Van der Pol oscillator to stationary narrowband Gaussian excitation is considered. The central frequency of excitation is taken to be in the neighborhood of the system limit cycle frequency. The solution is obtained using a non-Gaussian closure approximation on the probability density function of the response. The validity of the solution is examined with the help of a stochastic stability analysis. Solution based on Stratonovich's quasistatic averaging technique is also obtained. The comparison of the theoretical solutions with the digital simulations shows that the theoretical estimates are reasonably good.

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Zufallserregung eines Systems mit Grenzzyklus in einem schmalen Frequenzband

Übersicht Gegenstand der Untersuchung ist die Antwort des Van der Pol-Schwingers auf eine stationäre Gaußsche Erregung in einem schmalen Frequenzband. Die zentrale Frequenz der Erregung wird in der nachbarschaft zur Frequenz des Grenzzyklus gewählt. Die Lösung wird durch eine nicht-Gaußsche approximierende Einschließung für die Wahrscheinlichkeitsdichte der Antwort gewonnen. Die Gültigkeit dieser Lösung wird mit Hilfe einer stochastischen Stabilitätsanalyse überprüft. Darüber wird eine Lösung nach Stratonovichs quasistatischer Mittelungsmethode bestimmt. Der Vergleich der theoretischen Lösungen mit zahlenmäßigen Simulationen ergibt eine befriedigende Güte der theoretischen Abschätzungen.

     

地震作用下高拱坝损伤开裂分析

采用应变率相关的砼非线性损伤模型模拟拱坝横缝,研究了砼非线性本构情况下整体拱坝与考虑分缝拱坝的应力响应和损伤开裂的特点与差别。对实际拱坝的地震响应分析表明,基于非线性砼模型的整体拱坝动力响应模型可以基本反映拱坝的实际应力分布情况。     

Suppression of self-excited vibrations by a random parametric excitation

Previous theoretical and experimental studies have shown that some vibrating systems can be stabilized by zero-averaged periodic parametric excitations. It is shown in this paper that some zero-mean random parametric excitations can also be useful for this stabilization. Under some conditions, they can be even more efficient compared to the periodic ones. Two-mass mechanical system with self-excited vibrations is considered for this comparison. The so-called bounded noise is used as a model of the random parametric excitation. The mean-square stability diagrams are obtained numerically by considering an eigenvalue problem for large matrices.     

Stability of similar nonlinear normal modes under random excitation

Nonlinear Dynamics - Using both analytical and numerical techniques, we investigate the 3-degree-of-freedom, autonomous, autoparametric, Hamiltonian spring–mass–pendulum system in...     

Response of a non-linearly damped oscillator to combined periodic parametric and random external excitation

An analytical solution, using the Fokker-Planck-Kolmogorov equation, is obtained for the problem of response of a non-linearly damped oscillator to combined periodic parametric and random external excitation. The solution yields first-order probability densities of amplitude and phase. These expressions are employed to distinguish between oscillations excited by external and parametric periodic forces in the presence of additional broadband random external excitation. Through decoupling of fast and slow motions an approximate expression is obtained for expected value of time to phase “switch”.     

Investigation of a non-linear system under partially prescribed random excitation

The problem of non-linear systems excited by random forces with known power spectral density functions and unspecified probability structure is considered. Sufficient, but not necessary, conditions on the input under which the response can be a Gaussian process are investigated. The approach is illustrated by investigating the hardening spring cubic oscillator under wide and narrow band excitations. The non-Gaussian probability density of the input that leads to Gaussian response is determined.     

A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

In this paper, a direct probabilistic approach (DPA) is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process. The proposed method has the advantage of obtaining the response’s moments directly from the initial conditions and statistical characteristics of the corresponding external exci-tations. First, the response’s moment equations are directly derived based on a DPA, which is completely independent of the It?/filtering approach since no specific assumptions regarding the correlation structure of excitation are made. By solving them under Gaussian closure, the response’s moments can be obtained. Subsequently, a multiscale algo-rithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo (MC) simulation gives good agreement. Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.     

Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise

A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.     

Stability of a linear second order system under random parametric excitation

Summary The stability of a linear second order system with small, random, Gaussian parametric excitation will be investigated. It will be shown that if the spectrum of the parameter variation is continuous near twice the natural frequency of the system, stability in mean square is only dependent upon the value of the spectral density at this part of the spectrum.

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Übersicht Es wird die Stabilität eines linearen Systems zweiter Ordnung mit kleiner, zufälliger, gaußischer Parametererregung untersucht. Dabei zeigt sich, daß die Stabilität im quadratischen Mittel nur von dem Wert der Spektraldichte in der Nähe der doppelten Eigenfrequenz des Systems abhängt, sofern das Spektrum der Parametererregung in diesem Bereich stetig ist.