不平衡线性转子-轴承系统的非平稳地震激励响应分析

给出了受随机地震激励的线性转子-轴承系统动力响应的有效分析方法。应用虚拟激励法和数值积分法,采用Kanai-Tajimi地震模型,对一个四自由度非对称的刚性转子-轴承系统在地震激励和谐波激励联合作用下的位移响应、位移响应谱密度及响应时变方差进行了分析。讨论了不同转速对位移响应时变方差的影响和不同采样角频率对位移响应时变方差曲线的影响。     

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...     

转子系统的平稳／非平稳随机地震响应分析

应用虚拟激励法结合精细时程积分计算了转子系统受平稳／非平稳随机地震激励的动力响应。采用虚拟激励分析将平稳随机激励转化为稳态简谐激励，将非平稳随机激励转化为瞬态确定性激励，即使对于非对称的油膜刚度阵和阻尼阵，算法仍然简单高效，并得到精确的结果。     

An approximation of the first passage probability of systems under nonstationary random excitation

An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom （SDOF） linear systems under two special types of modulated white noise excitations.     

Vibrations of a piezoceramic cylinder subject to nonstationary electric excitation

The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder is examined. The region of end disturbances in a long cylinder is identified __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 73–79, March 2007.     

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.     

大跨率桥梁直接考虑拟静力位移影响的随机地震反应分析

对 Duhamel积分引入了改进的脉冲响应函数 ,建立了激励演变谱矩阵与总动力响应演变谱之间的关系 ,并对实际大跨度斜拉桥进行了数值计算。这一成果实现了全面考虑各种地震动时空变化特性下的直接求解结构总动力响应的时域法和频域法计算列式 ,使得地震动多点激励下考虑拟静力位移影响的结构响应计算过程大为简化。     

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.     

AN ANALYSIS ON RESPONSE OF STRUCTURE TO RANDOM EARTHQUAKE EXCITATION

In this paper the response of elastic structure to random earth-quqke excitation isanalysed.For a frame-wall system. practical calculating formulas are derived and aprogram in FORTRAN language is made. The program is checked with a numericalexample. The envelope of the lateral displacement of the system and the variation regularityof the internal forces are determined from given values of dynamic reliability (firstexcursion probability) based on the requirement of the operation of the structures.     

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.     

多相位激励随机地震响应快速算法

对多支承激励间存在相位差的平稳随机响应分析问题给出了计算各种自谱密度及互谱密度的快速直接算法。此法计入了所有参振振型间的互相关项，以及各激励间的互相关项，是快速、简便、精确的频域分析方法，并可用实振型方便地处理非正交阻尼矩阵。     

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.

     

Response of nonlinear oscillator under narrow-band random excitation

IntroductionThestudyoftheresponseofnonlinearsystemstonarrow_bandrandomexcitationofconsiderableimportance.Forexample ,theexcitationofsecondarysystemwouldbeanarrow_bandrandomprocessiftheprimarysystemcouldbemodeledasasingle_degree_of_freedomsystemwithlightdampingsubjecttowide_bandexcitation .Inthetheoryofnonlinearrandomvibration ,mostresultsobtainedsofarareattributedtotheresponseofnonlinearoscillatorstowide_bandrandomexcitation .Incomparison ,resultsontheeffectofnarrow_bandexcitationonnonlinearos…