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761.
The nonlinear dynamics of a two-degree-of-freedom mechanical system is considered. This system consists of a linear oscillator
under the action of a time-periodic force and a snap-through truss, which acts as an absorber of the forced oscillations of
the linear main system. The forced oscillations of the snap-through truss close to its equilibrium position are analyzed by
the multiple scales method. 相似文献
762.
This Note deals with the three-dimensional phenomenon of collision between two slender steel bars. The problem posed is whether the restitution concept developed in rigid-body theory is relevant in the case of such slender contactors. Some elements of an answer are provided through the use of two complementary approaches of collision, a theoretical one based on coefficients of restitution and series of experiments. Our main conclusion is that the alleged Newton coefficient of restitution varies according to the impact location on the rods. To cite this article: C. Le Saux et al., C. R. Mecanique 332 (2004). 相似文献
763.
We investigate the nonlinear response of an infinitely long, circularcylindrical shell to a primary-resonance excitation of one of itsflexural modes, which is involved in a one-to-two internal resonancewith the breathing mode. The excited flexural mode is involved in aone-to-one internal resonance with its orthogonal flexural mode. Thereare two simultaneous internal (autoparametric) resonances: two-to-oneand one-to-one. The method of multiple scales is directly applied to thepartial-differential equations to obtain a system of six first-ordernonlinear ordinary-differential equations governing modulation of theamplitudes and phases of the three interacting modes. In the absence ofdamping, the modulation equations are derivable from a Lagrangian,reflecting the conservative nature of the system. The modulationequations are used to study the equilibrium and dynamic solutions andtheir stability and hence their bifurcations. The response may be eithera two-mode or a three-mode solution. For certain excitation parameters,the equilibrium three-mode solutions undergo Hopf bifurcations. Acombination of a shooting technique and Floquet theory is used tocalculate limit cycles and their stability, and hence theirbifurcations. 相似文献
764.
The transverse vibrations of a circular disk of uniform thickness rotatingabout its axis with constant angular velocity are analyzed. The resultsspecialized to the linear case of disks clamped at the center and free atthe periphery are in good agreement with those reported in the literature.The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitraryspatially fixed transverse loads. Using the method of multiple scales, wedetermine a set of four nonlinear ordinary-differential equations governingthe modulation of the amplitudes and phases of two interacting modes. Thesymmetry of the system and the loading conditions are reflected in thesymmetry of the modulation equations. They are reduced to an equivalentset of two first-order equations whose equilibrium solutions aredetermined analytically. The stability characteristics of thesesolutions is studied; the qualitative behavior of the response isindependent of the mode being considered. 相似文献
765.
G. Lombaert G. Degrande D. Clouteau 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(10):661-678
Summary This paper deals with the influence of the soil stratification on the free field vibrations generated by the passage of a
vehicle on an uneven road. A two-stage solution procedure is applied for the numerical prediction of the free field traffic-induced
vibrations. First, a 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. Next,
the free field response is calculated with the dynamic Betti-Rayleigh reciprocity theorem, using a transfer function between
the road and the receiver. The dynamic road-soil interaction problem is solved with a substructure method. The road is modelled
as a beam of infinite length, while the boundary element method, based on the Green's functions for a horizontally layered
linear elastic halfspace is used for the soil. The influence of the soil stratification is demonstrated by a numerical example
where the free field vibrations during the passage of a vehicle on a traffic plateau are calculated. Three different cases
are considered for the layering of the soil: a homogeneous halfspace, a layer built in at its base and a layer on a halfspace.
Special emphasis goes to the dynamic interaction between the road and the soil. It is demonstrated that the stratification
of the soil has a considerable influence on both the peak particle velocity and the frequency content of the free field vibrations.
Received 28 November 2000; accepted 24 April 2001 相似文献
766.
Non-linear vibrations of cantilever beams with feedback delays 总被引:1,自引:0,他引:1
A comprehensive investigation of the effect of feedback delays on the non-linear vibrations of a piezoelectrically actuated cantilever beam is presented. In the first part of this work, we examine the linear and non-linear free responses of a beam subjected to a delayed-acceleration feedback. We show that the trivial solution loses stability via a Hopf bifurcation leading to limit-cycle oscillations. We analyze the stability of the dynamic response in the postbifurcation, close to the stability boundaries by examining the nature of the Hopf bifurcation and away from the stability boundaries by using the method of harmonic balance and Floquet theory. We find that, increasing the gain for certain feedback delays may culminate in quasiperiodic and chaotic oscillations of the beam.In the second part, we analyze the effect of feedback delays on a beam subjected to a harmonic base excitations. We find that the nature of the forced response is largely defined by the stability of the trivial solutions of the unforced response. For stable trivial solutions (i.e., inside the stability boundaries of the trivial solutions), the homogeneous response emanating from the feedback diminishes, leaving only the particular solution resulting from the external excitation. In this case, delayed feedback acts as a vibration absorber. On the other hand, for unstable trivial solutions, the response contains two co-existing frequencies. Depending on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency, the response is either periodic or quasiperiodic. 相似文献
767.
Yu. A. Gaponenko V. A. Volpert S. M. Zen'kovskaya D. A. Pojman 《Journal of Applied Mechanics and Technical Physics》2006,47(2):190-198
The effect of high-frequency vibrations of the field of external mass forces on convection in miscible fluids is considered
for a system of convection equations obtained by an averaging technique. The structures of flows formed under initial conditions
corresponding to physical experiments in microgravity are examined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 49–59, March–April, 2006. 相似文献
768.
769.
B. A. Khudayarov N. G. Bandurin 《Journal of Applied Mechanics and Technical Physics》2007,48(2):279-284
Nonlinear vibrations of viscoelastic elements of aviation structures are studied. A method and an algorithm for the numerical
solution of integrodifferential equations are proposed. The critical velocity of the flow past viscoelastic plates is determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 156–162, March–April, 2007. 相似文献
770.
Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction 总被引:1,自引:0,他引:1
N. Mihajlović N. van de Wouw P. C. J. N. Rosielle H. Nijmeijer 《Nonlinear dynamics》2007,50(3):679-699
In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused
by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental
bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional
vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both
the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations,
can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of
analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility,
mass-unbalance and discontinuous friction which support the design of such flexible rotor systems. 相似文献