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Roman Lewandowski 《Meccanica》1996,31(3):323-346
The amplitude — frequency relations of beams, membranes and plates in free vibration with moderately large amplitude are of interest. A two harmonics solution of motion equation and the reciprocal interaction of two modes of vibration are taken into account. The resulting backbone curves with loops, additional branches and bifurcation points are determined and discussed. The physical meaning of the considered curves is also explained.
Sommario Si studiano le vibrazioni libere di ampiezza moderatamente grande di travi, membrane e piastre. Si sviluppano soluzioni approssimate con due armoniche delle relative equazioni di moto in due diversi casi di risonanza interna, e si analizza l'effetto dell'interazione di due modi di vibrazione. Vengono determinate e discusse le curve frequenza-ampiezza con l'associata ricchezza di rami addizionali e punti di biforcazione. Il significato fisico di tali curve viene altresì evidenziato.相似文献
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讨论了接触面为圆面的Hertz接触问题。若压力分布是轴对称的,则该接触问题的解必是唯一的。且在上述条件下,该接触问题的积分方程可化为两个推广的Abel积分方程组,此方程组的解便给出此接触问题的解。 相似文献
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Timoshenko固端梁特征值问题近似计算方法 总被引:3,自引:2,他引:3
利用模态摄动法将Timoshenko梁特征值问题的求解转化为一组非线性代数方程组的求解,不仅可以简化计算过程,而且计算结果具有较高的精度,对同一类问题具有适用性。通过算例,计算了在不同长细比条件下,剪切变形和转动惯量对固端梁的各阶主频率的影响。 相似文献
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The local and global nonlinear dynamics of a two-degree-of-freedom model system is studied. The undeflected model consists
of an inverted T formed by three rigid bars, with the tips of the two horizontal bars supported on springs. The springs exhibit an elasto-plastic
response, including the Bauschinger effect. The vertical rigid bar is subjected to a conservative (dead) or non-conservative
(follower) force having static and periodic components. First, the method of multiple scales is used for the analysis of the
local dynamics of the system with elastic springs. The attention is focused at modal interaction phenomena in weak excitation
at primary resonance and in hard sub-harmonic excitation. Three different asymptotic expansions are utilised to get a structural
response for typical ranges of excitation parameters. Numerical integration of the governing equations is then performed to
validate results of asymptotic analysis in each case. A full global nonlinear dynamics analysis of the elasto-plastic system
is performed to reveal the role of plastic deformations in the stability of this system. Static 'force-displacement' curves
are plotted and the role of plastic deformations in the destabilisation of the system is discussed. Large-amplitude non-linear
oscillations of the elasto-plastic system are studied, including the influence of material hardening and of static and sinusoidal
components of the applied force. A practical method is proposed for the study of a non-conservative elasto-plastic system
as a non-conservative elastic system with an 'equivalent' viscous damping.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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Dr. H. P. Lee 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,65(8):564-571
Summary The dynamic behaviour of an Euler beam traversed by a moving concentrated mass, is analyzed for the general case of a mass moving with a varying speed. The equation of motion in a matrix form is formulated using the Lagrangian approach and the assumed mode method. The dimensionless form of the equation enables the numerical results to be applicable for a wide range of system parameters. The possibility of the mass separating from the beam is analyzed by examining the contact forces between the mass and the beam during the motion. 相似文献
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On the Computer Formulations of the Wheel/Rail Contact Problem 总被引:2,自引:0,他引:2
In this investigation, four nonlinear dynamic formulations that can be used in the analysis of the wheel/rail contact are presented, compared and their performance is evaluated. Two of these formulations employ nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail (constraint approach), while in the other two formulations the contact force is modeled using a compliant force element (elastic approach). The goal of the four formulations is to provide accurate nonlinear modeling of the contact between the wheel and the rail, which is crucial to the success of any computational algorithm used in the dynamic analysis of railroad vehicle systems. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as function of the penetration using Hertzs contact theory or using assumed stiffness and damping coefficients. The first elastic method is based on a search for the contact locations using discrete nodal points. As previously presented in the literature, this method can lead to impulsive forces due to the abrupt change in the location of the contact point from one time step to the next. This difficulty is avoided in the second elastic approach in which the contact points are determined by solving a set of algebraic equations. In the formulations based on the constraint approach, on the other hand, the case of a non-conformal contact is assumed, and nonlinear kinematic contact constraint equations are used to impose the contact conditions at the position, velocity and acceleration levels. This approach leads to a model, in which the wheel has five degrees of freedom with respect to the rail. In the constraint approach, the wheel penetration and lift are not permitted, and the normal contact forces are calculated using the technique of Lagrange multipliers and the augmented form of the system dynamic equations. Two equivalent constraint formulations that employ two different solution procedures are discussed in this investigation. The first method leads to a larger system of equations by augmenting all the contact constraint equations to the dynamic equations of motion, while in the second method an embedding procedure is used to obtain a reduced system of equations from which the surface parameter accelerations are systematically eliminated. Numerical results are presented in order to examine the performance of various methods discussed in this study. 相似文献
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There is promise in the use of bistable devices to transduce ambient vibrations into electrical power. However, it is critical to sustain the relatively large amplitude snap-through motion, or interwell motion, to significantly improve the responsiveness of bistable devices as compared to linear resonance-based approaches. This work posits that relatively stiff structural elements can be placed in the vicinity of the equilibria of bistable devices such that the discontinuous change in dynamics will tend to eject an otherwise small amplitude motion into the large amplitude interwell orbit that is to be preferred for energy harvesting applications. The discontinuous nonlinear dynamic equations of motion are derived and a proxy system parametrically studied. These numerical studies demonstrate that discontinuous nonlinear bistable devices have a significantly broadened frequency range that elicits the large amplitude snap through behavior. It is also seen that interwell motion is achievable at significantly reduced excitation amplitudes through these discontinuous structural elements. 相似文献
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This paper deals with a model for repeated impacts of a massattached to a spring with a massive, sinusoidally vibrating table. Thismodel has been studied in an attempt to understand the cantilever-sampledynamics in atomic force microscopy. In this work, we have shown thatfor some values of the frequency of the vibrating table, there arecountably many orbits of arbitrarily long periods and the system issensitive to the initial conditions with which the experiments areconducted. We have also shown existence of complex dynamics in the caseswhen the natural frequency of the spring-mass system is very low; andwhen it is the same as the oscillating frequency of the table. 相似文献
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地震作用下基于ADMF和系统参数组合的最优MTMD 总被引:6,自引:1,他引:6
多重调谐质量阻尼器 ( MTMD)是由许多频率成线性分布的调谐质量阻尼器组成。可能的系统参数组合形成 5种 MTMD,即 MTMD-1~MTMD-5。基于在基底加速度作用下具有一般 MTMD时结构的加速度传递函数 ,建立了 MTMD-1~ MTMD-5加速度动力放大系数 ( ADMF)的统一模式。利用 ADMF和数值寻优技术进行了详细的最优参数研究。最优参数包括 :最优频率间隔、最优阻尼比、最优调谐频率比。大量的数值比较表明 :在MTMD地震反应控制工程中 ,应优先选择 MTMD-1。 相似文献
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We investigate the nonlinear response of a clamped-clamped buckled beamto a primary-resonance excitation of its first vibration mode. The beamis subjected to an axial force beyond the critical load of the firstbuckling mode and a transverse harmonic excitation. We solve thenonlinear buckling problem to determine the buckled configurations as afunction of the applied axial load. A Galerkin approximation is used todiscretize the nonlinear partial-differential equation governing themotion of the beam about its buckled configuration and obtain a set ofnonlinearly coupled ordinary-differential equations governing the timeevolution of the response. Single- and multi-mode Galerkinapproximations are used. We found out that using a single-modeapproximation leads to quantitative and qualitative errors in the staticand dynamic behaviors. To investigate the global dynamics, we use ashooting method to integrate the discretized equations and obtainperiodic orbits. The stability and bifurcations of the periodic orbitsare investigated using Floquet theory. The obtained theoretical resultsare in good qualitative agreement with the experimental results obtainedby Kreider and Nayfeh (Nonlinear Dynamics
15, 1998, 155–177. 相似文献
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V. Yu. Liapidevskii 《Journal of Applied Mechanics and Technical Physics》2004,45(2):199-203
Twolayer miscible flow above an uneven bottom is considered. A mathematical model in the shallowwater approximation is constructed for the development of a turbulent layer between homogeneous layers of different density in a twolayer channel flow over a local obstacle. The influence of the mixing process on the formation of an initial segment of the steadystate densitystratified flow on the leeward side of the obstacle is studied. 相似文献
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The one-dimensional problem of the motion of a rigid flying plate under explosive attack has an analytic solution only when the polytropic index of detonation products equals to three. In general, a numerical analysis is required. In this paper, however, by utilizing the weak shock behavior of the reflection shock in the explosive products, and applying the small parameter purterbation method, an analytic, first-order approximate solution is obtained for the problem of flying plate driven by various high explosives with polytropic indices other than but nearly equal to three. Final velocities of flying plate obtained agree very well with numerical results by computers. Thus an analytic formula with two parameters of high explosive (i.e. detonation velocity and polytropic index) for estimation of the velocity of flying plate is established. 相似文献
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The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications. 相似文献
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This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail. 相似文献