Stress waves in a rod subjected to a moving load

The wave processes in a semi-infinite rod located in an elastic medium and subjected to a point load moving at a constant velocity are considered. The system of two differential equations of motion of Timoshenko beam theory is solved using the Laplace transform in time. The integrals obtained are determined numerically. Variation of the bending moment on the longitudinal coordinate behind the elastic-wave front and the region of action of the point force at various times is shown. The results of the solution are influence functions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 112–122, March–April, 2007.     

On the parametric stability of a Timoshenko beam subjected to a periodic axial load

Summary The dynamic buckling of a hinged bar under harmonic axial load is studied using Timoshenko's beam theory and considering the effects of longitudinal vibrations. Several new types of parametric resonances were found. The influences of the more accurate Timoshenko beam theory on the instability regions found with the Bernoulli-Euler theory is also discussed.

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Übersicht Die dynamische Stabilität eines gelenkig gelagerten Balkens mit harmonischer Axiallast wird mit Hilfe der Timoshenkoschen Balkentheorie und unter Berücksichtigung der Längsschwingungen untersucht. Verschiedene neue Arten von parametrischen Instabilitäten konnten gefunden werden. Der Einfluß der genaueren Timoshenkoschen Balkentheorie auf die sich aus der Bernoulli-Eulerschen Theorie ergebenden Instabilitätsbereiche wird diskutiert.

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Visiting Professors at COPPE, Universidade Federal do Rio de Janeiro, Brazil.     

The axially stressed LIM reaction rail subjected to a moving load

A recently developed high speed test track for the Linear Induction Motor (LIM) Vehicle at Pueblo, Colorado consists of a welded railroad track supplemented by a continuous reaction rail. Due to constrained thermal expansions, high axial compressive forces may occur in this rail. Since the reaction rail is a relatively slender plate, high axial forces may affect its lateral stability and dynamic characteristics. In this paper the stability of the reaction rail due to axial compressive force is studied first. Following this, the effect of axial forces upon the critical velocity of a moving lateral load is studied.Included in the analysis are representations of the rail, both as an isotropic and orthotropic entity. The moving lateral load applied to the rail is assumed to be a concentrated force, acting first at the top of the reaction rail, and then at two arbitrary points.     

A half-space saturated poro-elastic medium subjected to a moving point load

In this paper, an analytical solution for the dynamic response of a half-space porous medium subjected to a moving point load is derived. In the model, the displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vectorial potential. Based on Biot’s theory, the frequency domain Holmholtz equations for the potentials are derived through the Fourier transformation with respect to time. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinates. Numerical results suggest that moving loads have very complicated effects on the dynamic response of the porous medium. Generally speaking, a moving load with a high speed will generate a larger response in the porous medium than a static or a lower speed load.     

Multilayer spherical shell subjected to a uniformly distributed load over the area

International Applied Mechanics -     

Dynamic behaviour of the ring subjected to distributed impulsive load

Summary Dynamic behaviour of the ring subjected to distributed impulsive load is investigated. The ring is represented by the centroidal line and the problem is solved one-dimensionally. Impulsive load is assumed to be the step function with respect to time. The effects of shearing force and rotatory inertia to dynamic load factors with respect to axial force and bending moment are studied.From the results of theoretical analysis, it became evident that shearing force and rotatory inertia can not be neglected in such a problem as this, and that shear coefficient varies remarkably by the dimensions of the ring and the loading conditions.

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Übersicht Es wird das dynamische Verhalten eines Ringes untersucht, der einer verteilten Stoßlast unterworfen ist. Der Ring wird durch seine Mittellinie ersetzt, so daß das Problem als eindimensional behandelt werden kann. Die Stoßlast wird als Sprungfunktion bezüglich der Zeit angenommen. Die Einwirkungen von Schubkräften und Drchträgheit auf die dynamischen Lastfaktoren werden für Achsialkraft und Biegemoment untersucht. Die Ergebnisse zeigen, daß Schubkräfte und Drehträgheit nicht vernachlässigt werden dürfen. Ferner zeigt sich, daß der Schubbeiwert stark von den Ringabmessungen und den Belastungsbedingungen abhängt.

     

Stress-strain state of an ice sheet subjected to a moving load under shallow-water conditions

The following two classes of problems of determining the stress-strain state of an ice sheet under a moving load are considered: determination of the resonant velocity for a load moving over a continuous ice field and calculation of the deflections of an ice field with a bounded ice-free zone subjected to a moving load. The problems are solved in a dynamic formulation. The algorithm of solution is based on the finite-clement method and finite-difference methods. Examples of calculations are given. Komsomol'sk-on-Amur State Technical University, Komsomol'sk-on-Amur 681013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 4, pp. 206–210, July–August, 2000.     

On stability of moving autonomous mechanical systems under uncertainty

Conditions of stability with respect to two measures of autonomous mechanical systems under uncertainty are established by decomposing the phase space of the system, a space of fuzzy sets, and using the natural monotonicity of fuzzy differential equations __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 119–131, February 2008.     

On the stability of equilibrium of continuous systems

Summary A sufficiency theorem for the stability of a linearly viscoelastic solid subjected to partial follower surface tractions is established. It is shown that an appropriately defined functional metric space must be introduced in order to formulate a well-posed problem. The usual energy method, if applicable, and the Galerkin method, if convergent, yield stability conditions only in a functional space whose metric is defined in an average

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Übersicht Es wird ein hinreichendes Kriterium für die Stabilität eines viskoelastischen festen Körpers abgeleitet, der Kräften unterworfen wird, die teilweise den Verformungen der Oberfläche folgen. Es wird gezeigt, daß ein geeignet definierter metrischer Funktionalraum eingeführt werden muß, um das Problem vernünftig formulieren zu können. Die übliche Energie-Methode, sofern sie anwendbar ist, sowie das GalerkinVerfahren, wenn es konvergiert, ergeben lediglich Stabilitätsbedingungen in einem Funktionalraum, dessen Metrik im Mittel definiert ist.

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This research was supported by the National Aeronautics and Space Administration under Grant NsG 605.     

Response of railway track system on poroelastic half-space soil medium subjected to a moving train load

Based on the dynamic poroelastic theory of Biot, dynamic responses of a track system and poroelastic half-space soil medium subjected to moving train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.     

随从力作用下热弹耦合轴向运动梁的稳定性

研究了切向均布随从力作用下热弹耦合轴向运动梁的稳定性问题。建立了热弹耦合轴向运动梁 在随从力作用下的运动微分方程,采用归一化幂级数法,推导出了2种边界条件下热弹耦合轴向运动梁在随 从力作用下的特征方程。计算了系统的前3阶量纲一复频率,分析了量纲一运动速度、量纲一热弹耦合系数 和量纲一随从力等参数对梁的稳定性的影响。     

On the nonlinear stability of a truncated shallow spherical shell under A uniformly distributed load

A problem of practical interest for nonlinear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied in this paper. By using modified iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures. This paper was read at The Third East China Symposium on Solid Mechanics, Jiuhuashan, October, 1986. Fomerly at University of Science and Technology of China, Hefei.     

Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load

Meccanica - In the present investigation, free vibration and also forced vibration response of a graphene platelet reinforced composite (GPLRC) laminated curved beam is investigated. It is assumed...     

Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated.The analysis is based on the exact elasticity equations for the plane stress problem.The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate.The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the bound- ary conditions by a skilful deduction.The analytical solution is compared with FEM calculation,indicating a good agreement.     

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slender,non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam.The material of the cantilever is assumed to be nonlinearly elastic.Different nonlinear relations between stress and strain in tensile and compressive domain are considered.The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.