Waves induced by the longitudinal impact of a rod against a stepped rod in contact with a rigid barrier

The longitudinal elastic central impact of a rod system, consisting of a uniform rod having a pre-impact velocity against a stepped rod which is in a state of rest and interacts by means of unilateral constraints with a rigid barrier, is modelled.     

The longitudinal deformation of a rod in friction interaction with a compressing body

The deformation of a rod, confined in a fixed external housing, is considered. The friction forces in the contact surface are related to the deformation of the rod by a power relation. A wide range of variation of the friction parameter and the preliminary clearance parameter with which the rod is inserted into the housing is investigated and the characteristic features of the stress and strain distributions are revealed. The dissipation of energy due to friction and the formation of a hysteresis loop in the dependence of the stresses in the loaded end face on its displacement are considered. The problem is solved in a quasistatic formulation. Analytical relations are found for a number of important cases. Other results are obtained by numerical integration of the initial differential problem.     

Parametric resonances in the problem of longitudinal impact on a thin rod

The longitudinal impact on a thin elastic rod, which generates a periodic system of longitudinal waves in it, is considered. At definite values of the parameters of the problem in the linear approximation, these waves induce parametric resonances, which are accompanied by an unlimited increase in the amplitude of the transverse vibrations. To obtain finite values of the amplitudes, a quasilinear system is considered in which the effect of the transverse vibrations on the longitudinal vibrations is taken into account. This system was previously solved using the Bubnov–Galerkin method and beats accompanied by energy transfer between the transverse and longitudinal vibrations were obtained. In this work, an approximate analytical solution of the system has been derived that is based on double-scale expansions. A qualitative analysis of this solution has been carried out. An estimate of the maximum transverse bending has been obtained for various methods of loading. Both shortand long-term pulses have been considered. It has been shown that, in the case of a spontaneously applied long-term pulse that is lower than the Euler critical load, intensive transverse vibrations can occur.     

Investigation of longitudinal wave propagation in a polyethylene rod

Longitudinal wave propagation in a polyethylene rod has been investigated. A computer has been used to obtain a numerical solution of the problem of wave propagation in a rod, whose material is described by the Boltzmann-Volterra equation. The results of the computations are compared with the experimental data. The method of characteristics is employed to construct the dynamic – diagrams for the case of wave propagation in a prestressed rod on the basis of the model of a viscoelastic standard solid.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 59–67, January–February, 1970.     

Dynamics of oscillators coupled by a medium with adaptive impact

In this article, we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one‐dimensional direction and the movements of the base follow some functions of the phases of the metronomes (in other words, it is controlled to move according to a provided function). Because of the motor and the feedback, the phases of the metronomes affect the movements of the base, whereas on the other hand, when the base moves, it affects the phases of the metronomes in return. For a simple function for the base movement (such as y = γ_x[rθ₁ + (1 ? r)θ₂] in which y is the velocity of the base, γ_x is a multiplier, r is a proportion, and θ₁ and θ₂ are phases of the metronomes), we show the effects on the dynamics of the oscillators. Then, we study how this function changes in time when its parameters adapt by a feedback. By numerical simulations and experimental tests, we show that the dynamic of the set of oscillators and the base tends to evolve towards a certain region. This region is close to a transition in dynamics of the oscillators, where more frequencies start to appear in the frequency spectra of the phases of the metronomes. We interpret this as an adaptation towards the edge of chaos.     

Dynamics of a rigid body on rockers

We study the dynamics of a rigid body on rockers with a nonspherical contact surface. It is shown that in the case of small oscillations the equations of motion contain strong nonlinearity, which makes it possible to avoid resonance (nonperiodic) oscillations. We study free and forced oscillations under a harmonic force on the plane of whose parameters bifurcation curves are constructed separating the periodic and nonoscillatory processes. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 51–55.     

Bending of an anisotropic rod with longitudinal cavities

We study the stress state of hollow anisotropic rods bent by a force at the end. The complex potential is represented by a series in a specially constructed system of fundamental solutions of a suitable differential operator. As an example we consider the bending of a rod of square cross section with a centrally located square hole. Two figures. One table. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 44–48.     

Permanent rotations of a body with a viscous filler suspended on a rod

Problems of the existence, stability, and branching of the permanent rotations of a heavy, dynamically symmetrical rigid body suspended on a rod and which has an axisymmetric ellipsoidal cavity filled with a fluid are discussed. The phenomenological model of the friction of the fluid against the cavity wall proposed by Samsonov is used. All the trivial permanent rotations of the system and the non-trivial rotations that branch off from the trivial ones are found. Their stability and branching are investigated using a modified Routh's theory. The results obtained are presented in the form of an atlas of bifurcation diagrams.     

Experimental investigation of the correspondence between quasistatic tension and longitudinal wave propagation in a polyethylene rod

The propagation of longitudinal waves created by the impact of a rigid mass against a polyethylene rod of finite length has been investigated. The experimental procedure is described and oscillograms of the process are presented. The relaxation spectrum is calculated from the experimental data on the mechanical behavior of the material over a broad range of strain rates. The results of the experiments are compared with a numberical solution of the problem of the impact of a rigid mass against a rod whose material is characterized by a relaxation spectrum.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 564–567, May–June, 1971.     

Lateral Vortex Dynamics behind Ahmed body

The flow-field in the wake of Ahmed body was studied experimentally. The study is oriented on unsteady behavior of the lateral vortex pair arising in the wake as well as on the wake itself. The time-mean characteristics of the wake flow are presented. The dynamical behavior of the longitudinal vortex pair is studied in details. The Stereo Time-Resolved PIV method was applied in the wake plane perpendicular to the mean flow. Two variants of Ahmed Body with slat angle 25 and 35 degrees are investigated respectively. Comparison shows considerable differences in the vortex pair topology and dynamics of the cases in question. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of the impact problem for a rigid mass and a viscoelastic rod of finite length

The problem of the propagation and interaction of longitudinal waves in a rod struck by a rigid mass is considered. A numerical computer solution is obtained for the case when the mechanical behavior of the rod material is expressed by a rectangular relaxation spectrum. A numerical method of integral transform inversion is developed and applied to problems of polymer dynamics.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 450–456, May–June, 1971.     

Antiplane strain of a multiconnected anisotropic body with longitudinal cavities and plane cracks

Applying the theory of generalized complex potentials and the method of least squares, we solve the problem of the stressed state of a multiconnected anisotropic body under an antiplane strain. The problem is reduced to a system of linear algebraic equations in the unknown constants that occur in the required functions. By numerical studies we exhibit the influence of the elastic and geometric characteristics on the stress distribution and the variation of the stress intensity factors in a cylinder with one or two cracks and in an infinite body with circular cavities and cracks. One figure. Six tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25. 1995, pp. 56–62.     

Diffraction by a crack of a cylindrical longitudinal pulse

The diffraction of a cylindrical longitudinal pulse by a semi-infinite crack is studied analytically using integral transform techniques and the Wiener-Hopf method. The inverse transformations are performed by an extension of the Cagniard-de Hoop technique that enables three successive inversions to be performed in one step rather than the usual two successive inversions. Examination of both the reflected and diffracted displacements near the transverse-wave reflection boundary indicates the presence of a transition disturbance. Such a disturbance is not found if the incident pulse is plane or if the elastic solid is replaced by a medium supporting only one wave type such as an inviscid fluid. Asymptotic approximations to the most important diffracted pulses, that are valid near their wave fronts, are given and are compared with those predicted by the geometrical theory of diffraction.

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Résumé La diffraction d'une onde longitudinale initialement cylindrique et de profil arbitraire, par un écran en forme de demi-plan est étudiée. Ce problème est résolu complètement par la méthode de Wiener-Hopf et par une extension d'une méthode proposée par Cagniard et de Hoop. Les formules qui définissent les ondes réfléchies et diffractées indiquent qu'une onde de transition est présente. Cette onde est nouvelle. On ne la trouve pas si l'onde d'incidence est plane ou si le solide élastique est remplacé par un fluide idéal. Des approximations asymptotiques aux ondes diffractées les plus importantes, exactes au front de l'onde, sont données et sont comparées avec celles prévues par la théorie géométrique de la diffraction.

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This paper is based upon the author's dissertation that was submitted to Northwestern University, Evanston, Illinois, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.     

Dynamics of a rigid body in a two-dimensional incompressible perfect fluid and the zero-radius limit

Science China Mathematics - In this survey we report some recent results on the dynamics of a rigid body immersed in a two-dimensional incompressible perfect fluid, with an emphasis on the...     

Energy dissipation calculations for a linear viscoelastic body under impact loading

An expression is obtained for the dissipated energy of a linear viscoelastic body with a continuous relaxation spectrum in the case of an arbitrary law of variation of the strains with time. Lower bounds for the total and dissipated energies are constructed by the method proposed in [3]. The calculated values of the dissipated energy are compared with experiment.     

Local effects in a thermoelastic plate stiffened by a rod/ring

On the basis of the revised theory of plates, which makes it possible to determine the components of the stress tensor, we study the thermostressed state of an unbounded plate stiffened by a rod-ring. In the stiffening and in the contact zone of the plate the stresses differ significantly, both quantitatively and qualitatively, from those predicted by the classical theories of elasticity Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 26–30.