On damping properties of a frictionless physical pendulum with a moving mass

The damping effects are generated in a frictionless oscillating physical pendulum by a continuous motion of an auxiliary mass. The main parameters affecting the damping properties of the pendulum-mass system are identified. In particular, the effective damping ratio for a cycle is introduced and derived in a closed form from the energy considerations and then independently from Mathieu's equation. It is shown that a continuous damping can be achieved if the mass motion is synchronized with the pendulum rotation. Otherwise the system becomes prone to ‘beating’ phenomenon. The results presented may be useful for design of active control strategy of autonomous systems with negligible passive damping.     

Dynamic analysis of a flexible hub-beam system with tip mass

For a dynamic system of a rigid hub and a flexible cantilever beam, the traditional hybrid coordinate model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of some rigid–flexible coupling systems with high rotational speed. In this paper, characteristics of a flexible hub-beam system with a tip mass is studied. Based on the Hamilton theory and the finite element discretization method, and in consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam, the rigid–flexible coupling dynamic model (referred as the first-order approximation coupling (FOAC) model in this paper) and the corresponding model in non-inertial system for the flexible hub-beam system with a tip mass are presented firstly, then the dynamic characteristics of the system are studied through numerical simulations under twos cases: the large motion of the system is known and is unknown. Simulation and comparison studies using both the traditional zeroth-order model and the proposed first-order model show that even small tip mass may affect dynamic characteristics of the system significantly, which may result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam, and may affect end position of the hub-beam system as well. The effect of the tip mass becomes large along with the increasing of rotating speed of large motion of the system. When the large motion of the system is at low speed, the traditional ZOAC model may lead to a large error, whereas the proposed FOAC model is valid. When the large motion is at high speed, the ZOAC model may result in divergence to the dynamic problem of the flexible hub-beam system, while the proposed second model can still accurately describe the dynamic hub-beam system.     

Dynamic behaviour of a metamaterial system with negative mass and modulus

Different models of metamaterials have been developed to generate negative mass and/or negative modulus. The resulting mass and modulus in existing works, however, cannot be independently controlled. The current study presents a new representative cell of elastic metamaterials in an effort to provide a comprehensive model for generating negative mass and/or negative modulus. The current model consists of a series of properly arranged rigid bodies and linear springs. By introducing both translational and rotational motions in the representative cell, negative mass and negative modulus can be obtained in a controlled manner. The mechanisms and conditions under which negative mass and/or negative modulus can be achieved are studied in detail. Numerical examples indicate that by varying the design of the representative cell, different properties of the material system can be reliably generated, i.e., double negative (mass and modulus) or single negative (mass or modulus). The dynamic behaviour of the developed material system under different loading frequencies is evaluated and the longitudinal elastic wave propagation in such metamaterials is studied.     

RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

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Dynamic behaviour of cylinder with spring and concentrated mass collided with rigid body

Summary The Dynamic behaviour of a cylinder is investigated for the case where it collides with a rigid body with constant velocity. Spring and concentrated mass are attached to both ends of the cylinder. The relationships between the dimensions of cylinder and spring and the maximum values of dynamic stresses are obtained. Dynamic behaviour of the spring is also taken into consideration. The fundamental equations of oscillation are solved by the Laplace transformation method. From the results of theoretical analysis, it becames evident that impulsive stresses are damped considerably by the spring.

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Übersicht Es wird das dynamische Verhalten eines Zylinders untersucht, der mit konstanter Geschwindigkeit mit einem starren Körper zusammenstößt. An beiden Enden des Zylinders sind Federn und konzentrierte Massen angebracht. Für diesen Fall werden die maximalen Beanspruchungen in Abhängigkeit von den Abmessungen des Zylinders und der Feder abgeleitet. Dabei wird auch das dynamische Verhalten der Feder berücksichtigt. Die Schwingungsgleichungen werden mit Hilfe der Laplace-Transformation gelöst. Die Ergebnisse zeigen, daß die Stoßbeanspruchungen durch die Federn erheblich reduziert werden.

     

Numerical simulation of mass transfer to micropolar fluid flow past a stenosed artery

A mathematical model of unsteady non‐Newtonian blood flow together with the mass transfer through constricted arteries has been developed. The mass transport refers to the movement of atherogenic molecules, i.e. blood‐borne components, such as low‐density lipoproteins from flowing blood into the arterial walls or vice versa. The flowing blood is represented as the suspension of all erythrocytes assumed to be Eringen's micropolar fluid and the arterial wall is considered to be rigid having cosine‐shaped stenosis in its lumen. The mass transfer to blood is controlled by the convection–diffusion equation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell method and the results obtained are checked for numerical stability with the desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow‐field and the mass concentration along with their distributions over the entire arterial segment as well. The key factors, such as the wall shear stress and Sherwood number, are also examined for further quantitative insight into the flow and the mass transport phenomena through arterial stenosis. The present results show consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of a rigid body with an ellipsoidal cavity filled with viscous fluid

We revisit the approach proposed by F.L.  Chernousko to modeling the dynamics of a rigid body with a cavity entirely filled with a highly viscous fluid. Within the approach, a finite-dimensional model of the body+fluid system is offered and the influence of the fluid is represented as a special torque acting upon the body with solidified fluid. Our aim is to develop further and expand a few technical aspects of the Chernousko model. In particular, we offer a coordinate-free form for some essential formulas and consider the case of constrained dynamics. To illustrate the results obtained we explore the motion of a physical pendulum with a fluid-filled cavity on a rotating platform.     

Vertical motion of a spherical body with decreasing mass

The paper studies the fall and ascent in air of a spherical body with radius linearly decreasing with time. The first integral of the nonlinear equation of motion is expressed in closed form in terms of Bessel functions on the assumption that the aerodynamic drag depends on the velocity as a quadratic polynomial. The second integral is evaluated by an approximate formula. The reliability of the analytic solution is confirmed by comparing it with a numerical solution of the Cauchy problem __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 118–125, June 2008.     

Dynamic buckling of a single-degree-of-freedom system with variable mass

In this paper dynamic buckling of the single-degree-of-freedom system with variable mass is analyzed. In the system the mass variation is slow and is a function of slow variable time. Due to mass variation the impact force acts. The motion of the system is described with a nonlinear ordinary differential equation with time variable parameters. A new approximate analytic criterion of dynamic buckling for the non-autonomous systems which have the conservation law of energy type is developed. The conservation law is formed applying the Noetherian approach. The suggested method allows the determination of dynamic buckling load without solving the corresponding nonlinear differential equation of motion. For this value of dynamic load the motion of the system becomes unbounded. The obtained analytic value is compared with the numeric one. It shows a good agreement.     

Transient vibrations of a tau inclined cable with a riding accelerating mass

The objective of this paper is a theoretical and numerical study of the dynamics of a taut inclined cable with a riding accolerating mass, which is suspended from two points of different elevation. The moving mass is a trolley that is accelerated by a solid fuel rocket down the inclined cable and is aerodynamically brought to a halt. The thrust of the rocket is tangential to the deformed configuration of the cable.Methods of analysis consist of the dynamics of small deformations superimposed on the static catenary state. The problem is nonlinear due to presence of friction and the convective acceleration interaction of the moving mass and the cable. Galerkin's procedure for removal of spatial dependence and numerical integration are used to obtain convergent solutions.Deceased     

Dynamic analysis of a tethered satellite system with a moving mass

This paper presents a dynamic analysis of a tethered satellite system with a moving mass. A dynamic model with four degrees of freedom, i.e., a two-piece dumbbell model, is established for tethered satellites conveying a mass between them along the tether length. This model includes two satellites and a moving mass, treated as particles in a single orbital plane, which are connected by massless, straight tethers. The equations of motion are derived by using Lagrange’s equations. From the equations of motion, the dynamic response of the system when the moving mass travels along the tether connecting the two satellites is computed and analyzed. We investigate the global tendencies of the libration angle difference (between the two sections of tether) with respect to the changes in the system parameters, such as the initial libration angle, size (i.e. mass) of the moving mass, velocity of the moving mass, and tether length. We also present an elliptic orbit case and show that the libration angles and their difference increase as orbital eccentricity increases. Finally, our results show that a one-piece dumbbell model is qualitatively valid for studying the system under certain conditions, such as when the initial libration angles, moving mass velocity, and moving mass size are small, the tether length is large, and the mass ratio of the two satellites is large.     

Dynamic interaction of a magnetized solid body with a rarefied plasma flow

Dependences of the drag and lift coefficients of a magnetized sphere in a hypersonic rarefied plasma flow on the angle between the plasma flow velocity and the self-magnetic field induction vector of the body are obtained in a wide range of the ratio of the magnetic pressure to the plasma flow pressure. It is shown that changing the orientation of the magnetic field vector of the body and the incoming flow velocity can be used to control the dynamic interaction in the plasma–body system, namely, to decelerate and accelerate the magnetized sphere in a rarefied hypersonic plasma flow.     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of shape variation of projectile nose during high-speed penetration into concrete

A formula is developed to estimate the total mass loss of projectile, based on the assumptions that the peeling of molten surface layer in projectile nose is the primary cause of mass loss, and the frictional heat is totally absorbed by the projectile. Extrapolating this formula to predict the mass loss of local area of projectile, the receding displacement on projectile surface is obtained, which is vertical to the symmetry axis of projectile. Thereby, a finite difference method model is constructed to simulate the variation of projectile shape. The shape of residual projectile, depth of penetration of projectile and its mass loss obtained by calculation are found in good consistency with respective experimental data.     

Conservation of mass for a particle moving with high velocity

I.IntroductionItiswell-knownthatthe"lassofaparticleoranoh.jectisstrictlytoobservethelawofcollservatiollof1llasswbedmovewitlllowvelocity.Butathighvelocity,particularlynearthevelocityoflight,themass(restmass)oftheparticle,accordingtothetheoryofspecialrelativity,increasesrapidlywithitsincrementofthevelocity.Inotherwords,themassisnotinconservatioll\vitllitsvelocity.However.withtheoriesandresearchmethodsbringingforthflewideasandcomplement,andthehumanthoughtdevelopingconstantlywhatthemassisnotconse…     

Nonlinear vibration and thermal-buckling of a heated annular plate with a rigid mass

On the basis of Hamilton's principle and dynamic version of vonKàrmàn's equations,the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.     

Allowing for the plastic properties of rock in stability problems for a stratified rock mass

The paper addresses the important issue of allowing for the inelastic properties of rock in stability problems for a stratified rock mass. A three-dimensional nonlinear problem statement is used. An exact method to study the surface instability of a regularly layered semi-infinite medium is developed. New numerical results are obtained __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 68–81, December 2007.     

Dynamic and quasi-electromagnetostatic evolution of a thermoelectromagnetoelastic body

A standard technique of evolution equations in Hilbert spaces of possible states with finite energy supplies results of existence and uniqueness for the dynamic evolution of a thermoelectromagnetoelastic body and for its ‘‘quasi-electromagnetostatic approximation’’ whose relevance is established through a convergence result as a parameter, accounting for the ratio of the speed of elastic wave propagation to the celerity of the light, goes to zero.