Influence of swirl on the stability of a rod in annular leakage flow

The influence of swirl (flow rotation) on the stability of a rod in annular leakage flow is investigated. Under the assumption of laminar flow and plane vibrations (no whirling), it is shown that the swirl acts, in effect, as an elastic foundation with negative foundation stiffness, the magnitude being proportional to the mean circumferential flow rate squared. Consequently, swirl always lowers the critical axial flow speed in case of divergence instability of a rod of finite length. Numerical analysis is needed to predict the effect of swirl in case of flutter instability of a finite rod; this is not performed here. However, for the flutter-like instability of travelling waves in an infinite rod-channel system, it is shown analytically that swirl again always lowers the critical axial flow speed. Finally, it is found that by circumferential flow alone, the travelling waves are extinguished at a certain flow rate, followed by a divergence-like instability.     

On the Use of the Restitution Condition in Flexible Body Dynamics

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.     

An asymptotic approach to the problem of the free oscillations of a beam

Equations describing the free small longitudinal and transverse oscillations of a straight elastic beam of rectangular cross section are obtained using the plane linear theory of elasticity and the method of integrodifferential relations. The initial system of partial differential equations is reduced to a system of ordinary linear differential equations with constant coefficients. The effect of the geometrical and elastic characteristics of the beam on the frequency and form of the natural oscillations is investigated. For longitudinal motions it is shown that different types of natural displacements and internal stresses of the beam exist. For transverse oscillations, it is found that there are frequency zones corresponding to different forms of the solutions of the characteristic equation obtained using the proposed model.     

SOME GENERAL EFFECTS OF STRONG HIGH-FREQUENCY EXCITATION: STIFFENING, BIASING AND SMOOTHENING

Mechanical high-frequency (HF) excitation provides a working principle behind many industrial and natural applications and phenomena. This paper concerns three particular effects of HF excitation, that may change the apparent characteristics of mechanical systems: (1) stiffening, by which the apparent linear stiffness associated with an equilibrium is changed, along with derived quantities such as stability and natural frequencies; (2) biasing by which the system is biased towards a particular state, static or dynamic, which does not exist or is unstable in the absence of the HF excitation; and (3) smoothening, referring to a tendency for discontinuities to be effectively “smeared out” by HF excitation. Illustrating first these effects for a few specific systems, analytical results are provided that quantify them for a quite general class of mechanical systems. This class covers systems that can be modelled by a finite number of second order ordinary differential equations, generally non-linear, with periodically oscillating excitation terms of high frequency and small amplitude. The results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems, for calculating effects for specific systems using well-defined formulas, and for possibly designing systems that display prescribed characteristics in the presence of HF excitation.     

Characterization of strongly interacted multiple cracks in an infinite plate

Based on the Kachanov method and the alternating iteration technique, a new method is proposed to deal with the problem of the strongly interacted multiple cracks in an infinite plate. Unlike the Kachanov method which neglects the interaction of the tractions of the non-uniform components, the tractions of the non-uniform components on the surfaces of cracks are considered through the alternating technique. The accuracy and efficiency of present method are validated by comparing the results of two collinear and two parallel overlapped open the cracks obtained by the present method with those of the exact solutions, the results of the Kachanov method and the alternating iteration technique. Applications of present method in solving sliding close crack problems and evaluating the plastic zones demonstrate the versatility of present method.     

The force on a lattice defect in an elastic body

It is shown that the force on a lattice defect in an elastic body is, like the force on a disclination in a nematic liquid crystal, a real force which, for equilibrium, must be balanced by an external force applied to the closed surface enclosing the defect.     

Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays

A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.     

Meshfree analysis of softening elastoplastic solids using variational multiscale method

A meshfree multiscale method is presented for efficient analysis of elastoplastic solids. In the analysis of softening elastoplastic solids, standard finite element methods or meshfree methods typically yield mesh-dependent results. The reason for this well-known effect is the loss of ellipticity of the boundary value problem. In this work, the scale decomposition is carried out based on a variational form of the problem. A coarse scale is designed to represent global behavior and a fine scale to represent local behavior. A fine scale region is detected from the local failure analysis of an acoustic tensor to indicate a region where deformation changes abruptly. Each scale variable is approximated using a meshfree method. Meshfree approximation is well-suited for adaptivity. As a method of increasing the resolution, a partition of unity based extrinsic enrichment is used. In particular, fine scale approximations are designed to appropriately represent local behavior by using a localization angle. Moreover, the regularization effect through the convexification of non-convex potential is embedded to represent fine scale behavior. Each scale problem is solved iteratively. The proposed method is applied to shear band problems. In the results of analysis about pure shear and compression problems, straight shear bands can be captured and mesh-insensitive results are obtained. Curved shear bands can also be captured without mesh dependency in the analysis of indentation problem.     

Scaling impacted structures

Summary The problem of non-scalability of structures under impact loads caused by strain-rate effects is solved in this article by properly correcting the impact velocity. The technique relies on the use of an alternative dimensionless basis, together with a mathematical model which allows the calculation of a correction factor for the impact velocity. This new velocity, when applied to the model, makes it to assure the satisfaction of the scaling laws. The indirect similitude method detailed here is applied to two strain-rate sensitive structures, a double plate under in-plane impact and a beam subjected to a blast load. The results show a very good agreement so that the model and a prototype made from strain rate sensitive materials behave the same.accepted for publication 3 March 2004