Oscillations of a?beam with a?time-varying mass

This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well.     

Interaction of an unsteady two‐phase jet with a layer of a disperse medium

Discharge of a twophase jet from a cylindrical channel into a bounded layer of a disperse medium is numerically simulated using the equations of the mechanics of heterogeneous media with allowance for the differences in velocity, temperature, and phase stresses. The effect of separation of the gas phase from the disperse phase in the layer is revealed and verified experimentally. A comparison with a similar process of gas discharge at equal initial pressures shows that in the interaction with the disperse layer, the twophase flow has a longer momentum and direction.     

Simulation of Wind Flow Around a Building with a k–ε Model

The three-dimensional numerical simulation of airflow around a building using a k–ε two-equation turbulence model is presented in this paper. Several cases of numerical simulation of airflow around a building are carried out to estimate the influence of mesh spacing on simulated results. The accuracy of simulations is examined by comparing the predicted results with wind-tunnel experiments. It is confirmed that numerical simulations by means of the k–ε model reproduce the velocity fields well when using fine mesh resolution. In the latter part of the paper, the simulation method is applied to predict the flow field around a building with different width-to-height ratios, under light wind conditions. Received 16 June 1999 and accepted 20 July 2000     

The Minimal Thickness of a Semicircular Arch with a Tension-Free Crown∗

ABSTRACT

When a semicircular elastic arch is loaded with a single point force at the vertex, the stress at interior points depends on the thickness of the arch and on the way the abutments react. Applying the theory of plane elasticity, three typical load-bearing abutment constraints are evaluated to find the minimal thickness at which no tensile stress occurs at a given interior point. Such thickness is found to be quite large.     

Stressed state near a wedge‐shaped twin with a disbalance of densities of twinning dislocations

The influence of disbalance of densities of twinning dislocations at the boundaries on the stressed state inside a wedgeshaped twin, near its top, and in external regions adjoining the twinning boundary is studied using a dislocation model.     

Relaminarization of a turbulent boundary layer with a mach number M∞=4

Results of experimental studies are presented on relaminarization of a supersonic turbulent boundary layer behind an expansion fan for a freestream Mach number M=4 within a range of Reynolds numbers Re₁=8·10⁶ – 26·10⁶ m^–1. Experimental data on distributions of the mean velocity and massflow fluctuations and the skin friction force are obtained. Partial relaminarization of the boundary layer is reached in the experiments. The calculations of relaminarization criteria show that they can be used to predict the onset of the relaminarization process at high supersonic flow velocities.     

Lag synchronization of a class of chaotic systems with unknown parameters

Research on chaos synchronization of dynamical systems has been largely reported in literature. However, synchronization of different structure—uncertain dynamical systems—has received less attention. This paper addresses synchronization of a class of time-delay chaotic systems containing uncertain parameters. A unified scheme is established for synchronization between two strictly different time-delay uncertain chaotic systems. The synchronization is successfully achieved by designing an adaptive controller with the estimates of the unknown parameters and the nonlinear feedback gain. The result is rigorously proved by the Lyapunov stability theorem. Moreover, we illustrate the application of the proposed scheme by numerical simulation, which demonstrates the effectiveness and feasibility of the proposed synchronization method.     

Deformations of a clamped–clamped elastica inside a circular channel with clearance

In this paper, we study the planar deformations of an elastica inside a circular channel with clearance. One end of the elastica is fully clamped, while the other end is partially clamped in the lateral direction and is subject to a pushing force longitudinally. In the experiment we first observe various deformation patterns after pushing the elastica through the partial clamp. Both symmetric and asymmetric deformations are recorded. Special attention is focused on the contact conditions between the elastica and the circular channel. In order to analyze the elastica deformation theoretically, we first divide the elastica into several elementary sub-domains depending on the contact condition between the elastica and the circular channel. In each sub-domain the elastica is either loaded only at the ends or in full contact with the outer wall. Armed with these basic equilibrium analyses, we proceed to calculate and classify the loaded elastica into several deformation patterns. Finally, we present the load-deflection curves, both theoretically and experimentally, which relate the longitudinal forces at both ends to the elastica length increase inside the channel. The branching phenomena predicted theoretically agree fairly well quantitatively with the experimental measurements.     

Analysis of a Belyakov homoclinic connection with ?2-symmetry

We study the existence, in a two-parameter plane, of double- and triple-pulse homoclinic orbits in a ?₂-symmetric three-dimensional system, in the vicinity of a Belyakov point (a?point where the involved equilibrium in the homoclinic connection changes from saddle to saddle-focus) in the Shil??nikov zone. The first-order computation of these global connections allows us to describe their position and organization in the parameter plane. The analytical results are successfully applied in the study of such degeneration in Chua??s equation.     

Kinematics of Bulkley–Herschel fluid flow with a free surface during the filling of a channel

The non-Newtonian fluid flow with a free surface occurring during the filling of a plane channel in the gravity field is modeled. The mathematical formulation of the problem using the rheological Bulkley–Herschel model is presented. A numerical finite-difference algorithm for solving this problem is developed. A parametric investigation of the main characteristics of the process as functions of the control parameters is performed. The effect of the rheological parameters of the fluid on the distribution of the quasisolid motion zones is demonstrated.     

One-Dimensional Interaction of a Cylindrical Unloading Wave with a Moving Elastic–Plastic Boundary

The one-dimensional dynamic problem of the theory of large elastic–plastic deformations is considered for the interaction of an unloading wave with an elastic–plastic boundary. It is shown that before the occurrence of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elasti©viscoplastic material filling the round tube, which is retained in the tube due to friction on its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment of the onset of slippage of the material along the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.     

Dynamical response of a pendulum driven horizontally by a DC motor with a slider–crank mechanism

Nonlinear Dynamics - The pendulum is excited horizontally by a system of a DC motor and a slider–crank mechanism. Mathematical modeling is realistic and based on experimental rig, taking into...     

Dynamics of a cylindrical shell with elastic bottom filled with a gas–liquid mixture and subject to two-frequency excitation

The paper reports experimental data on the nonlinear dynamic deformation of the elastic bottom of a cylindrical shell and the formation of bubbles and their clusters under two-frequency excitation     

Effort dynamics of a delay-induced prey–predator system with reserve

This paper describes a prey?Cpredator fishery system with prey dispersal in a two-patch environment, one of which is a free fishing zone and the other a protected zone. The proposed system reflects the dynamic interaction between the net economic revenue and the fishing effort used to harvest the population in presence of a suitable tax. Local as well as global stability of the system is analyzed. The optimal taxation policy is formulated and solved with the help of Pontryagin??s maximal principle. The objective of the paper is to achieve the sustainability of the fishery, keeping the ecological balance, and maximize the monetary social benefit. The dynamical behavior of the delay system is further analyzed through incorporating discrete type gestational delay of predators, and the existence of Hopf bifurcation phenomenon is checked at the interior equilibrium point. Moreover, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Theoretical results are verified with the help of numerical examples and graphical illustrations.     

Slipping–rolling transitions of a body with two contact points

Nonlinear Dynamics - In this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling...     

Spatio-temporal dynamics of a reaction-diffusion system for a predator–prey model with hyperbolic mortality

We investigate the effects of diffusion on the spatial dynamics of a predator–prey model with hyperbolic mortality in predator population. More precisely, we aim to study the formation of some elementary two-dimensional patterns such as hexagonal spots and stripe patterns. Based on the linear stability analysis, we first identify the region of parameters in which Turing instability occurs. When control parameter is in the Turing space, we analyse the existence of stable patterns for the excited model by the amplitude equations. Then, for control parameter away from the Turing space, we numerically investigate the initial value-controlled patterns. Our results will enrich the pattern dynamics in predator–prey models and provide a deep insight into the dynamics of predator–prey interactions.     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Entrance of a body with a lifting force and a heat‐conducting surface into the earth's atmosphere

The problem of gliding descent of a smooth blunted body possessing a lifting force and a heatconducting surface in the Earth's atmosphere is solved. The descent trajectory is represented not only by the altitude and velocity as functions of the flight time but also by angles of attack and sideslip varying with time. Threedimensional equations of a parabolized viscous shock layer for a multispecies mixture of gases are solved jointly with a threedimensional equation of unsteady heat conduction in the solid phase.     

Gamma Convergence of a Family of Surface–Director Bending Energies with Small Tilt

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in \({\mathbb{R}^3}\) equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such types of energies arise, for example, in a model for bilayer membranes introduced by Peletier and Röger (Arch Ration Mech Anal 193(3), 475–537, 2009). Here we prove in three space dimensions in the vanishing-tilt limit a Gamma-liminf estimate with respect to a specific curvature energy. In order to obtain appropriate compactness and lower semi-continuity properties we use tools from geometric measure theory, in particular the concept of generalized Gauss graphs and curvature varifolds.     

Stabilizability of Two-Dimensional Navier—Stokes Equations with Help of a Boundary Feedback Control

For 2D Navier--Stokes equations defined in a bounded domain W \Omega we study stabilization of solution near a given steady-state flow [^(v)](x) \hat v(x) by means of feedback control defined on a part G \Gamma of boundary ?W \partial\Omega . New mathematical formalization of feedback notion is proposed. With its help for a prescribed number s > 0 \sigma > 0 and for an initial condition v₀(x) placed in a small neighbourhood of [^(v)](x) \hat v(x) a control u(t,x'), x￠ ? G x' \in \Gamma , is constructed such that solution v(t,x) of obtained boundary value problem for 2D Navier--Stokes equations satisfies the inequality: ||v(t,·)-[^(v)]||_H¹\leqslant ce^-st    for  t \geqslant 0 \|v(t,\cdot)-\hat v\|_{H^1}\leqslant ce^{-\sigma t}\quad {\rm for}\; t \geqslant 0 . To prove this result we firstly obtain analogous result on stabilization for 2D Oseen equations.