A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading

An extension of the upper bound shakedown theorem to load histories in excess of shakedown has been presented elsewhere in this issue. Here the minimisation process described therein is applied to the solutions of the ratchet limit as well as shakedown and limit load for a range of simple problems. The solutions provide an estimate of the maxima of the varying plastic strain magnitudes, which is compared with the Neuber approximate values. The position of the ratchet boundary is confirmed by comparison step-by-step analysis.     

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

A global stability and bifurcation analysis of the transverse galloping of a square section beam in a normal steady flow has been implemented. The model is an ordinary differential equation with polynomial damping nonlinearity. Six methods are used to predict bifurcation, the amplitudes and periods of the ensuing Limit Cycle Oscillations: (i) Cell Mapping, (ii) Harmonic Balance, (iii) Higher Order Harmonic Balance, (iv) Centre Manifold linearization, (v) Normal Form and (vi) numerical continuation. The resulting stability predictions are compared with each other and with results obtained from numerical integration. The advantages and disadvantages of each technique are discussed. It is shown that, despite the simplicity of the system, only two of the methods succeed in predicting its full response spectrum. These are Higher Order Harmonic Balance and numerical continuation.     

Effect of amplitude and frequency of limit cycle oscillators on their coupled and forced dynamics

The occurrence of synchronization and amplitude death phenomena due to the coupled interaction of limit cycle oscillators (LCO) has received increased attention over the last few decades in various fields of science and engineering. Studies pertaining to these coupled oscillators are often performed by studying the effect of various coupling parameters on their mutual interaction. However, the effect of system parameters (i.e., the amplitude and frequency) on the coupled interaction of such LCO has not yet received much attention, despite their practical importance. In this paper, we investigate the dynamical behavior of time-delay coupled Stuart–Landau (SL) oscillators exhibiting subcritical Hopf bifurcation for the variation of amplitude and frequency of these oscillators in their uncoupled state. For identical SL oscillators, a gradual increase in the amplitude of LCO shrinks the amplitude death regions observed between the regions of in-phase and anti-phase synchronization leading to its eventual disappearance, resulting in the occurrence of phase-flip bifurcations at higher amplitudes of LCO. We also observe an alternate existence of in-phase and anti-phase synchronization regions for higher values of time delay, whose prevalence of occurrence increases with an increase in the frequency of the oscillator. With the introduction of frequency mismatch, the region of amplitude death. The forced response of SL oscillator shows an asymmetry in the Arnold tongue and the manifestation of asynchronous quenching of LCO. An increase in the amplitude of LCO narrows the Arnold tongue and reduces the region of asynchronous quenching observed in the system. Finally, we compare the coupled and forced response of SL oscillators with the corresponding experimental results obtained from laminar thermoacoustic oscillators and the numerical results from van der Pol (VDP) oscillators. We show that the SL model qualitatively displays many features observed experimentally in coupled and forced thermoacoustic oscillators. In contrast, the VDP model does not capture most of the experimental results due to the limitation in the independent variation of system parameters.

     

Estimate of the limit displacement wave amplitude in the dynamic problem on an out-of-plane crack

The paper presents several results of structural fracture macromechanics used to study the integrity of continuum under impulse loading conditions. The dynamic problem on a semi-infinite steady-state crack of longitudinal shear is considered. Exact analytical expressions for the stress tensor and displacement vector components on the crack line are obtained. The values of the threshold displacement amplitude on the wave front are determined for several structural materials.     

Stability and bifurcation for limit cycle oscillations of an airfoil with external store

In this paper, stability and local bifurcation behaviors for the nonlinear aeroelastic model of an airfoil with external store are investigated using both analytical and numerical methods. Three kinds of degenerated equilibrium points of bifurcation response equations are considered. They are characterized as (1) one pair of purely imaginary eigenvalues and two pairs of conjugate complex roots with negative real parts; (2) two pairs of purely imaginary eigenvalues in nonresonant case and one pair of conjugate complex roots with negative real parts; (3) three pairs of purely imaginary eigenvalues in nonresonant case. With the aid of Maple software and normal form theory, the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves are obtained, which can lead to static bifurcation and Hopf bifurcation. Under certain conditions, 2-D tori motion may occur. The complex dynamical motions are considered in this paper. Finally, the numerical solutions achieved by the fourth-order Runge–Kutta method agree with the analytic results.     

Application of bounds for creeping structures subjected to load variations above the shakedown limit

Previous work established upper bounds on work and displacement for creeping structures subjected to load variations above the shakedown limit. The present paper applies these bounds to three structures subjected to constant mechanical loading and to variable imposed strains. The results are in good agreement with those of more detailed calculations.     

A note on bounding solutions for creeping structures subjected to load variations above the shakedown limit

Previous work has established upper bounds on the deformations which occur in the cyclic stationary state of a creeping structure. The present note extends the results to describe the transitional behaviour in reaching the cyclic stationary state and also to allow non-cyclic loading. A particular form of the upper bound is applied to experiments reported in the literature of a cylinder subjected to cyclic internal pressure and repeated thermal shocks.     

Effects of an axial flow component on the Honji instability

This paper is concerned with a numerical study of the three-dimensional Honji instability that can arise in an oscillatory flow impinging on a circular cylinder. It is well known that when the fluid motion far from the cylinder is perpendicular to its axis then the flow is liable to a three-dimensional breakdown via this instability which initially appears as an axially periodic mushroom-like structure attached to the surface of the cylinder. Here the focus is on examining the Honji instability under an oblique inflow. The obliqueness of the free stream is represented by an angle of attack through introducing an axial flow component. It is found that the Honji mode is suppressed by increasing the axial flow component, and when this component is sufficiently large the instability mechanism is no longer operative so that all that remains is a featureless two-dimensional columnar flow. At smaller values of angle of attack, though the Honji structure remains, it is deformed by the axial flow component. The developed two-layer near-cylinder vortical structures can be related to the energy and momentum transfer between the two layers.     

航空遥感惯性稳定平台振动特性分析与隔振系统设计

针对航空遥感三轴惯性稳定平台隔离高频线振动的要求,在振动环境分析的基础上,以振动传递率为评价指标,对周期性干扰下惯性稳定平台的一次和二次隔振系统动力学模型进行了Matlab仿真及振动特性分析,进而对某轻小型惯性稳定平台的隔振系统进行了设计,最后为验证隔振系统效果,对惯性稳定平台进行了振动测试实验。实验结果表明:惯性稳定平台在受到30~500 Hz的外界干扰时能够平稳工作,且指向精度保持在0.2°以内,表明隔振系统设计合理有效。     

Experimental investigations of the compressibility of soils subjected to short-term loads using an automated system

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 126–129, May–June, 1990.     

A study on the cycle characteristics of an auto-cascade refrigeration system

This study presents experimental results on the cycle characteristics of an auto-cascade refrigeration system. The auto-cascade refrigeration (ACR) system is driven by a single compressor, using zeotropic mixture as refrigerant, which achieves cascade between high and low boiling point components by an evaporative condenser for the purpose of obtaining a lower evaporation temperature comparing with single refrigerant system. The coefficient of performance, cooling capacity, evaporation temperature, and pressures and temperatures of refrigerant at the inlet and outlet were measured and parameter analyses were conducted with different charging concentrations, different temperatures of cooling water and different matches of cycle flux between high and low boiling point components under the same evaporating pressure. The systematic theoretical analyses and experimental results depict the relations between the above parameters in an auto-cascade refrigeration system, which constitute a useful source for the auto-cascade refrigeration system’s design and analysis.     

Piecewise constrained optimization harmonic balance method for predicting the limit cycle oscillations of an airfoil with various nonlinear structures

A method is proposed to calculate the periodic solutions of piecewise nonlinear systems. The method is based on analytical derivation of nonlinear multi-harmonic equations of motion. Since periodic variations of nonlinear forces are characterized by different states, the vibration cycle is broken into sequential transition intervals according to the instant sets of state transitions. Analytical formulations of the harmonic coefficients of the nonlinear forces and its derivatives with respect to the harmonic coefficients of displacements are developed. Sensitivities of the harmonic coefficients of periodic solutions are determined for constructing explicit expressions for vibration amplitude levels as a function of structural parameters. Numerical investigations of the limit cycle oscillations and its sensitivities of an airfoil with different piecewise nonlinearities have been performed. The results show that the developed method is capable of determining the periodic solutions and its sensitivities with respect to the structural parameters. In order to guarantee time continuity of the nonlinear force, for the hysteresis model it is not right to track the periodic solutions by using the preload or freeplay as the continuation parameters.     

Three routes to chaos for a three-degree-of-freedom articulated cylinder system subjected to annular flow and impacting on the outer pipe

In this paper, the dynamics of a cantilevered articulated system of rigid cylinders interconnected by rotational springs, within a pipe containing fluid flow is studied. Although the formulation is generalized to any number of degrees-of-freedom (articulations), the present work is restricted to three-degree-of-freedom systems. The motions are considered to be planar, and the equations of motion, apart from impacting terms, are linearized. Impacting of the articulated cylinder system on the outer pipe is modelled by either a cubic spring (for analytical convenience) or, more realistically, by a trilinear spring model. The critical flow velocities, for which the system loses stability, by flutter (Hopf bifurcation) or divergence (pitchfork bifurcation) are determined by an eigenvalue analysis. Beyond these first bifurcations, it is shown that, for different values of the system parameters, chaos is obtained through three different routes as the flow is incremented: a period-doubling cascade, the quasiperiodic route, and type III intermittency. The dynamical behaviour of the system and differing routes to chaos are illustrated by phase-plane portraits, bifurcation diagrams, power spectra, Poincaré sections, and Lyapunov exponent calculations.     

Effects of tyre inflation pressure and forward speed on vibration of an unsuspended tractor

Relationships among intensity of vibrations, tractor speed, soil moisture content and tyre inflation pressure are important for the design of tractor suspension systems. This study was designed to evaluate the effect of tyre inflation pressure and forward speed on tractor vibration in the paddy fields of Southern China by using a two-wheel-drive unsuspended tractor with different combinations of forward speed, tyre inflation pressure and soil moisture content. During experiments, the vertical vibration accelerations in front and rear axles and triaxial vibration accelerations of the tractor body were measured using three accelerometers. Fourier analysis was applied to determine root mean square acceleration values in the low frequency range from 0.1 to 10 Hz. The results of the study indicate that tractor vibration is strongly affected by changing forward speed and tyre inflation pressure, and especially by changing forward speed and rear tyre inflation pressure. The research also shows the variation in the pattern of vibration intensity especially at the tractor’s front axle when field soil moisture content is changed.     

The optimality conditions for an upper bound on the displacement of a creeping body subjected to variable loading

A displacement bound for a creeping structure subject to variable thermal and mechanical loading was derived in a previous paper [1]. Here we discuss a sufficient condition for the bound to be optimal and suggest simple methods by which near optimal bounds may be computed. The theory is illustrated by evaluation of the bound for a beam problem with a single redundancy.