Nonlinear longitudinal forced vibration of a hysteretic bar: An analytical solution

This work investigates the nonlinear longitudinal forced vibrations of a bar with hysteretic dynamics typical of rocks and man-made geomaterials. The material properties are described by a constitutive relation that includes energy dissipation effects consistently with hysteretic dynamics. The harmonic balance method and a perturbation technique that uses the material's modulus defect as perturbation parameter are employed to solve the equation of motion. The spatial dependence of the modulus defect, which is disregarded in earlier solutions of this problem, is duly accounted for. According to this model, the resonance frequency shift is proportional to the amplitude of the excitation, while the inverse of the quality factor increases as the square root of the latter. Further, the spatial variation of the modulus defect is shown to affect the modulation of the fundamental component along the bar. The nonlinear spectral components are of odd order, with amplitude proportional to the maximum value of the modulus defect and to the square of the excitation's amplitude, and decreases non-monotonically with increasing harmonic order. The motivation for this work is twofold. Analytical models may improve our understanding of the dynamics of hysteretic materials in general, and of the mutual interaction of material defects in particular. Secondly, this work establishes a bench-mark result on a mathematically simple hysteretic system against which alternative mathematical approaches, possibly concerning material with complex constitutive relations, could be tested.     

Dynamic responses of a solid wall in contact with a bubbly liquid excited by thermal shock loading

Several MW-class spallation neutron sources are being developed in the world. Specifically, intensive and high energy protons are injected into heavy liquid metals (mercury, lead or lead-bismuth eutectic) to induce the spallation reaction that produces neutrons. At the moment when the proton beams are injected, thermal shock occurs in the liquid metal, causing pressure waves to propagate in the liquid metal, collide against the container and damage it.It is proposed that microbubbles are injected into the liquid metal to mitigate the impulsive pressure waves by means of absorption and attenuation effects. These effects are dependent on the relationship between bubble size and the rate of pressure increase. In the present experiment, a very rapid rise in pressure in the order of MPa/μs, equivalent to the rise in pressure due to proton beam injection, was simulated by the electric discharge method in a water loop test to investigate the impulsive pressure mitigation effect of injected microbubbles. The solid wall response was measured using an accelerometer, and the dynamic responses of microbubbles were observed using an ultra-high-speed camera filming at 5 × 10⁵ frame/s. The sound velocity in bubbly water was estimated using a differential image technique. It was confirmed from the experimental results that microbubbles are effective in reducing impulsive pressure waves and to suppressing the impact vibration of the solid wall in contact with the liquid.     

多用途输液立管涡激振动实验研究与疲劳分析

为研究输运不同流体的海洋立管在海流作用下的振动规律,在大型波浪流水槽中进行涡激振动模型实验。实验分别将四种不同质量比的立管模型竖直固定于支架上,立管外部承受不同速度的流体作用,上端施加顶张力。立管模型上均匀布置六个测点,根据每个测点布置的两个应变计,分别测得来流向和横向两个方向振动响应。通过小波变换对实验数据进行去噪处理,利用振型分解法求解立管各点涡激振动位移。考察输运不同流体对立管自振频率以及涡激振动响应的影响,并利用雨流计数法对模型进行疲劳分析。实验结果表明,随质量比增加立管涡激振动频率降低;低质量比的立管更容易产生大位移。     

函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

Prediction and assignment of site occupation and energy levels for Pb ions in crystal hosts

The environmental factor h_e of the host was calculated quantitatively in Pb²⁺-doped 23 compounds based on the dielectric theory of chemical bond for complex crystals. The relationship between the A band energy E_A of Pb²⁺ and the environmental factor h_e was intensively studied. The results indicate that E_A of Pb²⁺ decreases linearly with increasing of h_e. A linear model was proposed which allows us to correctly predict and assign the site occupations and the position of A band for Pb²⁺-doped compounds if the crystal structure and the refraction index were known. Applied to SrGa₂O₄:Pb²⁺, CaAl₂B₂O₇:Pb²⁺ and SrAl₂B₂O₇:Pb²⁺, the theoretical predictions are in very good agreement with the experimental data. In SrGa₂O₄:Pb²⁺, the excitation spectrum of Pb²⁺ from two different cation sites was identified: the higher energy band of A (265 nm) from the site of Sr2, and the lower ones (280 nm) from the site of Sr1.     

Passenger grouping with risk levels in an airport security system

This is a follow-up to the recent paper by Lazar Babu et al. [V.L. Lazar Babu, R. Batta, L. Lin, Passenger grouping under constant threat probability in an airport security system, European Journal of Operational Research 168 (2006) 633–644] which investigated the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. A basic assumption in that paper was that the threat probability is constant across all passengers. In this paper, we relax this assumption and consider the case where passenger risk levels are incorporated. We assume that passengers are classified into several risk classes via some passenger prescreening system, for example, Computer-Assisted Passenger Prescreening System II (CAPPS II). We consider the separate grouping of every class of passengers such that the overall false alarm probability is minimized while maintaining the overall false clear probability within specifications set by a security authority. Meanwhile, we consider the staffing needs at each check station. The problem is formulated as a mixed integer linear program. An illustrative example of the model is presented with comparisons to the model in Lazar Babu et al. (2006) using two performance measures: probability of false alarm and total number of screeners needed. Our conclusion is that incorporation of risk levels through passenger grouping strategies leads to a more efficient security check system.     

Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory

A gradient-enriched shell formulation is introduced in the present study based on the first order shear deformation shell model and the stress gradient and strain-inertia gradient elasticity theories are used for dynamic analysis of single walled carbon nanotubes. It provides extensions of the first order shear deformation shell formulation with additional higher-order spatial derivatives of strains and stresses. The higher-order terms are introduced in the formulation by using the Laplacian of the corresponding lower-order terms. The proposed shell formulation includes two length scale size parameters related to the strain gradients and inertia gradients. The effects of the transverse shear, aspect ratio, circumferential and half-axial wave numbers and length scale parameters on different vibration modes of the single-walled carbon nanotubes are elucidated. The results are also compared with those obtained from a classical shell theory with Sanders–Koiter strain-displacement relationships.     

Implantation angle influence on penetration of boron channelled ions into silicon

Experiments on the dependence of penetration of boron ions channelled into silicon are described.     

Manufacturer's optimal pricing and lot-sizing policies under trade-credit financing

In the year 2006, Teng et al considered an appropriate economic production quantity (EPQ) model in which the manufacturer receives the supplier's trade credit and provides trade credit to the customer simultaneously. The following two payment methods were discussed by Teng et al: The main purpose of this paper is summarized below: Finally, with a view to further motivating the interested researchers for using the methodology and mathematical analytic techniques in several other contexts in the field, we have chosen to include, in Section 12, a number of related recent works in the field.     

Vibration of a rectangular plate with a central power-law profiled groove by the Rayleigh–Ritz method

The prediction of natural frequencies of rectangular plates where a profiled indentation is present is made using a Rayleigh–Ritz variational energy method. Panels with holes are often found for access cables and access gaps, and it is shown that the application of damping to the profile leads to a more efficient method of reducing vibration than covering a whole rectangular plate, which is advantageous where weight saving is necessary.