Parkes problems revisited - Application of response number

Response number R-n(n), proposed in [3, 4], is an important independent dimensionless number for the dynamic response of structures [2]. In this paper, the response number is applied to the dynamic plastic response of the well-known Parkes' problem, i.e., beams struck by concentrated mass.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Effective dielectric response of nonlinear composites with external ac and dc electric field

The perturbation method is developed to investigate the effective nonlinear dielectric response of Kerr composites when the external ac and dc electric field is applied. Under the external ac and dc electric field E-app=E-a(1+sin omegat), the effective coupling nonlinear response can be induced by the cubic nonlinearity of Kerr nonlinear materials at the zero frequency, the finite basic frequency omega, the second and the third harmonics, 2omega and 3omega, and so on. As an example, we have investigated the cylindrical inclusions randomly embedded in a host and derived the formulas of the effective nonlinear dielectric response at harmonics in dilute limit. For a higher concentration of inclusions, we have proposed a nonlinear effective-medium approximation by introducing the general effective nonlinear response. With the relationships between the effective nonlinear response at harmonics and the general effective nonlinear response, we have derived a set of formulas of the effective nonlinear dielectric responses at harmonics for a larger volume fraction. (C) 2004 American Institute of Physics.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.

考虑多种非线性因素的张力腿平台动力响应

建立了一种考虑多种非线性因素的张力腿平台(TLP)分析模型,其中包括六自由度有限位移,各自由度之间的耦合,瞬时湿表面,瞬时位置,自由表面效应及粘性力等因素引起的非线性.推导出TLP六自由度非线性运动方程.对某典型张力腿平台ISSC TLP进行了时域上的数值计算,求得该平台在规则波作用下的六自由度运动响应.用退化到线性范围的解与已有解进行了对比,吻合良好.数值结果表明,综合考虑非线性因素后响应明显改变,建议在设计TLP平台的时候,考虑非线性因素的影响.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

Effects of fundamental structure parameters on dynamic responses of submerged floating tunnel under hydrodynamic loads

This paper investigates the effects of structure parameters on dynamic responses of submerged floating tunnel (SFT) under hydrodynamic loads. The structure parameters includes buoyancy-weight ratio (BWR), stiffness coefficients of the cable systems, tunnel net buoyancy and tunnel length. First, the importance of structural damp in relation to the dynamic responses of SFT is demonstrated and the mechanism of structural damp effect is discussed. Thereafter, the fundamental structure parameters are investigated through the analysis of SFT dynamic responses under hydrodynamic loads. The results indicate that the BWR of SFT is a key structure parameter. When BWR is 1.2, there is a remarkable trend change in the vertical dynamic response of SFT under hydrodynamic loads. The results also indicate that the ratio of the tunnel net buoyancy to the cable stiffness coefficient is not a characteristic factor affecting the dynamic responses of SFT under hydrodynamic loads.

Influences of Structural Damping and Buoyancy-Weight Ratio on Dynamic Responses of Submerged Floating Tunnel

The recent progress of submerged floating tunnel (SFT) investigation and SFT prototype (SFTP) project in Qiandao Lake (Zhejiang Province, P.R. China) is the background of this research. Structural damping effect is brought into present computation model in terms of Rayleigh damping. Based on the FEM computational results of SFTPs as a function of buoyancy-weight ratio (BWR) under hydrodynamic loads, the effect of BWR on the dynamic response of SFT is illustrated. In addition, human comfort index is adopted to discuss the comfort status of the SFTP.

Multimode-interference-type thermo-optic variable optical attenuator with a response frequency of 10 kHz

A thermo-optic variable optical attenuator based on a multimode interference coupler principle is fabricated. The propagation loss of the fabricated device is 1.6 to 3.8 dB at the wavelength range 1510 to 1610 nm, which is very near the calculated value (1.2 dB) by the finite difference beam propagation method. The maximum power consumption is 363 mW and the dynamic attenuation range is 0 to 26 dB. The response frequency of the fabricated attenuator is about 10 kHz. (C) 2003 Society of Photo-Optical Instrumentation Engineers.

Preparation and nonlinear optical properties of ultrathin composite films containing both a polyoxometalate anion and a binuclear phthalocyanine

An ultrathin composite film containing both polyoxometalate anion [PMo12O40](3-) ( PMo12) and a planar binuclear phthalocyanine, bi-CoPc, has been prepared by the electrostatic layer-by-layer self-assembly method. UV-vis measurements revealed regular film growth with each four-layer {PMo12/bi-CoPc/PSS/PAH} adsorption. The lm structure was characterized by small-angle X-ray reflectivity measurements, X-ray photoelectron spectra, and AFM images. The nanothick film shows a third-order nonlinear optical response of chi((3)) = 4.21 x 10(-12) esu. Experimental investigations also indicate that the combination of polyoxometalate anions [PMo12O40](3-) with the phthalocyanine bi-CoPc in multilayer films can enhance the third-order NLO susceptibility and modify the third-order NLO absorption of bi-CoPc.

降雨触发滑坡的非线性模型与斜坡演化的混沌效应

This paper analyzes landsliding process by nonlinear theories, especially the influence mechanism of external factors (such as rainfall and groundwater) on slope evolution. The author investigates landslide as a consequence of the catastrophic slide of initially stationary or creeping slope triggered by a small perturbation. A fully catastrophe analysis is done for all possible scenarios when a continuous change is imposed to the control parameters. As the slip surface continues and erosion due to rainfall occurs, control parameters of the slip surface may evolve such that a previously stable slope may become unstable (e.g. catastrophe occurs), when a small perturbation is imposed. Thus the present analysis offers a plausible explanation to why slope failure occurs at a particular rainfall, which is not the largest in the history of the slope. It is found, by analysis on the nonlinear dynamical model of the evolution process of slope built, that the relationship between the action of external environment factors and the response of the slope system is complicatedly nonlinear. When the nonlinear action of slope itself is equivalent to the acting ability of external environment, the chaotic phenomenon appears in the evolution process of slope, and its route leading to chaos is realized with bifurcation of period-doublings. On the basis of displacement time series of the slope, a nonlinear dynamic model is set up by improved Backus generalized linear inversion theory in this paper. Due to the equivalence between autonomous gradient system and catastrophe model, a standard cusp catastrophe model can be obtained through variable substitution. The method is applied to displacement data of Huangci landslide and Wolongsi landslide, to show how slopes evolve before landsliding. There is convincing statistical evidence to believe that the nonlinear dynamic model can make satisfied prediction results. Most important of all, we find that there is a sudden fall of D, which indicates the occurrence of catastrophe (when D=0).

Novel experimental phenomena of fine-particle fluidized beds

The dynamic response of bed height and concentration waves in liquid-solid fluidized beds to a step change in the fluidization velocity is considered. We experimentally study the liquid-solid fluidized beds, spherical beadings, with sizes ranging from 230 to 270 mesh and the inner diameter of columns made from glass is 2.4 mm. Experimental results find that under certain conditions, fine particles with large Richardson-Zaki exponent n display different dynamic behavior from usual particles with smaller n during expansion and collapse of the fluidized state. (c) 2007 Elsevier Inc. All rights reserved.

Crack propagation in structures subjected to periodic excitation

In the present paper, a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten (mimicking crack growth) if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.