Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Relationships Between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Conical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Linear Stability Analysis of Convection in Two-Layer System with an Evaporating Vapor-Liquid Interface

Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer.A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Bénard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Biot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Biot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below.

可压剪切层线性稳定性特征直接数值模拟=Direct Simulation of the Linear Instabilities in Compressible Shear Layers

基于伪随机数生成技术促生白噪声扰动,以高精度迎风/对称紧致混合差分算法求解二维/三维非定常可压Navier-Stokes方程,揭示了可压自由剪切层初始剪切过程中扰动的线性演化特征,以及该过程对扰动波数和方向的内在选择性.验证了所用算法的有效性,表明线性理论同数值模拟相结合是可压剪切层研究的合理途径之一.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

On the design of the piecewise linear vibration absorber

This paper explores the potential of the piecewise linear vibration absorber in a system subject to narrow band harmonic loading. Such a spring is chosen because the design of linear springs is common knowledge among engineers. The two-degrees-of-freedom system is solved by using the Incremental Harmonic Balance method, and response aspects such as stiffness crossing frequency and jump behaviour are discussed. The effects of mass, stiffness, natural frequency ratios, and stiffness crossing positions on the suppression zone are probed. It is shown that a hardening absorber can deliver a wider bandwidth than a linear one over a range of frequencies. The absorber parameters needed to produce good designs have been determined and the quality of the realized suppression zone is discussed. Design guidelines are formulated to aid the parameter selection process.

Study Of The Damage-Induced Anisotropy Of Quasi-Brittle Materials Using The Component Assembling Model

Damage-induced anisotropy of quasi-brittle materials is investigated using component assembling model in this study. Damage-induced anisotropy is one significant character of quasi-brittle materials coupled with nonlinearity and strain softening. Formulation of such complicated phenomena is a difficult problem till now. The present model is based on the component assembling concept, where constitutive equations of materials are formed by means of assembling two kinds of components' response functions. These two kinds of components, orientational and volumetric ones, are abstracted based on pair-functional potentials and the Cauchy - Born rule. Moreover, macroscopic damage of quasi-brittle materials can be reflected by stiffness changing of orientational components, which represent grouped atomic bonds along discrete directions. Simultaneously, anisotropic characters are captured by the naturally directional property of the orientational component. Initial damage surface in the axial-shear stress space is calculated and analyzed. Furthermore, the anisotropic quasi-brittle damage behaviors of concrete under uniaxial, proportional, and nonproportional combined loading are analyzed to elucidate the utility and limitations of the present damage model. The numerical results show good agreement with the experimental data and predicted results of the classical anisotropic damage models.

Quasi-Dammann Grating With Proportional Intensity Array Spots

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity orders are given. The experimental results with a third-order quasi-Dammann grating, which has an intensity proportion of 3:2:1 from zero order to second order, are presented. (C) 2008 Optical Society of America

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

Molecular/Cluster Statistical Thermodynamics Methods To Simulate Quasi-Static Deformations At Finite Temperature

The rapid evolution of nanotechnology appeals for the understanding of global response of nanoscale systems based on atomic interactions, hence necessitates novel, sophisticated, and physically based approaches to bridge the gaps between various length and time scales. In this paper, we propose a group of statistical thermodynamics methods for the simulations of nanoscale systems under quasi-static loading at finite temperature, that is, molecular statistical thermodynamics (MST) method, cluster statistical thermodynamics (CST) method, and the hybrid molecular/cluster statistical thermodynamics (HMCST) method. These methods, by treating atoms as oscillators and particles simultaneously, as well as clusters, comprise different spatial and temporal scales in a unified framework. One appealing feature of these methods is their "seamlessness" or consistency in the same underlying atomistic model in all regions consisting of atoms and clusters, and hence can avoid the ghost force in the simulation. On the other hand, compared with conventional MD simulations, their high computational efficiency appears very attractive, as manifested by the simulations of uniaxial compression and nanoindenation. (C) 2008 Elsevier Ltd. All rights reserved.

Energy Dissipation In Fracture Of Bulk Metallic Glasses Via Inherent Competition Between Local Softening And Quasi-Cleavage

Compression, tension and high-velocity plate impact experiments were performed on a typical tough Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) over a wide range of strain rates from similar to 10(-4) to 10(6) s(-1). Surprisingly, fine dimples and periodic corrugations on a nanoscale were also observed on dynamic mode I fracture surfaces of this tough Vit 1. Taking a broad overview of the fracture patterning of specimens, we proposed a criterion to assess whether the fracture of BMGs is essentially brittle or plastic. If the curvature radius of the crack tip is greater than the critical wavelength of meniscus instability [F. Spaepen, Acta Metall. 23 615 (1975); A.S. Argon and M. Salama, Mater. Sci. Eng. 23 219 (1976)], microscale vein patterns and nanoscale dimples appear on crack surfaces. However, in the opposite case, the local quasi-cleavage/separation through local atomic clusters with local softening in the background ahead of the crack tip dominates, producing nanoscale periodic corrugations. At the atomic cluster level, energy dissipation in fracture of BMGs is, therefore, determined by two competing elementary processes, viz. conventional shear transformation zones (STZs) and envisioned tension transformation zones (TTZs) ahead of the crack tip. Finally, the mechanism for the formation of nanoscale periodic corrugation is quantitatively discussed by applying the present energy dissipation mechanism.

Comparison Of The Quasi-Static Method And The Dynamic Method For Simulating Fracture Processes In Concrete

Concrete is heterogeneous and usually described as a three-phase material, where matrix, aggregate and interface are distinguished. To take this heterogeneity into consideration, the Generalized Beam (GB) lattice model is adopted. The GB lattice model is much more computationally efficient than the beam lattice model. Numerical procedures of both quasi-static method and dynamic method are developed to simulate fracture processes in uniaxial tensile tests conducted on a concrete panel. Cases of different loading rates are compared with the quasi-static case. It is found that the inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, an unrealistic result will be obtained if a fracture process including unstable cracking is simulated by the quasi-static procedure.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Numerical-simulation of ac plasma-arc thermodynamics

A mathematical model and approximate analysis for the energy distribution of an ac plasma arc with a moving boundary is developed. A simplified electrical conductivity function is assumed so that the dynamic behavior of the arc may be determined, independent of the gas type. The model leads to a reduced set of non-linear partial differential equations which governs the quasi-steady ac arc. This system is solved numerically and it is found that convection plays an important role, not only in the temperature distribution, but also in arc disruptions. Moreover, disruptions are found to be influenced by convection only for a limited frequency range. The results of the present studies are applicable to the frequency range of 10-10(2) Hz which includes most industry ac arc frequencies. (C) 1994 Academic Press, Inc.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.