Reduction Approaches for Vibration Control of Repetitive Structures

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Analytical Interaction of the Acoustic Wave and Turbulent Flame

A modified resonance model of a weakly turbulent flame in a high-frequency acoustic wave is derived analytically. Under the mechanism of Darrieus-Landau instability, the amplitude of flame wrinkles, which is as functions of the expansion coefficient and the perturbation wave number, increases greatly independent of the 'stationary' turbulence. The high perturbation wave number makes the resonance easier to be triggered but weakened with respect to the extra acoustic wave. In a closed burning chamber with the acoustic wave induced by the flame itself, the high perturbation wave number is to restrain the resonance for a realistic flame.

Numerical and Analytical Study on the Pull-in Instability of Micro-Structure under Electrostatic Loading

The one-mode analysis method on the pull-in instability of micro-structure under electrostatic loading is presented. Taylor series are used to expand the electrostatic loading term in the one-mode analysis method, which makes analytical solution available. The one-mode analysis is the combination of Galerkin method and Cardan solution of cubic equation. The one-mode analysis offers a direct computation method on the pull-in voltage and displacement. In low axial loading range, it shows little difference with the established multi-mode analysis on predicting the pull-in voltages for three different structures (cantilever, clamped-clamped beams and the plate with four edges simply-supported) studied here. For numerical multi-mode analysis, we also show that using the structural symmetry to select the symmetric mode can greatly reduce both the computation effort and the numerical fluctuation.

Vaporization of heated materials into discharge plasmas

The vaporization of condensed materials in contact with high-current discharge plasmas is considered. A kinetic numerical method named direct simulation Monte Carlo (DSMC) and analytical kinetic approaches based on the bimodal distribution function approximation are employed. The solution of the kinetic layer problem depends upon the velocity at the outer boundary of the kinetic layer which varies from very small, corresponding to the high-density plasma near the evaporated surface, up to the sound speed, corresponding to evaporation into vacuum. The heavy particles density and temperature at the kinetic and hydrodynamic layer interface were obtained by the analytical method while DSMC calculation makes it possible to obtain the evolution of the particle distribution function within the kinetic layer and the layer thickness.

Analytical Study of Idealized Two-Dimensional Cellular Detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Seismic Responses of a Hemispherical Alluvial Valley to SV Waves: A Three-Dimensional Analytical Approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

A New Analytical Model for Residual Stresses due to Thermal Surface Coating

发展了一种新的分析涂层结构（平板、梁）热残余应力的模型,可以研究骤冷过程(Quenching)和冷却过程(Cooling)在涂层结构内引发的残余应力分布。与以往模型相比,其优势在于：它可以考虑源于喷涂过程的涂层孔隙率、温度梯度等因素对于涂层和基底内残余应力的影响。其中孔隙率和温度分布由计算机模拟涂层沉积过程得到。另外,当基底的材料和几何参数被固定时,我们分析了诸如涂层的理想模量、厚度、热膨胀系数等参数,对于涂层结构中最终残余应力分布的改变机理。

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

Electromechanical influence of crack velocity at bifurcation for poled ferroelectric materials

The piezoelastodynamic field equations are solved to determine the crack velocity at bifurcation for poled ferroelectric materials where the applied electrical field and mechanical stress can be varied. The underlying physical mechanism, however, may not correspond to that assumed in the analytical model. Bifurcation has been related to the occurrence of a pair of maximum circumferential stress oriented symmetrically about the moving crack path. The velocity at which this behavior prevails has been referred to as the limiting crack speed. Unlike the classical approach, bifurcation will be identified with finite distances ahead of a moving crack. Nucleation of microcracks can thus be modelled in a single formulation. This can be accomplished by using the energy density function where fracture initiation is identified with dominance of dilatation in relation to distortion. Poled ferroelectric materials are selected for this study because the microstructure effects for this class of materials can be readily reflected by the elastic, piezoelectic and dielectric permittivity constants at the macroscopic scale. Existing test data could also shed light on the trend of the analytical predictions. Numerical results are thus computed for PZT-4 and compared with those for PZT-6B in an effort to show whether the branching behavior would be affected by the difference in the material microstructures. A range of crack bifurcation speed upsilon(b) is found for different r/a and E/sigma ratios. Here, r and a stand for the radial distance and half crack length, respectively, while E and a for the electric field and mechanical stress. For PZT-6B with upsilon(b) in the range 100-1700 m/s, the bifurcation angles varied from +/-6degrees to +/-39degrees. This corresponds to E/sigma of -0.072 to 0.024 V m/N. At the same distance r/a = 0.1, PZT-4 gives upsilon(b) values of 1100-2100 m/s; bifurcation angles of +/-15degrees to +/-49degrees; and E/sigma of -0.056 to 0.059 V m/N. In general, the bifurcation angles +/-theta(0) are found to decrease with decreasing crack velocity as the distance r/a is increased. Relatively speaking, the speed upsilon(b) and angles +/-theta(0) for PZT-4 are much greater than those for PZT-6B. This may be attributed to the high electromechanical coupling effect of PZT-4. Using upsilon(b)(0) as a base reference, an equality relation upsilon(b)(-) < upsilon(b)(0) < upsilon(b)(+) can be established. The superscripts -, 0 and + refer, respectively, to negative, zero and positive electric field. This is reminiscent of the enhancement and retardation of crack growth behavior due to change in poling direction. Bifurcation characteristics are found to be somewhat erratic when r/a approaches the range 10(-2)-10(-1) where the kinetic energy densities would fluctuate and then rise as the distance from the moving crack is increased. This is an artifact introduced by the far away condition of non-vanishing particle velocity. A finite kinetic energy density prevails at infinity unless it is made to vanish in the boundary value problem. Future works are recommended to further clarify the physical mechanism(s) associated with bifurcation by means of analysis and experiment. Damage at the microscopic level needs to be addressed since it has been known to affect the macrocrack speeds and bifurcation characteristics. (C) 2002 Published by Elsevier Science Ltd.

A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application

An infinite elastic solid containing a doubly periodic parallelogrammic array of cylindrical inclusions under longitudinal shear is studied. A rigorous and effective analytical method for exact solution is developed by using Eshelby's equivalent inclusion concept integrated with the new results from the doubly quasi-periodic Riemann boundary value problems. Numerical results show the dependence of the stress concentrations in such heterogeneous materials on the periodic microstructure parameters. The overall longitudinal shear modulus of composites with periodic distributed fibers is also studied. Several problems of practical importance, such as those of doubly periodic holes or rigid inclusions, singly periodic inclusions and single inclusion, are solved or resolved as special cases. The present method can provide benchmark results for other numerical and approximate methods. (C) 2003 Elsevier Ltd. All rights reserved.

The positive floating potential of high-temperature particles in plasma

It has been predicted that the floating potential of particles in plasma may become positive when the particle surface temperature is high enough, but, to our knowledge, no positive floating potential has been obtained yet. In the present paper the floating potential theory of high-temperature particles in plasma is developed to cover the positive potential range for the first time, and a general approximate analytical formula for the positive floating potential with a thin plasma sheath and subsonic plasma flow is derived from the new model recently proposed by the authors. The results show that when the floating potential is positive, the net flux of charge incident on the particle approaches a constant similar to the 'electron saturation' phenomena in the case of the electric probes.