This paper is to develop the background phase subtraction method to determine the resonance frequency of a two-dimensional alluvial valley subjected to an incident plane SH-wave. The scattered wave due to the alluvium can be expressed in a series of basis functions, and the associated coefficients are related to the coefficients of free field by the so-called T-matrix method. By applying the resonance scattering theory, the effects among all normal modes can be decoupled and hence one can obtain the phase shift of each eigen partial wave. Similarly, the phase shift of each eigen partial wave due to a canyon with the same geometrical shape of the alluvium can be determined, and is recognized as the background effect. Furthermore, based on the phase represented scattering matrix, the resonance frequencies of each normal mode and its overtones can be determined by the subtraction of the associated phase dependent function due to the canyon from that due to the alluvium.

In this paper, the recursive T-matrix formalism is developed to determine the dynamic Green's function for SH-wave in the multi-dipping layers with arbitrary shape embedded in a half-space. In each layer, the wave field generated by a harmonic line load can be separated into two parts: the source term and the complementary part. The source term is exactly the Green's function for SH-wave in two-dimensional half-space, and the complementary part which causes the SH-wave to satisfy the boundary conditions at the interface is determined by the wave function expansion method. Using the polar coordinates, the basis functions are constructed by Bessel typed cylindrical functions, and their orthogonality conditions at the corresponding interfaces can be derived by means of Betti's third identity. Applying the conditions of continuity at the interface, the recursive T-matrix formalism is developed for determining the expansion coefficients of the complementary part from the associated source dependent constants.

Applications of the EndoFEM with node-released methods had been used successfully to simulate the plastic wakes left behind the advancing fatigue crack. In this paper, employing the plastic zone size estimated by LEFM as a guideline, four strategies with various plans of node-released rates and two plans of finite element discretization near crack tip, are proposed to generate various fatigue cracked lengths of A12024-T3 CCT specimen under all tensile-cyclic loading. Evaluations based on the mechanical responses near crack tip and the crack opened/closure behaviors, it can be concluded that the EndoFEM with the rc dominant node-released strategy can lead to not only economical but also reliable results.

The average settling rate of spherical solid particles, 〈vs〉, under a body force field is studied numerically in decaying homogeneous isotropic turbulent flows generated by the direct numerical simulation of the continuity and Navier-Stokes equations. The increase of the average settling rate, 〈Δvs〉, is maximized when Tp/Tk ≈ 1 and vd/u′ ≈ 0.5, and is of order 0.lu′, which is qualitatively similar to that in stationary turbulence. Here 〈Δvs〉 = 〈vs〉 − vd, Tp is the particle's relaxation time, Tk is the Kolmogorov time scale, vd is the settling rate of particles in still fluid, and u′ is the root mean square of the fluid velocity fluctuation. However, the magnitude of the maximum value of 〈Δvs〉 in decaying turbulence is substantially greater (about 40%) than that in the corresponding stationary turbulence due to the inertia response of particles to turbulence decay. Although 〈Δvs〉/u′ does not reach a stationary state as the flow is evolving, it is a slowly time varying function for the parameters of interest as Tp (≈ Tk when 〈Δvs〉 is maximized) is in general of one order less than the time scale of turbulence decay.

A general theory for multilayered anisotropic elastic shells is developed in an asymptotic variational framework of 3-D elasticity. The generic shell continuum considered is heterogeneous through the thickness. It is shown that the classical laminated shell theory based on Love's assumption arises naturally as the first-order approximation to the 3-D theory. Higher-order corrections can be determined by solving the 2-D shell equations hierarchically. The associated edge conditions at each level of approximation are derived. Various types of shells such as shells of revolution, conical shells, spherical shells, circular cylindrical shells can be treated within the context.

An innovative computation procedure is developed to solve the external flow problems for viscous fluids. The method is able to handle the infinite domain so that it is convenient for the external flows. The code is based on the projection method of the Navier-Stokes equations. We use the three-step explicit finite element method to solve the momentum equation by extracting the boundary effects from the finite computation domain. The pressure Poisson equation for the external field is treated by the boundary element method. The arbitrary Lagrangian-Eulerian (ALE) scheme is employed to incorporate the present algorithm to deal with the moving boundary, such as the motion of an impulsively moving circular cylinder in a viscous fluid. The model demonstrates that drag force is well predicted for a circular cylinder moving in a still viscous fluid starting from rest, to a constant acceleration, and then maintaining at a uniform velocity. In the constant acceleration phase, the drag force is closed to the added mass effect from the ideal flow theory. On the other hand, the drag force is equal to viscous flow theory in the constant velocity phase.

Dynamic propagation of a crack along the interface in an anisotropic material subjected to remote uniform anti-plane shear is studied. The crack is assumed to nucleate from an infinitesimal microcrack and expands with a constant velocity. Explicit expressions for the stress intensity factor and the energy release rate are derived.

The problem of two circular inclusions of arbitrary radii and of different elastic moduli, which are perfectly bonded to an infinite matrix subjected to arbitrary loading, is solved by the heterogenization technique. This implies that the solution of the heterogeneous problem can be readily obtained from that of the corresponding homogeneous problem by a simple algebraic substitution. Based on the method of successive approximations and the technique of analytical continuation, the solution is formulated in a manner which leads to an approximate, but arbitrary accuracy, result. The present derived solution can be also applied to the problem with straight boundaries. Both the problem of two circular inclusions embedded in an infinite matrix and the problem of a circular inclusion embedded in a half-plane matrix are considered as our examples to demonstrate the use of the present approach.

This paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

Viscoelastic (VE) dampers have been shown to be an effective energy dissipation device for structures subjected to seismic excitations. When a VE damper is under shear deformation, the temperature within the damper material will rise due to the conversion of mechanical energy into heat. The effect of temperature rise in the VE damper on a viscoelastically damped structure may be significant because the damper stiffness can decrease due to the temperature rise in the VE damper and its energy dissipation capacity may reduce under strong earthquake ground motions. This paper is intended to quantify the temperature rise effect. A VE element which can accurately describe the frequency and temperature dependent behavior of the test results of a VE damper is first presented. The effect of temperature rise within the VE material is included. Seismic response analyses of a viscoelastically damped structure which was studied extensively by shaking table tests are carried out by two analytical methods: a frequency domain analysis and a time domain analysis. Both analyses consider the effects of frequency and ambient temperature of the VE dampers. The frequency domain approach is computationally more efficient. However, it neglects the effect of temperature rise in the analysis. The time domain method is computationally less efficient. However, it can explicitly calculate the temperature rise during the earthquake and evaluate its influence on the structural responses. Finally, parametric studies on the effect of temperature rise within the VE damper material on the seismic response of a viscoelastically damped structure are analyzed and its implications on practical applications are discussed.

Active control of noise radiation from vibrating plate excited by a harmonic line moment is analytically investigated. This study model of simple supported rectangular plate with a line moment excitation is used to simulate the vibration of ship hull or fuselage from the flutter of ship deck or aircraft wing respectively. The control is achieved by various configurations of piezoelectric actuators. The strategy of radiated power minimization is used to obtain the optimal control input unit voltage. The numerical results show that the significant attenuation of noise radiated power for volumetric modes in the low frequency range can be achieved with one control actuator located at the center of plate, irrespective of whether the excitation is on or off resonance. The efficiency of the active control is dependent on the location of the line moment and the actuators. It is also shown that the modal suppression and modal restructuring are two physical mechanisms of radiated power attenuation.

The transition of a viscous incompressible laminar flow behind a circular cylinder from a steady state to its wake, counterpart at a Reynolds number Re = 100, based on the free stream velocity (U) and the cylinder diameter (D), is directly simulated. The two-dimensional unsteady Navier-Stokes equations are solved numerically by taking advantage of the splitting technique and the spectral element method. The main goal of this work is to explore the frequency-selection mechanism of the wake through the use of the absolute/convective instability theory, which in turn is performed by investigating the one-dimensional Orr-Sommerfeld equation. It is found that the predicted onset frequency based on the maximum-growth criterion is in a good agreement with the numerically observed one, although the measured growth rate is found smaller. The saturated frequencies predicted by the maximum-growth criterion and Kock's transition criterion are the same and also close to the measured one. More simulation or experimental data are needed for a further conclusion however.

The objective of the present study is to investigate the buoyancy effects induced by various body forces in non-isothermal rotating fluids. The buoyancy effects stemmed from the gravity, the centrifugal and Coriolis forces generated by system rotation, and the curvilinear motion of the fluids are all taken into account. Mixed convection between two disks rotating at different rates is employed as the physical model. The present work is the first study for detailed investigation of the various buoyancy forces in the class of non-isothermal flows. Complete system of axially-symmetric thermal flow model with assumption of Boussinesq fluids is formulated. By a scaling analysis and the solutions of a novel similarity model developed in this work, the relative importance of the buoyancy effects induced by various body forces is explored. The present work discloses the significance of the rotation-induced buoyancy effects under various conditions and is useful in understanding the mechanisms as well as modeling the mixed convection heat transfer in the class of rotating thermal flows.

In this paper, the problem of a debonding crack at the interface between a circular fiber and an infinite matrix opened by internal pressure is discussed. We concentrated on the effect of contact near the crack tips within the content of linear elastic fracture mechanics. The Muskhelishvili complex variable method is used in this analysis. The frictionless contact crack tip condition is adopted in this study in order to avoid the oscillatory stress singularity at the crack tip as shown in the classical solution. By using the crack opening displacement gradient as the primary variable, the problem is then reduced to two coupled singular integral equations, and the final discretization of the equations employs the method given by Erdogan and Gupta (1972). The comprehensive numerical results of stress fields and the mode II SIF at the closed crack tip will be given in the paper. It is also found from the numerical evidences that the contact length at the crack tip is independent of one of the Dundurs parameters, α.

A problem independent, equation decomposition scheme of parallel computation is adopted and tested using a two-dimensional turbulent channel flow. The incompressible Navier-Stokes equations, incorporated with the SIMPLEC algorithm and a two-layer turbulence model, were distributed to four nodes of IBM SP2 parallel machine using the PVM software and solved simultaneously. The computation domain and the interior iteration loop for the solution of every transport equation is the same, load balancing among different machines is automatically satisfied. Since all the transport equations and the flow field was solved and updated simultaneously, the solutions obtained from the equation decomposition scheme at each time step were more accurate than those obtained from a unit process code, which in turn sharply reduced the required convergence time steps. Without modifying any of the solution algorithm, or tuning the computer code, the rate of convergence speeds up more than four times by invoking four nodes of parallel machines using the equation decomposition scheme.

Phase shifting technique is one of the most important technologies in the metrology field. Simply by performing an interferogram measurement, and then adopting the phase shifting technique to unwrap the interferogram into a phase map, tasks such as object surface profile reconstruction, holographic interferometry, electronic speckle pattern interferometry, etc., can all be easily accomplished. An innovative phase shifting system, which uses piezoelectric actuators to execute phase shifting first and then implementing a cellular automata algorithm to unwrap phase data, was designed, built, and tested. Since cellular automata is a true parallel process, and noise appearing within the interferogram will not get propagated, this novel system is far more robust than the systems based on the traditional path following phase-unwrapping algorithm. In addition, this new algorithm also provides us with a way to adopt phase-masks within the cellular automata implementations of the phase unwrap operations. All these newly developed techniques make this newly developed system adaptable to many metrology applications, even when high noise is present or when lateral shear exists within the image field. The successful incorporation of the phase-mask approach into the cellular automata phase unwrapping algorithm essentially makes this newly developed system adaptable to take phase map measurements in many practical applications.

This paper deals with the optimal shape/topological design of plate/shell like structures subjected to a harmonic, periodic excitation using an improved Homogenization Based Optimization Algorithm (HBOA), proposed by Cheng et al., [7]. The major goal of this work is to improve or control the frequency response of structures via the optimal distribution of a given amount of material in a fixed design space. Based upon the improved HBOA, two types of frequency response optimization problems are extensively explored: (1) structures subjected to a periodic excitation with a single excitation frequency, (2) structures subjected to a periodic excitation with excitation frequencies in a frequency domain. To this end, the basic mathematical formulation and a solution method are proposed as well as two numerical examples of obtaining the optimum layout of three-dimensional plate/shell structures. An interesting result is reported from the current optimization problems in comparison with static optimization problems.

By diagonalizing a matrix via a similarity transformation, we provide a new and direct proof of Sylvester's theorem in matrix theory. Several known theorems are reconstructed. In some places we offer new connections which are unnoticed in the literature before.

In this study, a computer program DBFWD is developed for data analysis of Falling Weight Deflectometer (FWD) test on flexible pavements. To backcalculate the layer moduli of the pavement, a number of iterative backcalculation schemes were employed with the forward analysis of the Green's flexibility influence functions. The temperature and the moisture influences on material moduli of the asphalt surface and the subgrade soils were considered in the analysis. As the result, the iterative scheme based on the peak deflection ratios was selected to backcalculate the layer moduli of local pavements. Owing to the correction procedure used in the program, interpretations with four original deflections were found more accurate than those with equivalent number of modified deflections. Comparisons of program DBFWD with other static backcalculation programs on theoretical and experimental deflections indicated that dynamic interpretation is more effective in providing the layer modulus information. Despite of the requirements of accurate inputs of the layer thickness and the testing load for the analysis, a generalized application of the program needs to be clarified with model road test in demand.

In light of incessant quest of better propulsion performance, it would be opportune to probe some propulsion insights for jet engine (JE) from a power point of view. In this study, we endeavor to prescribe logic reasoning process for obtaining the JE total kinetic power and prove its degenerated counterpart. With the Lagrangian Reynolds transport approach, we also rigorously derive the highly generalized equation for this power. Moreover, the validity, significance, and importance of this novel generalized power equation are delicately demonstrated by an interesting spring/mass model with known total kinetic power. Notably, the JE total kinetic power equations are quite reasonable physically speaking, since all the velocity quantities involved are of relative nature; otherwise, the JE total kinetic power may violate the energy conservation law under certain conditions. This total kinetic power produced by jet engine involves a few more physical effects including vehicle acceleration, relative flow velocity/steadiness, inlet/exit pressures, and gravity, thus open an original route for more efficient propulsion design.