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.

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.

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.

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.

We propose a new path following control algorithm. The algorithm decomposes the trajectory errors into tangential and normal components. The normal component minimizes the tracking error, while the tangential component maintains the desired speed. Experimental results using an X-Y table indicate that the proposed method possesses satisfactory tracking characteristics. It resolves certain previously difficult to control problems.