This paper proposes a robust Kalman-filter-based optimal model-following control (OMFC) methodology for actively suppressing the vibration of the mechanical structure system, which is modeled by the modal force technique (MFT) and subjects to both disturbance/noise uncertainties and linear structured time-varying parameter perturbations. The proposed method can not only avoid the problem of how to choose appropriate weighting matrices in the quadratic cost function of the linear quadratic Gaussian (LQG) control but also make the controlled closed-loop system to have desired system response characteristics. Besides, this paper also presents a robust stability criterion to guarantee that the designed controller can keep the controlled mechanical structure system from the possibility of time-varying-parameter-perturbation-induced instability. An example of L-shaped cantilever beam structure system is employed to demonstrate the application of the proposed method and the use of the robust stability criterion. Numerical simulation is performed to evaluate the improvement of the vibration response.

The dynamic Green's function due to an impulse in an infinite anisotropic medium under anti-plane deformation is derived by the method of Smirnov [1] for two-dimensional wave equation. The Green's function is inversely proportional to the time t and an effective dynamic shear modulus. It is shown that the tractions on the planes passing through the source point vanish identically. Based on the free-space Green's function, the Green's functions for wedges, semi-infinite media and strips are obtained.

An efficient boundary weight function method for the determination of mode I stress intensity factors in a three-dimensional cracked body with arbitrary shape and subjected to arbitrary loading is presented in this study. The functional form of the boundary weight functions are successfully demonstrated by using the least squares fitting procedure. Explicit boundary weight functions are presented for through cracks in rectangular finite bodies. If the stress distribution of a cut out rectangular cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple integration. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the proposed boundary weight function method.

The problem of a stable stratified fluid heated by a point source of heat at various depths is treated in this paper. A hot plume is formed with a series of layer around and above it. Quantitative estimates for the criterion of onset of doubly diffusive instability are obtained in this work. The linear differential system governing stability is then solved. The results show that the stationary onset of this doubly diffusive problem caused by a point source may be led to a similar form of small-gap Taylor- Couette problem.

A new computational procedure is developed to solve the external field problems of the incompressible viscous flows. The method is able to solve the infinite boundary value problems by extracting the boundary effects coming from the finite computational domain. The present method is based on the projection method of the Navier-Stokes equations. We use three-step explicit finite element method to solve the momentum equation of the flow motion. The external field solver of the boundary element is used to treat the pressure Poisson equation. The arbitrary Lagrangian-Eulerian method is employed to deal with the moving boundary, such as wind-structure interaction problems. For illustration of the present numerical code, a vortex-induced cross-flow oscillations of a circular cylinder mounted on an elastic dashpot-spring system is considered. The phenomena of the beat, lock-in, and resonance are revealed in the Reynolds number range between 100 and 110, which are much narrower than the previous studies.