Mode inverse problem for a beam with overhangs is discussed.Flexural rigidity and density of beam with overhangs are solved with two groups of displacement modes or two groups of strain modes and corresponding frequency.Necessary and sufficient conditions for unique existence of solution of the problem are discussed.An algorithm is proposed and numerical calculations are carried out.Two examples show that better results can be attained if strain modes instead of displacement mode are employed.

In a homogeneous equilibrum cavity model with solution of transport equations of liquid mass fraction, source terms controlling the transformation between gas and liquid and a compression method for pressure-density coupling are introduced. The RANS equations in a k-ε model with modified low Re of gas-liquid mixture are solved. Cavitation flows around an underwater vehicle at extremely small cavity numbers (σ=0.2~0.01) are simulated successfully. Clear cavity shape and inner structure are obtained. The variation of cavity length and maximal cavity diameter with cavity numbers is simulated and relation between drag force coefficients of the vehicle and cavitation number is shown. The method shows good convergence and stability in simulation of natural cavity at extremely small cavitation numbers, and shows high accuracy in predication of cavity shapes.