Dynamic response and stability of a gas-lubricated Rayleigh-step pad

The quasi-static, pressure characteristics of a gas-lubricated thrust bearing with shrouded, Rayleigh-step pads are determined for a time-varying film thickness. The axial response of the thrust bearing to an axial forcing function or an axial rotor disturbance is investigated by treating the gas film as a spring having nonlinear restoring and damping forces. These forces are related to the film thickness by a power relation. The nonlinear equation of motion in the axial mode is solved by the Ritz-Galerkin method as well as the direct, numerical integration. Results of the nonlinear response by both methods are compared with the response based on the linearized equation. Further, the gas-film instability of an infinitely wide Rayleigh step thrust pad is determined by solving the transient Reynolds equation coupled with the equation of the motion of the pad. Results show that the Rayleigh-step geometry is very stable for bearing number A up to 50. The stability threshold is shown to exist only for ultrahigh values of Lambda equal to or greater than 100, where the stability can be achieved by making the mass heavier than the critical mass

A similarity law for stressing rapidly heated thin-walled cylinders

When a thin cylindrical shell of uniform thickness is very rapidly heated by hot high-pressure gas flowing inside the shell, the temperature of material decreases steeply from a high temperature at the inside surface to ambient temperatures at the outside surface. Young's modulus of material thus varies. The purpose of the present paper is to reduce the problem of stress analysis of such a cylinder to an equivalent problem in conventional cylindrical shell without temperature gradient in the wall. The equivalence concept is expressed as a series of relations between the quantities for the hot cylinder and the quantities for the cold cylinder. These relations give the similarity law whereby strains for the hot cylinder can be simply deduced from measured strains on the cold cylinder and thus greatly simplify the problem of experimental stress analysis

Classification of finite irreducible modules over the Lie conformal superalgebra CK6

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, for which E(1, 6) is the annihilation algebra

Coupled BE/FE/BE approach for scattering from fluid-filled structures

NASHUA is a coupled finite element/boundary element capability built around NASTRAN for calculating the low frequency far-field acoustic pressure field radiated or scattered by an arbitrary, submerged, three-dimensional, elastic structure subjected to either internal time-harmonic mechanical loads or external time-harmonic incident loadings. Described here are the formulation and use of NASHUA for solving such structural acoustics problems when the structure is fluid-filled. NASTRAN is used to generate the structural finite element model and to perform most of the required matrix operations. Both fluid domains are modeled using the boundary element capability in NASHUA, whose matrix formulation (and the associated NASTRAN DMAP) for evacuated structures can be used with suitable interpretation of the matrix definitions. After computing surface pressures and normal velocities, far-field pressures are evaluated using an asymptotic form of the Helmholtz exterior integral equation. The proposed numerical approach is validated by comparing the acoustic field scattered from a submerged fluid-filled spherical thin shell to that obtained with a series solution, which is also derived here