A simple yet accurate solution procedure based on the improved Fourier series method (IFSM) is applied to the vibration characteristics analysis of a cylindrical shell-circular plate (S-P) coupled structure subjected to various boundary conditions. By applying four types of coupling springs with arbitrary stiffness at the junction of the coupled structure, the mechanical coupling effects are completely considered. Each of the plate and shell displacement functions is expressed as the superposition of a two-dimensional Fourier series and several supplementary functions. The unknown series-expansion coefficients are treated as the generalized coordinates and determined using the familiar Rayleigh-Ritz procedure. Using the IFSM, a unified solution for the S-P coupled structure with symmetrical and asymmetrical boundary conditions can be derived directly without the need to change either the equations of motion or the expressions of the displacements. This solution can be verified by comparing the current results with those calculated by the finite-element method (FEM). The effects of several significant factors, including the restraint stiffness, the coupling stiffness, and the situation of coupling, are presented. The forced vibration behaviors of the S-P coupled structure are also illustrated.
A numerical study was conducted to investigate the effects of blade surface roughness on compressor performance and tonal noise emission. The equivalent sand-grain roughness model was used to account for blade surface roughness, and a hybrid method that combines computational fluid dynamics and boundary element method was used to predict compressor performance and tonal noise. The numerical approach was validated against experimental data for a baseline compressor. Nine different cases with different blade surface roughness were studied in this paper, the global performance was analyzed under compressor design speed, and the tonal noise level was predicted under the design condition. The results indicate that compressor total-to-total pressure ratio and isentropic efficiency were gradually decreased with the increasing blade surface roughness. Besides, the blade total pressure loss coefficient and the efficiency loss coefficient were also increased. It was found that the reverse flow at the leading edge of compressor rotor blades reduced blade loading. The pressure fluctuation at the leading edge showed that the peak of pressure fluctuations increased as the blade surface roughness was increased. The sound pressure level at blade-passing frequency shows a significant change with variation in blade surface roughness, which results in an increased total noise level. Furthermore, it was shown that the blade surface roughness had nearly no influence on acoustic directivity, but the sound pressure level increased with the increase in roughness, especially at blade-passing frequency.
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