In this paper, the mode coupling between bending, stretching, and torsional deformations is mainly studied by presenting an analytical model of a rotating cantilever beam with pre-twist angle and arbitrary cross section. Equations of motion of the beam are derived using Hamilton's principle. The Coriolis effect due to the coupling of the bending deformation and stretching deformation, the eccentricity caused by inconsistency between elastic center and centroid, spin softening effect, stress stiffening effect, shear deformation, and rotary inertia are included in the model. Equations of motion are solved by the Rayleigh-Ritz method. The natural frequencies obtained by the proposed analytical modal are in good agreement with those obtained by finite element method (FEM) which proved the accuracy of the analytical model. Finally, the coupling between different mode components is studied in detail based on a quantitative method. The transformation/conversion between different mode components is revealed, the influence of rotational speed, setting angle, and pre-twist angle on this conversion mode is studied. Results show that a specific mode shape is usually composed of multiple mode components. The essence of mode coupling is the coupling between different mode components. The influence of rotational speed, setting angle, and pre-twist angle on the mode coupling is that they cause the transformation/conversion between different mode components.

The problem of sound propagation inside a rigid-walled room containing a rectangular obstacle was solved by dividing an acoustic field into subregions and using the continuity conditions. Acoustic waves were generated by a point source. The formulas valid for an impedance obstacle extending from a room floor to its ceiling were obtained. The considered obstacle can model such elements as a ventilation shaft, furniture, or construction pillar. The solution was expressed in the form of convergent series. To obtain accurate results, the error resulting from the use of truncated series was controlled. Additionally, to check the correctness of the proposed solution and its computer implementation, the results obtained for a negligibly small obstacle were compared with those given by the empty room model. An excellent agreement was achieved which proves a high accuracy of the used methodology. The numerical analysis shows that the calculation time of acoustic pressure in a part of an empty room can be significantly reduced using the obtained solution. An appropriate source location for noise reduction was found. The distribution of acoustic field was illustrated and some conclusions were formulated. The changes in acoustic field due to the presence of an obstacle were predicted and discussed.

This study focuses on the prediction of the stability behavior of an industrial automotive brake system under structural and environmental uncertainties. Uncertainties are modeled with a random distribution or an interval and are propagated with a hybrid surrogate model associating polynomial chaos and kriging. The objective is to create a surrogate model of each eigenvalue computed with the complex eigenvalue analysis (CEA). As the modes can be tracked only when unstable, the effective size of the training sets can become extremely small. Despite this limitation, it is shown the hybrid meta-model is still able to predict the stability of the brake system. Moreover, the hybrid meta-model gives a direct access to the mean and variance of the eigenvalues with respect to the design parameters without any additional Monte Carlo simulations (MCS). By considering different probability density function for the friction coefficient, it is shown it has a high influence on the stability and the latter should be accurately estimated.

This paper focuses on the radiation modes and efficiency of propeller tonal noise. The thickness noise and loading noise model of propellers has been formulated in spherical coordinates, thereby simplifying numerical evaluation of the integral noise source. More importantly, the radiation field can be decomposed and projected to spherical harmonics, which can separate source-observer positions and enable an analysis of sound field structures. Thanks to the parity of spherical harmonics, the proposed model can mathematically explain the fact that thrusts only produce antisymmetric sound waves with respect to the rotating plane. In addition, the symmetric components of the noise field can be attributed to the thickness, as well as drags and radial forces acting on the propeller surface. The radiation efficiency of each mode decays rapidly as noise sources approach the rotating centre, suggesting the radial distribution of aerodynamic loadings should be carefully designed for low-noise propellers. The noise prediction model has been successfully applied to a drone propeller and achieved a reliable agreement with experimental measurements. The flow variables employed as an input of the noise computation were obtained with computational fluid dynamics (CFD), and the experimental data were measured in an anechoic chamber.