This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the prop...This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.展开更多
The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and t...The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor sys- tem. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodic motion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.展开更多
This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation d...This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.展开更多
文摘This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.
基金the National Natural Science Foundation of China (No. 10572087)the National High Technology Research and Development Program (863) of China (No. 2002AA526138)
文摘The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor sys- tem. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodic motion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.
基金supported by a collaboration scheme from University of Science and Technology of China-City University of Hong Kong Joint Advanced Research Institute and by City University of Hong Kong of China (Grant No. 7002699 (BC))
文摘This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.
