Immersed cylinder piles are usually modelled as immersed carrying a tip mass and rotary moment of inertia. In this paper, an immersed cylinder pile along transversal modes of vibration are of water and structural damp...Immersed cylinder piles are usually modelled as immersed carrying a tip mass and rotary moment of inertia. In this paper, an immersed cylinder pile along transversal modes of vibration are of water and structural damping are included in the formulation. cantilever cylinder columns the equations of motion of developed. Compressibility Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.展开更多
A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is m...A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with parallel linear and torsional dampers(Kelvin-Voigt model). The superstructure adds to the kinetic energy of the system without affecting the potential energy, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its natural frequencies further. The empty space factor due to the truss-type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes satisfying the end condition. The weights are evaluated by the Rayleigh-Ritz(RR) method, and verified using finite element method(FEM). The weight of the superstructure acts as an axial compressive load on the beam. Kelvin-Voigt model of structural damping is included.A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. A parametric study is done for various magnitudes of tip mass and various levels of submergence. The computational efficiency and accuracy of the Rayleigh-Ritz method, as compared to the FEA, has been demonstrated. The advantage of using closed-form trial functions is clearly seen in the efficacy of calculating the various energy components in the RR method.展开更多
The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations ...The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are estab- lished. It is clearly elucidated for the first time that, dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. The modeling approach in this paper successfully solves problems of popular modeling methods nowadays: the derivation process is too complex by using only one dynamic principle; a clearly theoretical mechanism for dynamic stiffening can' t be offered. First, the mass at non-tip po- sition is incorporated into the continuous dynamic equations of the system by use of the Dirac lunch tion and the Heaviside function. Then, based on the conclusions of orthogonalization about the nor- mal constrained modes, the finite dimensional state space equations suitable for controller design are obtained. The numerical simulation results show that: dynamic stiffening is included in the first-or- der model established in this paper, which indicates the dynamic responses of the rigid flexible cou- pling system with large overall motion accurately. The results also show that the mass has a soften- ing effect on the dynamic behavior of the flexible beam, and the effect would be more obvious when the mass has a larger mass, or lies closer to the tip of the beam.展开更多
The distribution of hydrogen near the notch tip of the austenitic steel 21Cr9Ni9MnN under mode Ⅰ loading has been studid with ion microprobe mass analyzer.Two peaks of hydrogen accumulation,one at notch tip and other...The distribution of hydrogen near the notch tip of the austenitic steel 21Cr9Ni9MnN under mode Ⅰ loading has been studid with ion microprobe mass analyzer.Two peaks of hydrogen accumulation,one at notch tip and other far apart from it,were found.The distribution of hydrostatic stress and plastic strain in front of the notch tip under planar stress condition were calculated using ADINA non-linear finite element method.The calculated result in compari- son with data measured showed that the hydrogen concentration peak at the notch tip is caused by trapping effect of dislocation on dissolved hydrogen,while the other from the hydrostatic stress.The influence of stress intensity factor on the distribution of hydrogen con- centration and the process of hydrogen accumulation near notch tip was also discussed.展开更多
基金supported by the Ministry of Science and Technology of China (SLDRCE09-B-08)the National Nature Science Foundation of China (50978194 and 90915011)Kwang-Hua Fund for College of Civil Engineering,Tongji University
文摘Immersed cylinder piles are usually modelled as immersed carrying a tip mass and rotary moment of inertia. In this paper, an immersed cylinder pile along transversal modes of vibration are of water and structural damping are included in the formulation. cantilever cylinder columns the equations of motion of developed. Compressibility Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.
文摘A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with parallel linear and torsional dampers(Kelvin-Voigt model). The superstructure adds to the kinetic energy of the system without affecting the potential energy, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its natural frequencies further. The empty space factor due to the truss-type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes satisfying the end condition. The weights are evaluated by the Rayleigh-Ritz(RR) method, and verified using finite element method(FEM). The weight of the superstructure acts as an axial compressive load on the beam. Kelvin-Voigt model of structural damping is included.A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. A parametric study is done for various magnitudes of tip mass and various levels of submergence. The computational efficiency and accuracy of the Rayleigh-Ritz method, as compared to the FEA, has been demonstrated. The advantage of using closed-form trial functions is clearly seen in the efficacy of calculating the various energy components in the RR method.
文摘The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are estab- lished. It is clearly elucidated for the first time that, dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. The modeling approach in this paper successfully solves problems of popular modeling methods nowadays: the derivation process is too complex by using only one dynamic principle; a clearly theoretical mechanism for dynamic stiffening can' t be offered. First, the mass at non-tip po- sition is incorporated into the continuous dynamic equations of the system by use of the Dirac lunch tion and the Heaviside function. Then, based on the conclusions of orthogonalization about the nor- mal constrained modes, the finite dimensional state space equations suitable for controller design are obtained. The numerical simulation results show that: dynamic stiffening is included in the first-or- der model established in this paper, which indicates the dynamic responses of the rigid flexible cou- pling system with large overall motion accurately. The results also show that the mass has a soften- ing effect on the dynamic behavior of the flexible beam, and the effect would be more obvious when the mass has a larger mass, or lies closer to the tip of the beam.
文摘The distribution of hydrogen near the notch tip of the austenitic steel 21Cr9Ni9MnN under mode Ⅰ loading has been studid with ion microprobe mass analyzer.Two peaks of hydrogen accumulation,one at notch tip and other far apart from it,were found.The distribution of hydrostatic stress and plastic strain in front of the notch tip under planar stress condition were calculated using ADINA non-linear finite element method.The calculated result in compari- son with data measured showed that the hydrogen concentration peak at the notch tip is caused by trapping effect of dislocation on dissolved hydrogen,while the other from the hydrostatic stress.The influence of stress intensity factor on the distribution of hydrogen con- centration and the process of hydrogen accumulation near notch tip was also discussed.