Analysis theory of spatial vibration of high-speed train and slab track system

The motor and trailer cars of a high-speed train were modeled as a multi-rigid body system with two suspensions. According to structural characteristic of a slab track, a new spatial vibration model of track segment element of the slab track was put forward. The spatial vibration equation set of the high-speed train and slab track system was then established on the basis of the principle of total potential energy with stationary value in elastic system dynamics and the rule of ＂set-in-right-position＂ for formulating system matrices. The equation set was solved by the Wilson-θ direct integration method. The contents mentioned above constitute the analysis theory of spatial vibration of high-speed train and slab track system. The theory was then verified by the high-speed running experiment carried out on the slab track in the Qinghuangdao-Shenyang passenger transport line. The results show that the calculated results agree well with the measured rcsults, such as the calculated lateral and vertical rail displacements are 0.82 mm and 0.9 mm and the measured ones 0.75 mm and 0.93 mm, respectively; the calculated lateral and vertical wheel-rail forces are 8.9 kN and 102.3 kN and the measured ones 8.6 kN and 80.2 kN, respectively. The interpolation method, that is, the lateral finite strip and slab segment element, for slab deformation proposed is of simplification and applicability compared with the traditional plate element method. All of these demonstrate the reliability of the theory proposed.

Effect of cross-wind on spatial vibration responses of train and track system

By taking cross-wind forces acting on trains into consideration, a dynamic analysis method of the cross-wind and high-speed train and slab track system was proposed on the basis of the analysis theory of spatial vibration of high-speed train and slab track system. The corresponding computer program was written by FORTRAN language. The dynamic responses of the high-speed train and slab track under cross-wind action were calculated. Meanwhile, the effects of the cross-wind on the dynamic responses of the system were also analyzed. The results show that the cross-wind has a significant influence on the lateral and vertical displacement responses of the car body, load reduction factor and overturning factor. For example, the maximum lateral displacement responses of the car body of the first trailer with and without cross-wind forces are 32.10 and 1.60 mm, respectively. The maximum vertical displacement responses of the car body of the first trailer with and without cross-wind forces are 6.60 and 3.29 mm, respectively. The maximum wheel load reduction factors of the first trailer with and without cross-wind forces are 0.43 and 0.22, respectively. The maximum overturning factors of the first trailer with and without cross-wind forces are 0.28 and 0.08, respectively. The cross-wind affects the derailment factor and lateral Sperling factor of the moving train to a certain extent. However, the lateral and vertical displacement responses of rails with the crnss-wind are almost the same as those without the cross-wind. The method presented and the corresponding computer program can be used to calculate the interaction between trains and track in cross-wind.

Spatial Vibration and Its Numerical Analytical Method of Four-high Rolling Mills

The rolls in contemporary four-high mills cannot be maintained parallel during the rolling process. There- fore, four-high rolling mill vibrations take place in six degree of freedom （DOF） leading to spatial behaviors invol- ving vertical, horizontal, axial, torsional, cross and swinging vibration modes resulting in complex relative motions between the rolls. Two numerical methods, modified Riccati-transfer matrix method （Riccati-TMM） and finite ele- ment method （FEM）, are presented to analyze a spatial vibration characteristic of two four-high rolling mills with different stability. The natural frequency and mode shape of four-high rolling mills are obtained, and the clearance has a great effect on natural frequency and mode shape. In addition, field testing experiment is also conducted to measure natural frequency by power spectrum analysis of rolling mill vibration. Experimental results basically agree with those calculated by Riccati-TMM and FEM, which means that the Riccati-TMM and the FEM can be used for analysis of spatial vibration of four-high rolling mill. Meanwhile, the spatial vibration shows more compound vibra- tion behaviors and the negative effect of horizontal, vertical, cross and swinging vibration modes are effectively con- trolled after redesign of rolling mill. These advantages have a great significance for the rolling mill to be operated with a much higher rolling speed and improved yield of products.

Exact Boundary Controllability for the Spatial Vibration of String with Dynamical Boundary Conditions

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact boundary controllability of this system by means of a constructive method with modular structure.

Path integral Monte Carlo study of(H_2)_n@C_(70)(n = 1, 2, 3)

The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.