It is pointed out that on the condition that the parameter DL~3/EI is very small, the system of linear equations satisfied by the displacements of generalized structural nodes is ill-conditioned, where EI is the flexural rigidity of the continuous beam, D the rigidity coefficient of the elastic supports and D the span. of the continuous beam.

An approach to calculate the double continuous beam on discrete elastic supports(a practical engineering structure) by finite element method is provided in this paper.

The adopted model is a structure in which the rail joint is considered to be two semiinfinite long beams,on discrete elastic supports,joined with an elastic hinge.

Considering the wheel and trac as a big coupling system,the rails as simplified Euler-beam with limit length lying on an elastic point support,and contact relation between wheel and rail as spring contact,the dynamics model of the system is established.

According to deflection function of the beam supported by elastic point of interior,the vibration of slab supported by elastic point of interior were analyzed and got better results,adopting multiple domain approach and Galerkin approach.

Using Fourier series, this paper presents a solution to the free vibration of rectangular orthotropic plates which carry concentrated masses and rest on symmetrically distributed elastic point supports or line supports or partial surface supports.

to investigate strain increase in the transverse direction of the slab when the rigid supports are replaced by the elastic supports.

When existing simple span bridges are converted into continuous spans, rigid support conditions have to be changed to elastic supports in order to absorb and distribute the energy of horizontal motion due to an earthquake loading.

However, development of additional reaction forces and stresses on the slab due to unequal displacement of the elastic supports have been overlooked.

Durability of the concrete slab under the elastic supports is also discussed.

This is useful for certain bending problems of rectangular plate on elastic supports.

On the basis that the deflection curves of track rails and continuous beam on elastic point supports are cubic curves, we establish the simultaneous matrix equation satisfied by the deflection and differential quotient of second order of the deflection curve, using the knowledge of spline function and engineering mechanics. Thereby we can solve the deflection, moment and share of the rail. At the same time, the deflection curve is obtained naturally. Compared with the finite element method, the method put forward...

On the basis that the deflection curves of track rails and continuous beam on elastic point supports are cubic curves, we establish the simultaneous matrix equation satisfied by the deflection and differential quotient of second order of the deflection curve, using the knowledge of spline function and engineering mechanics. Thereby we can solve the deflection, moment and share of the rail. At the same time, the deflection curve is obtained naturally. Compared with the finite element method, the method put forward in this paper has the following merits: derivation of the formula is forthright; the train of thought is clear it is easily adapted for computation on computer and the amount of computation is comparatively small.

In this paper, a finite element dynamic analytical model of railway train/frog system is presented, where the vertically loaded cast frog is simplified as a continuous nonuniform beam on many discrete unequal elastic supports. By means of the minimum potential energy principle and a direct integration algorithm superior in both stability and accuracy for linear problems-the average acceleration method (the trapezoidal rule), the train/frog vertical vibration equations are established and solved. Dynamic response...

In this paper, a finite element dynamic analytical model of railway train/frog system is presented, where the vertically loaded cast frog is simplified as a continuous nonuniform beam on many discrete unequal elastic supports. By means of the minimum potential energy principle and a direct integration algorithm superior in both stability and accuracy for linear problems-the average acceleration method (the trapezoidal rule), the train/frog vertical vibration equations are established and solved. Dynamic response of train, frog and sleeper at all necessary locations is obtained. The influences of many factors e. g. Frog pad stiffness, train speed, frog wear to dynamic response are analysed. The optimum stiffness range of frog pad for 60 kg/m track is 2.94 × 10~4～5.88 × 10~4kN/m.

From the point of view of systems engineering, a unified model for the railway vehicle and track as a whole system is established in this paper. The theory of vehicle-track coupling dynamics is advanced for the first time by the author. This unified model is a mixed one involving both the lumped and the distributed parameters in which the vehicle is considered as a multi-body system and the track as a Euler beam on a continuous elastic foundation consisting of the three layers of rail. sleeper and ballast. The...

From the point of view of systems engineering, a unified model for the railway vehicle and track as a whole system is established in this paper. The theory of vehicle-track coupling dynamics is advanced for the first time by the author. This unified model is a mixed one involving both the lumped and the distributed parameters in which the vehicle is considered as a multi-body system and the track as a Euler beam on a continuous elastic foundation consisting of the three layers of rail. sleeper and ballast. The Hertzian nonlinear elastic contact theory is used to describe the wheel/rail coupling characteristics. The fast numerical analysis method is applied to simulate the responses of the vehicle-track cupling system, and the numerical experiment method is used to study the numerical stability of integration, the modal convergency of rail and the effective calculated length of rail. The theoretical simulation results are compared with the test data of a few major experiments carried out at home and abroad, showing the soundness of the vertical model of vehicle-track system.