The weight of the moving vehicle creates a dynamic force acting on the bridge. The speed of this vertical force resembles the frequency of this dynamic force which is comparable to the vibration frequency of the bridge. Depending on the speed and the natural frequency of the bridge the response may increase or decrease. For more detail, do a research on dynamic response of beams under moving loads. 

The weight of the moving vehicle creates a dynamic force acting on the bridge. The speed of this vertical force resembles the frequency of this dynamic force which is comparable to the vibration frequency of the bridge. Depending on the speed and the natural frequency of the bridge the response may increase or decrease. For more detail, do a research on dynamic response of beams under moving loads. 

The bridge model is incorrect.

If you give the natural time period of the bridge maybe I can advise for you the solutions. 

Hello Elham,

I would look into the interface between the mass-oscillator and the bridge and how the load is being transferred from the train to the bridge.

Please check out the attached paper. You may find it helpful.

Good luck,

Safa

It depends on bridge natural frequencies and vehicle speed. There are two excitation frequencies in VBI problem. First one is due to driving frequency (pi V/L) and another is bridge surface roughness spatial frequency which in turn temporal frequency due to movement of vehicle. These two excitation frequencies are dependent on vehicle speed. I hope with this concept you could have better understanding on moving load problem

Thanks researcher for your answers

dear Said Elias, natural time period of the bridge is 0.125 sec.

what is incorrect in my bridge simulation ? could you explain it for me?

thanks a lot

You can model this bridge studied by Yau and Yang (2004). Because the natural of the bridge you have model is too low. It shows you have model a rigid structure. The 2D bridge they have modelled you can extend to 3D. However, the nataural frequency will not differ too much. Yau, J. D.,  and Yang, Y. B.  (2004) “A wideband MTMD system for reducing the dynamic response of continuous truss bridges to moving train loads”, Engineering Structures, Vol. 26, Issue 12, Pages 1795-180.

The results of this research paper are 100% correct and we were able to model and reproduce them by different approches. 

Good Luck

By looking their previous works, driving frequency (pi V/L) comes from decoupling of beam  based on concept of continuous system. 

...............= P sin[ (pi V/L)* t ]

But, for such a complicated structure like truss bridge, how driving frequency still hold a simple beam mode shape variables ?. Besides, in reality , frequency produced by undulated surface profile must also be taken into account for excitation frequency.

Also simply you can think of the second law of Newton.

When going faster the time the force is exerted on the span is smaller..

It is not possible to depend on that I suppose. Because as the speed increased there will be n number of frequencies will be domanated. Since then it is not possible that the response reduces. As I given some publication references already for validation of the model. 

Dear Mrs. Askari,

Have you checked the displacements after the passage of the mass?

It is a common behavior in sagged cable under moving mass effects. Please check the attached conference paper.

Marcelo Greco

No, I checked it when the vehicle is passing bridge, not after vehicle passage.

Thanks Mr. Nikfar

But how I could calculate the frequency of this dynamic force? when the force is a series of wheels of train?

Can you introduce a reference for "dynamic response of beams under moving loads" please?

Hi Elham, 

Here are some references.

FN

All the matter in resonance. Maximum deflection corresponds to the frequency of the oscillator is close to the natural frequency of the bridge.

Hi Elham,

The bridge, theoretically, has an infinite number of natural frequencies of vibration. The deflection is a combination from all the modes

As you increase the speed of passing train, the forcing function frequencies gets higher, and amplitude contribution from fundamental mode become less. The higher modes amplitudes can be smaller at mid-span ( as what you have noticed).

You can check the deflection contribution from each mode for different train speed.

For High Speed Railway Bridges, resonance problem reported more for shorter span bridges (higher natural frequencies in the lower modes), rather than the longer span bridges.

I know because of the repetitive character of the wheel or bogie load, a moving train usually contains some inherent frequencies, plus an excitation frequency associated with the moving speed. If any of these frequencies coincides with any of the frequencies of vibration of the bridge, the resonance phenomenon will be induced on the bridge by the moving train.

The excitation frequency associated with the moving speed is calculated by f=(pi v/L) which v: train velocity and L: the bridge span

Now do you know how we could calculate the moving train inherent frequencies Because of the repetitive character of the wheel or bogie load?

I found it for a beam subjected to an infinite sequence of equal loads with uniform interval d and constant speed v , the period equals : d/v

but what is the formula for a real train with its wheel pattern?

This bridge with this properties will not get resonance with its higher modal frequencies. Thus, the speed increases the displacment is not inreasing.

The train manufacturer usually capture the "signature" loading function of their particular model of train during testing.

     The moving vehicle acts as a movable tmd tuned mass damper, and the frequency of this dynamic force might be close to the frequency of the vibrating bridge ...so will act as a damper and reduce the displacement when the velocity increases because the frequency of the moving vehicle approaches the frequency of the dominant mode of vibration in the bridge.....this is a firm rule of vibration control using tuned mass damper tmd in bridges.