Both options are used in the literature, but option 2 is definitely more correct because of considering inertial effects.

Neira, can you please give me reference for second..thank you...

This depends on the nature of the problem. For example, a moving vehicle on a short span bridge can be modelled as a moving force as inertia effects will not be important over the short vehicle crossing time. It will also depend on the relative weight of the vehicle to the weight of the bridge itself.

Intuitively, when modelled as a moving mass it should be more realistic. However, a moving force is easier to model and may be sufficiently accurate when bridge weight is high relative to vehicle weight. Also it depends on whether you are going to use a transient model or mode superposition in your solution.

Paul,

I am trying to include inertia effect of the moving load in the Transient Dynamic Problem. However, response is calculated by modal superposition & New-mark scheme given in ANSYS. I would highly appreciate if you may cite some reference / comment using equations of Dynamic Equilibrium showing how such moving mass acting has be modeled. I tried it on the beam first, but the solution is not converging when you add the moving mass in addition to its force effect in the equilibrium equation. Especially i feel, it may be having effects like changing natural frequencies since mass is changing position & accordingly changing mass matrix of the Bridge-Vehicle system.

Thank you for valuable comments, I appreciate.

~Fayaz

Thanking you sir for the literature and guidance...

Sincerely,

Fayaz

Thank You, I appreciate Professor Ayman for your time. This fundamental formulation , i wanted to understand. Your papers is worth lot of understanding for my problem.

Sincerely,

Fayaz Sofi (Student)

First , vehicle-bridge dynamic problem is essentially the transient response analysis.

Option 2 seems much better. Many papers are available on this topic. It is a little bit challenging to write the codes.

Thank you Dr Aria & Dr Wenai.

Transient dynamics for vehicle-bridge interaction can be performed with the LS-DYNA commercial software package. The academic version is available at many universities (Hallquist J.O., LS-DYNA Keyword User's Manual, Livermore Software Technology Corporation (LSTC), Livermore, CA, 2009). Using explicit time integration would eliminate convergence problems, although it may require more CPU time. Finite element models for the vehicle can be constructed using simplified approximations aimed at spatially representing the vehicles distributed mass and exactly modeling the suspension system (stiffness, damping). For example, a semi-tractor trailer truck would have independent suspension components at each of the wheel locations (Li H., Dynamic response of Highway Bridges Subjected to Heavy Vehicles, PhD Dissertation, Florida State University, Tallahassee, Florida, November, 2005). The interaction between the vehicle and bridge is achieved using LS-DYNA keywords: RAIL_TRACK and RAIL_TRAIN. A path over the bridge is defined by beam elements embedded in the bridge deck. The beam elements use MAT009 (Null Material) so as not to add any stiffness to the bridge deck. The RAIL_TRAIN keyword card defines the wheel-to-bridge contacts. A penalty formulation handles the contact between the wheels and rails.

Fayaz, there are a number of ways to model the additional mass. One straightforward method is to model the vehicle as a mass element and use contact elements between the vehicle and the bridge and then you can displace the mass along the bridge at your desired velocity. You can also include a spring-damper element if required. I have done it for simulating pedestrians in a similar way to simulating vehicles using quarter-car models.

Thank you Ronald and Paul. I appreciate your useful information.

Paul Could you please forward me basic literature in terms of theoretical dynamic equilibrium equations governing the physics of your model if it is possible. Thanking you.

SOFiSTiK (www.sofistik.de) is FEM software that is using moving spring to simulate train/car – construction interaction. In the dynamic time step analysis moving springs simulate the wheel springs of a train which goes over the bridge, searching themselves for the current contact nodes of the bridge. Thus a train ride is implemented with all effects of the train−structure−interaction. The mass of the train is considered with the current train position. The contact nodes are determined from the particular relative displacement of the going train and the deformed bridge. Damper which are acted parallelly to the contact springs are converted also to the particular interpolated contact node.

TYPE=1 The spring searches for the contact nodes of the nodes

TYPE=2 The spring acts on one of the QUAD elements

Thank you sir..

A more accurate model is moving oscillator for the vehcile. Of course, the vehicle may be modelled as a multi-degrees-of-freedom model or an FEM model.

You may read an easy-to-read tutorial and review on moving-laod dynamci problems: doi:10.1016/j.ymssp.2010.12.010