I have a 2004 Hyundai Accent. When my car was new and I drove over railroad tracks it drove over those tracks relatively smoothly and quietly. In the last couple of months when I drive over railroad tracks the car rattles and sounds bumpy and noisy. Do I need a new part under my car? If so, what is the name of that part? Thank you very much. Nick
Have the shocks or struts checked.
Shocks or struts are the most likely, but there are many other possibilities. In any case the same shop that handles shocks and struts should be able to check out the other likely issues. It may be more than one.
Don’t go the the shop and tell them what you want replaced, rather go and tell them what you told us and see what they say.
The real trick is to find an honest and qualified shop. Ask your friends and neighbors for recommendations.
Chains are known for low quality and less than stellar business practices. They like to add on additional work. Dealers may be a little better (on average) but they are generally more expensive and tend to follow an very aggressive repair theory of replacing what is bad and what might be bad.
Those are only general rules and there certainly are exceptions.
Quick lube places are always a bad idea. 
How many miles do you have on the car?
In addition to shocks/struts (your car probably has struts) the noises could represent worn ball joints and/or tie rod ends. While shocks/struts are somewhat of a safety issue, bad ball joints and/or tie rod ends are a major safety issue.
I suggest that you have this checked out a.s.a.p. by a trusted independent mechanic, NOT by Sears or any other chain operation–unless you want to pay for unnecessary repairs.
Addendum: If you have not been slowing down for those RR tracks, that could have led to excess wear on front-end parts. Always slow down for those RR tracks, and be sure that you don’t apply the brake while you are going over them. Apply the brake prior to hitting those tracks.
It could also be as simple as a loose heat shield. Only from under the car can the cause be found.
Worn or overinflated tires make a car ride rough too…How many miles on the car?
The same thing happened with my 02 Accent. I don’t think there’s a problem, really, just that the car is very cheap, and the plastic inside isn’t the greatest. I’ve had several plastic trim pieces fall off just driving down the highway. It also creaked and squeaked a lot. I think it’s just a side effect of driving one of the cheapest cars available.