To be honest, I don't quite understand what you are saying, but I can correct these phrases:
Past researches have shown > Past research has shown
inside tyre cavity > inside the tyre cavity
to passenger compartment > to the passenger compartment
If I tried to improve the first part of your sentence (which I THINK I understand), it might be:
"Research has shown that resonance in the tyre cavity (OR inside the tyre) caused by road inputs through the tyre is transmitted to the passenger compartment in the form of vibration; ..."