bro, i can show you a diesel car of 85 model, when it is started you can hardly tell its diesel. it has no sound of diesel and when u sit inside it has no vibration too.
the vibration comes due to conversion. if you have converted your vehicle to diesel engine it is vibrant in case of lose or badly mounted engine.
check exhaust pipe fitting, get its nozzle work done. see if you re having prolem with its clutch plates. check the mounting for sure.
bad shocks or altered ones create problems. so vibration may be the reason of different problems.
get it inspected by some technical person.