Do you know any method/equipment which I can use to measure density of sediment at river bed without taking any sample of the material (perhaps with ultrasonic equipment) ???
The ideal solution is a shallow water seismic profiling system. These units profile the subsea or river bed and give you precise variations in density of material in the river/seabed. Saves a lot geotechnical core sample time and money.
Find a specialised marine survey company who offers this service in your region.