Puzzling rattling sound only on wet road

In normal running condition the car runs perfectly fine, bumpy road or not. But when driving while it is raining, even on the sweetest road, completely leveled/flat road, I hear a continues thud sound (like shaking a shoe box with a stone inside) concentrated just under the hand break area, and I can feel it as well while holiding the gear (2nd, third, fourth, or fifth). And after just a few seconds of continued thud my engine would sound and feel as though it were towing something/climbing a very steep hill. All these disappears when I come to a stop. But as soon as the car runs again it comes back. All these when it is just raining/the road is really realy wet - not flooded. Local mechanic checked all the moving parts underneath and found no cause for the mysterious continuing sound. Please help.