Artifacts of Christianity/Judaism have, as a rule, not been preserved, despite the fact that you can buy a forest full of “pieces of the cross” when visiting the area...
Looking around Noah takes a good look at the ark which is now empty of animals.
Noah: "Looks like we survived, praise be to God. What a muddy mess. Shem, get some of that rice stored in the ark and start planting. Japheth, you plant some wheat. Ham, you gather the sheep and goats and watch over them. The children can get eggs from the chickens and watch over the rest of the livestock, make sure those baby tyrannosauruses don't eat them all."
Mrs. Japheth: "I ain't living in that ark with Mrs. Ham. I'm sick of her!" She did nothing but moan and complain the whole 40 days and nights.
Mrs. Ham: "Well I ain't gonna live in that ark anymore with you neither, you spiteful hag!"
Mrs. Shem: "You both are getting on my nerves. Just shut up will you?"
Noah: "That is ENOUGH! Now we all know the northlands are frozen, no use going up there. Shem, take your family and 1/3 of the ark wood and go east. Ham, take your family and 1/3 of the wood go south. Japheth, you go west. Me, I'll just stay here on the mountain and keep tending these grape vines, tee-hee.
It is almost certain the ark was dismantled for firewood and building material. They just survived a disaster so that is what they would have done.