What is the participaial phrase clapping wildly the audience shouted for the band to come back on the stage for an encore.

Clapping wildly is the participial phrase.

A participial phrase includes a verbal that ends in ed or ing (clapping) that functions as ad adjective modifying a noun (the audience). It stated how the audience acted.

newbie construction workers preparing to work at a job cite but are first going over safety concerns?

the simple predicate of the sentence is camped.