Intent upon her work, she didn't notice the cold.

=Being intent upon her work, she didn't notice the cold.

=As he was intent upon her work, she didn't notice the cold

intent 这里作形容词，专注，形容词放句首，作状语，请问下老师们adj+upon sth.这是什么结构呢？

属于形容词短语作原因状语，相当于一个原因状语从句结构。

be intent upon/on sth/doing sth:下定决心要实行/抱定决心要实行; 热衷于/专注于某事/做某事

He was intent on the job he was doing.  

他专心致志于正在做的工作.

A merchant is intent on making money.  

商人热衷于赚钱.

The rebels are obviously intent on keeping up the pressure.  

叛乱分子显然决心继续施压。

He's intent upon revenge.  

他一心想报仇.

But everybody was talking, and intent upon the grisly spectacle before them.  

可是大家都在谈话, 一心关注的是眼前的这个惨状.

They were so intent upon getting somewhere.  

他们都那么急着要赶到什么地方去.