请问下句子的成分问题

1 She will come to be ashamed of what she had done today.

2 Soon theyre getting to have a better understanding of the problem.

两个例句中的of 部分，请问是干什么成分？

第二句中的 theyre getting to 是表示以后还是目前进行时？

第一句：be ashamed of “为…….感到羞愧/惭愧”是惯用短语，其后接宾语从句what she had done today。

第二句：a better understanding of the problem是名词短语作不定式to have的宾语，假如必须要细分的话，可理解为of短语作定语修饰中心名词understanding。又如：

I have only a limited understanding of French. 我懂的法语非常有限。

第二句中的 theyre getting to是表示以后。