put a lid on vs shut down

put a lid on

verb
  • To get under control, to prevent (something) from increasing or becoming more of a problem. 

shut down

verb
  • To turn off or stop. 

  • To pass (another vehicle), especially quickly. 

  • To close, terminate, or end. 

  • To emotionally withdraw into oneself as a defense mechanism; to block out external stressors. 

How often have the words put a lid on and shut down occurred in a corpus of books? (source: Google Ngram Viewer )