“Be concerned” can be used with preposition “about”, “with”. What is very interesting depends on the preposition it is followed by, the meaning of the adjective in question changes a lot. The Kenneth Katzner’s English-Russion Dictionary says that if it is followed by the preposition “about”, it has the meaning be worried about someone. When “concerned” has preposition “with” after it, the meanings changes to “be engaged in an activity”,” to do something”.
COCA gives examples when someone is concerned about economical, political and social problems, a class, what someone says, their mistakes, various things happened, “...many people are concerned about the future developments of genetically modified organisms”.
. I like very much definition of The Free Dicionary (www.thefreedictionary.com): “to be concern about - feeling or showing worry or solicitude”. According to Google, people concerned about resume, android, lead. And there is my example of usage. There was a tsunami warning in California coastline. I was concerned about the tsunami in Santa Cruz and San Francisco because I live in the San Francisco Bay Area and many people I know could be hurt.
To be concerned with means to participate or to be involved in a process of someone doing something. Google gives good example what people might be concerned with: a child’s speech, teaching English, someone doing something etc. For example, from COCA:
There are examples provided by COCA when people are concerned with federal spending, client’s personal well-being, academic, career, “...medicine is concerned with the short-term survival of the human species” and so on.
This research has helped me to learn the difference between the adjective phrases “to be concerned with” and “to be concerned about”. I found out a way helped me to identify correct preposition. Try to substitute the phrase with either “worry about” or “participate/help”. You should use the preposition either “about” or “with” accordingly:
To be concerned of tsunami = to worry about tsunami
To be concerned with your child’s homework = to help your child with a homework.