On the first day of class, do the orientation lecture from the back of the room. Stand right next to the students who are trying to stay far away from you. That's sending the message that no one can hide in this class.
Icebreakers aren't just for the first class. Get to know your students on that first day, but continue to break the ice with them throughout the term. Do different exercises, not necessarily even task related, at different points that raise the comfort level among students and with you.
Let the brainy engaged students start the discussions and interject when they want, but also call on the people not raising their hands, not offering comments. And do that often. You will send the message that you better come prepared, or you will embarrass yourself.
Regularly use the random draw for comments. That means either write the names of students on a piece of paper and draw them from a hat, asking them to comment, or use a computer program, such as The Hat, to do that for you. It's a fun way to hold people accountable for being ready to participate.
Create contests among the students. Instead of just a quiz, make a game in which competing sides try to outscore each other. Peer pressure is as much a motivator as grades.
Have fun. Be playful. Learning doesn't have to be boring, or even a chore. The most enjoyable a class is, the more the students will learn and the more they will participate. If you only are feeding them spinach and not giving them cake every once in a while, it's no wonder that people aren't opening their mouths.