There are many reasons for non-participation during meetings including lack of preparation, shyness, being overawed by rank or someone’s specialist knowledge, being put off by another’s aggressiveness or dominant behaviour or just pure laziness.
To draw out the silent type and protect them from intimidation it might be helpful to ask questions that tap their expertise, praise their good ideas, openly note their contributions, call on those that are shy or junior first.
Of course you may also have to limit the long winded. This can be done by setting the ground rules at the start including how long any one person can speak for at a time. You should also request that remarks be confined to the topic of discussion. If someone still insists on an opera length speech you may have to tactfully but firmly insist that you move on.
It is equally important to remain focused on the agenda and what needs to be achieved. To do this you will want to summarise progress and remind everyone of the meeting’s objectives. You will also have to interrupt if the discussion gets out of hand, off topic, too heated or rowdy. Act quickly if a serious disagreement arrises.
Sometimes a participant may have something worthy to contribute but may not be the best public speaker. At such times it is the chair’s job to rescue that person by helpfully summating what they think he/she was trying to say.
As the meeting chair you should work to encourage diverse points of view, especially if it is a problem solving or brainstorming session. Well run meetings enable a group of people to achieve more than the sum of their individual efforts, through the creation of synergy and the combination of their collective expertise.
As the chair you should encourage all opinions and perspectives to be explored but be prepared to hightlight bias and oversights. Some participants will need to broaden their viewpoints while others must be encouraged to be more realistic.
To generate ideas you may want to try brainstorming, asking open questions (ones that cannot be simply answered by yes or no), encourage partial ideas, reserve your own ideas until the end, clarify and paraphrase for others (make sure you ask them to confirm that you have it right), and the use of verbal and non-verbal reinforcement.