Steven,
You are correct in that the dynamic across generations can be strained, especially when the team is working on high profile projects that results in promotions or other rewards.
One idea would be to create sub-teams that you assign, making sure that you separate the generational clichés. Learning to cope with and trust one or two people to start with is easier than getting along with the entire team.
If that doesn’t work, perhaps you could have your HR department set up a training related to age bias and tolerance.
Hope that helps.
Jamie