Yes, there are a number of books that address the American dream from various theoretical perspectives. One that directly addresses the question is Jim Cullen's The American Dream: A Short History of an Idea that Shaped a Nation. It is about 10 years old, but it provides a solid overview of how the ideal of the American dream influenced people throughout the nation's history.
Hendrick Smith's Who Stole the American Dream? is more recent. It is an economic perspective on how this longstanding dream has faltered in recent decades. It's more narrowly focused.
Rank, Hirschi, and Foster's 2014 Chasing the American Dream combines an economic approach with a sociological one. It examines social mobility, specifically how people rise and fall economically.
If you combine all of these, you'll have a range of sociological, historical, and economic perspectives on the American dream, and be able to put specific representations of the dream in context.