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Your conclusion is incorrect in that the lowest mode automatically contains the highest mass. It just so happens that the 3DOF system you are considering happens to have the predominance of the mass located in mode 1. This should not be considered as a generalised case for all modal analysis...

All, In terms of physical meaning, the dominant mode is the one that dominates the response of the system. If one were to "ping" (technical term) a tuning fork the same would respond in modes 1,2,3,4 etc. However the vast majority of the response will be governed by mode 1. The higher modes...

The reason is relatively simple.... In structural dynamics there is an "orthogonality property of the modes of oscillation". You may ask what is this... It means essentially that you can decouple the equations of motion, solve for each mode independently and combine the effects of each mode...

I am unsure which code will have jurisdiction on your tanks but would hazard a guess at API 650? This contains a resonably section on seismic design but to be honest would be somewhat lacking in terms of California's performance based seismic design. You may need to consider the effects of...

Apologies for coming in at the end but I couldn't resist. You have come across a paradox that invariably gets ignored by most engineers; more often due to the difficulties in interfacing and establishing the actual seismic effects. Referenced within threads are "magic" factors taken from ASCE...