Irregular free-free beam, non-numerical solutions

What are the simplest, even if not very accurate, non-numerical ways (for example a variation of Euler-Bernoulli) for describing the deflection relative to a given load of a free-free beam with irregular shape (variable second moment of area and/or lumped masses distributed at some points)? In finite element methods there would be the need of knowing exactly the second moment of area and weight of such lumped masses at given positions in the long axis of the beam. Isn't there an otherwise method that uses more macroscopic characteristics of the whole beam like center of mass, center of oscillation relative to center of mass or something like that, in order to reduce the partitioning of the beam?
 

Baluncore

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Isn't there an otherwise method that uses more macroscopic characteristics of the whole beam like center of mass, center of oscillation relative to center of mass or something like that, in order to reduce the partitioning of the beam?
There is no quick and simple solution to complex problems. Engineering involves designing safe solutions based on measurements, not on guesses. If you think you have found a shortcut that works, then clearly label and file your notes as your insurance company may be needing them after the coroners court.
 

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