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002234
2026-02-20

Equivalent Mass per Unit Length for Finite Element Representation

Equivalent mass per unit length for a finite element representation

μe=∫0lm(s)·ϕi2(s)ds∫0lϕi2(s)ds≈∑j=1N∆sj·ϕi2(sj,m)·m(sj,m)∑j=1N∆sj·ϕi2(sj,m)
where:
l=∑j=1N∆sj

μe

Equivalent mass per unit length

l

Height or span of the structure or the structural element

i

Mode number

∆sj

Part number j of the structure or the structural element

m(sj,m)

Mean value of the mass per unit length within the interval ∆sj

ϕi2(sj,m)

Square of the mean value of the mode shape within the interval ∆sj
;