Euler-Bernoulli Beam formulas

cantilever: mode shape

y = cos(kx) - cosh(kx) - ${\frac{{sin(kL)-sinh(kL)}}{{cos(kL)+cosh(kL)}}}$$\left[\vphantom{sin(kx)-sinh(kx)}\right.$sin(kx) - sinh(kx)$\left.\vphantom{sin(kx)-sinh(kx)}\right]$,where k is found from cos(kL)*cosh(kL) = - 1 and L is the length of the beam. First five values: kL = 1.875, 4.694, 7.855, 10.996.

Harris+Piersol pg 7.17

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