Kelvin-Voigt cantilever creep ($\tau \dot{\delta }+\delta =F{\ell }^3/(3EI)$)

For a quasistatic cantilever of Kelvin-Voigt material, the bending moment is $M=EI{y}_{xx}+{\eta }_{s}I{y}_{xxt}$. A tip load gives $M=F(t)(\ell -x)$, so the free-tip displacement obeys the displayed equation with $\tau ={\eta }_s/E$. A step load gives a finite asymptotic deflection. If inertia is retained, the interior equation is $\rho A{y}_{tt}+EI{y}_{xxxx}+{\eta }_{s}I{y}_{xxxxt}=0$, with the corresponding moment and shear conditions at the tip.