ABSTRACT
It remains to determine tan θ. Consider a differential beam element abdc as before. The deformation of the beam due to the rotation of the beam cross section is illustrated in Figure 6.24. From Figure 6.24, it follows that
θ ≈ tan θ ≈ y(t, x+ ∆x)− y(t, x)
∆x
≈ ∂y ∂x ,
where ∆x is small. Here we utilize the assumptions that plane sections remain planes and that there is no shear deformation. Hence the boundary condition at x = L is given by
∂M
∂x (t, L) +m
∂2
∂t2
[ δ ∂
∂x y(t, L) + y(t, L)
] = g(t).
