A uniform semi-infinite elastic beam moving along the x-axis with a constant velocity v0
Chapter 15, Problem 8(choose chapter or problem)
A uniform semi-infinite elastic beam moving along the x-axis with a constant velocity \(-v_{0}\) is brought to a stop by hitting a wall at time t = 0. See FIGURE 15.2.3. The longitudinal displacement u(x, t) is determined from
\(a^{2} \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial^{2} u}{\partial t^{2}}\), x>0, t>0
u(0, t)=0, \(\lim _{x \rightarrow \infty} \frac{\partial u}{\partial x}=0\), t>0
u(x, 0)=0, \(\left.\quad \frac{\partial u}{\partial t}\right|_{t=0}=-v_{0}\), x>0
Solve for u(x, t).
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