2. Benchmark solution#

2.1. Calculation method used for the reference solution#

_images/100021AA0000170C00002D94868D3395584CE4D3.svg
\(f(t)\)

contact force in \(A\)

;

\(V(z,t)\) speed; \(U(z,t)\) displacement;; \({\tau }_{0}=\frac{{U}_{0}}{{V}_{0}}\);; \({\tau }_{1}={\tau }_{0}+\frac{L}{{c}_{p}}\); Any shock duration; \(\tau -{\tau }_{0}=\frac{\mathrm{2L}}{{c}_{p}}\) \({c}_{p}=\sqrt{\frac{E(1-\nu )}{\rho (1+\nu )(1-2\nu )}}\) \(S={a}^{2}\) section.

_images/100002BC0000271000002710CD2F459F1DBDD5B0.svg

for point \(A\)

_images/100000B0000004720000003573C4257F10B00D20.svg

for point \(B\)

2.2. Benchmark results#

2.3. Bibliographical references#

  1. R.J. GIBERT, « Vibrations of structures », Summer School for Numerical Analysis, 1988, (Edition EYROLLES).