1. Reference problem#

1.1. Geometry#

_images/10000848000021B1000010A43B723D343AAF0CE7.svg

Square section beam:

\(c=0.014m\)

\(L\): length of the beam

\(L=0.783m\)

Strain gauge

\(x=0.462m\)

1.2. Material properties#

Young’s module:

\(E=6.7E10\mathrm{Pa}\)

Density:

\(\rho =2400\mathrm{kg}/{m}^{3}\)

Poisson’s ratio:

\(\nu =0.\)

Spring stiffness:

case no. 1 \(k=18000N/m\)

case no. 2 \(k=45\mathrm{000N}/m\)

1.3. Boundary conditions and loads#

At point \(A\):

\(u=v=0\) (ball joint)

At point \(B\):

free end before impact (\(t<0\))

Charging:

No other load.

The effects of gravity are negligible at first approximation.

1.4. Initial conditions#

For \(t<0\) at any point on the abscissa \(x\)

  • \(\mathrm{dv}/\mathrm{dt}=\omega \mathrm{.}x\)

  • \(\omega =–3.8\mathrm{rd}/s\)

For \(t=0\), \(v(L\mathrm{,0})=0\): contact of the free end with the spring.