1. Reference problem#

1.1. Geometry#

Two problems are considered (1 and 2), corresponding respectively to models A and B. The aim is to calculate the natural modes of a supported and supported beam (problem 1) and free-free (problem 2), with a plane modeling.

_images/100002010000050600000171F61441F7BAE88C7D.png

For problem 2 the beam is identical to problem 1 but without the supports at points \(A\) and \(C\).

Dimensions of the rectangular straight beam:

diameter:

\(R=0.05m\)

length:

\(L=6.m\)

Point coordinates (\(m\)) :

\(A\)

\(B\)

\(C\)

\(x\)

\(y\) and \(z\)

1.2. Material properties#

\(E={2.10}^{11}\mathrm{Pa}\)

\(\nu =0.3\)

\(\rho =7800.\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

Problem 1:

Point \(A\)

\(\mathit{DX}=\mathit{DY}=0.\)

Point \(C\)

\(\mathit{DY}=0.\)

Problem 2:

Point \(A\)

Point \(C\)