1. Reference problem

1.1. Geometry

In the diagram above, the measurement points on the initial structure are represented by arrows, the tip of which indicates the sensitive direction of the sensor. These measurement points are located at the abscissa \(0.2m\), \(0.4m\),,, \(0.6m\) and \(0.8m\) in the directions \(y\) and \(z\). Measured information is only available at these measurement points.

The initial structure is a rectangular beam (\(9\mathrm{mm}\times 38\mathrm{mm}\)) with a length of \(0.9m\).

The modification is an additional beam, with a rectangular cross section (\(9\mathrm{mm}\times 38\mathrm{mm}\)), which is applied between the coordinates \(0.6m\) and \(0.8m\).

1.2. Material properties

Young’s module: \(E=2.1{10}^{11}N/{m}^{2}\)

Poisson’s ratio: \(\nu =0.3\)

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

1.3. Boundary conditions and loads

The beam is embedded at one of its ends (origin of the axes) and free at the other end.

1.4. Initial conditions

Not applicable.