CantileverBeam_abg.tex

MTT command:

mtt CantileverBeam abg tex

Figure 1.1: System CantileverBeam: acausal bond graph

The acausal bond graph of system CantileverBeam is displayed in Figure 1.1 (on page ) and its label file is listed in Section 1.1.1 (on page ). The subsystems are listed in Section 1.1.2 (on page ).

This example represents the dynamics of a uniform beam with one fixed and one free end. The beam is approximated by 20 equal lumps using the Bernoulli-Euler approximation with damping. The input is the angular velocity of the fixed end, the output is the linear velocity of the free end.

The system parameters are given in Section (on page ). Note that the numer of ban segments has been set to 21.

The system has 20 states (10 modes of vibration), 1 inputs and 1 outputs.

The first 5 vibration frequencies are given in Table 2.2 togtherr with the theoretical (based on the Bernoulli-Euler beam with the same values of $EI$ and $\rho A$.

Table 1.1: Mode frequencies (rad $s^{-1}$)

Mode	Frequency	Theoretical frequency
1	76.14	76.14
2	477.11	484.50
3	1330.62	1334.55
4	2586.77	2617.19
5	4225.14	4323.77