In this example we compute the sound pressure generated by the natural vibrations of an elastic beam attached to a rigid reflecting foundation. The computational domain for the air was taken to be a half circle around the beam. The Sommerfeld (far field) radiation condition was imposed along the circular edge.

The vibration frequencies and mode shapes of the beam were computed using the standard linearized elasticity theory. The results were then used as input data for the Helmholtz equation by which the pressure was determined. The equations were solved numerically using quadratic triangular finite elements.

The figures show the mode shapes and pressure fields (real part) corresponding to the three lowest natural frequencies of the beam.

This animation shows pressure waves generated by 10 lowest vibration modes of an elastic beam mpeg: [~10 MB!!!!!]