Membrane Vibration modeled with Simscape

Physical model of a tensioned membrane.

Mode 1 Mode 4 Mode 6

This submission provides a Simscape model of a vibrating rectangular membrane under tension. The theory for this model is available in the acoustics book by Garrett [1]. The membrane is modeled as a two-dimensional array of square or rectangular connected segments. Each segment is modeled as a lumped mass connected to its four neighbors by damped springs whose spring constant is calculated from the membrane tension.

The files that are include are

membrane.m – creates a membrane .slx model file for parameters specified in the first lines of the file

mem_11by25.slx – a membrane model file created by membrane.m for a membrane that is 11 segments in the y direction and 25 segments in the x direction.

membrane_surf_11by25.m – when run on the output of the .slx file above, this creates surface plots like those shown in the MATLAB File Central listing for this toolbox.

mode_n_rect – animated GIF files showing the nthresonant mode shape

[1] Steven L. Garrett, Understanding Acoustics, Chapter 6, Springer, 2017.