Appendix providing the mathematical theory behind concepts discussed in the article from Coupled membranes: A mechanism of frequency filtering and transmission in the field cricket ear evidenced by micro-computed tomography, laser Doppler vibrometry, and finite element analysis

Appendix S4. Mathematical theory explaining: 1) the difference between a driving-force and the natural resonance of a membrane; 2) strain energy density and torque multiplication; 3) the relationship between the flexural rigidity of a membrane and its thickness. [Latham B, Reid A, Jackson-Camargo JC, Williams JA, Windmill JFC. Coupled membranes: A mechanism of frequency filtering and transmission in the field cricket ear evidenced by micro-computed tomography, laser Doppler vibrometry, and finite element analysis. J. R. Soc. Interface.]