Dependency between amplitude and modeshape on vibrating diaphragms

Two theories governing the vibration of plates were compared: one, considering the amplitude is independent of modeshape (method of separation of variables) and the other, considering it dependent (Lord Rayleigh's approach). An exhaustive and thorough study was made, both theoretical for an homogeneous diaphragm and experimentally for several piezoelectric diaphragms, showing that Lord Rayleigh's theory is the correct one and that amplitude of vibration is dependent on modeshape through the coupling factor C. To verify this dependency, several equations were graphically compared showing that accounting for C is critical for a correct prediction. Moreover, the meaning of the coupling factor is explained from a mathematical and physical point of view. The theory predicts correctly both qualitatively and quantitatively the vibration of a diaphragm for varying excitation frequency having only as an input the geometrical and physical properties of the diaphragm.