Effect of damping and relaxed clamping on a new vibration theory of piezoelectric diaphragms

A new mathematical and experimental study on the vibration behaviour of a unimorph clamped piezoelectric diaphragm is presented. The diaphragm was segmented into an inner and an outer section. The interconnection of both segments required two distinct eigenvalues λi and λo, being one function of the other. An experimental validation campaign was conducted. From a qualitative sense, the model predicted correctly the frequency behaviour. From a quantitative sense, the perfect clamping theory overestimated it by 20%. The reason for this was attributed to unaccounted factors such as damping and imperfect clamping conditions. It was determined that damping contributed to 5 percentage points of the 20%, clamping relaxation 13 percentage points, leaving 2 percentage points unexplained. As a conclusion, two additional effects must be accounted when modelling the vibration of piezoelectric diaphragms: damping through the coefficient ξ ≈ 0.06 and imperfect clamping condition through the relaxation factor Ψ = 0.03.