Detailed presentation: exciting a suspended membrane via an exterior force
Description of the studied membrane
Let us consider the case of a circular membrane attached to a rigid structure by a peripheral elastic suspension.
By applying an exterior mechanical force
to the membrane,it will move and may emit sound from its two faces.For frequencies situated below its first mode, this membrane can be considered like a mass-spring system comprised of a rigid piston and an elastic peripheral suspension.
The mechanical elements representing the membrane are thus the total mobile mass
, the compliance
of the suspensions, and the mechanical resistance
mainly due to the viscous losses in the suspension.The pressure in front of the membrane (on the right, by convention) and behind (on the left) are noted
and
.The associated pressure forces are noted
and
. These forces which act upon the membrane correspond to the reaction of the air on the membrane, which moves due to the force
.
