Volume estimation of symmetrical branching structures by resonance mode analysis

An exact resonance condition is derived for rigid symmetric second-order bifurcating structures. In the low-frequency range, the resonance condition can be reduced into forms that facilitate volume estimation of bifurcating structures. Two such volume approximation techniques are presented: (1) a fundamental frequency method, in which the lowest resonant frequency is inversely proportional to the structure volume, and (2) an equivalent-length method, in which an equivalent length of two daughter branches is calculated for all branches distal to the first bifurcation. An experimental study to determine the resonance modes of seven bifurcating glass structures was performed. The volume estimates obtained by either method were in very close agreement with the true volumes.