Dynamic Optimal Arches With Constant Volume

This paper deals with dynamic optimal arches, built with a constant volume of arch material, that have the largest fundamental natural frequencies. The cross-section of each arch is a solid regular polygon with its depth varying in a functional fashion. Three shapes of arch (circular, parabolic, and sinusoidal) and three kinds of taper type (linear, parabolic, and sinusoidal) are considered. Differential equations governing free vibrations of such tapered arches are derived, in which the effect of rotatory inertia is included; these equations are numerically solved to calculate the natural frequencies. The numerical results are presented in tables and figures that relate the frequency curves to arch parameters. Typical examples of obtaining the geometry of the dynamic optimal arch are presented. Laboratory scale experiments were conducted to measure the natural frequencies.