Vibration of Arches Under the Influence of Self-weight

This paper investigates the in-plane vibration characteristics of arches under self-weight-induced compression using the Hencky bar-chain model (HBM) combined with an energy-based formulation. Extensive studies on circular, parabolic and catenary arches reveal that self-weight produces a substantial reduction in vibration frequencies. For all three arch types and both pinned and fixed supports, the reduction in frequency is more pronounced for the fundamental mode, while the higher mode frequencies diminish at a slower rate. The results further show that self-weight transforms the frequency-rise behavior from monotonic decay (for negligible or small self-weight) to a non-monotonic curve with an interior maximum. A key finding is that a similar classical beam-based approximate formula [Formula: see text] (where [Formula: see text] is the [Formula: see text]th frequency mode of arch with self-weight effect, [Formula: see text] of corresponding arch without self-weight effect, [Formula: see text] the self-weight parameter and [Formula: see text] the [Formula: see text]th self-weight buckling load) accurately captures the frequency-self-weight relationships of all three arch geometries, pinned or fixed support conditions and all modes, providing a unified and computationally efficient means to estimate frequency reduction due to self-weight.