Vibration analysis of transversely loaded arches using Hencky bar-chain model

This study focuses on the vibration analysis of loaded arches utilizing the Hencky bar-chain model in conjunction with an energy-based approach to derive the governing eigenvalue equations. The formulation is comprehensive, accommodating arbitrary arch shapes, loading and support conditions, and asymmetrical or symmetrical vibration modes. By discretizing the arch into rigid segments connected by frictionless hinges and elastic rotational springs, the Hencky bar-chain model transforms the complex differential equations of continuum mechanics into a solvable set of algebraic equations, facilitating efficient analysis of structural vibrations. This general framework addresses existing gaps in the vibration analysis of loaded arches. To demonstrate its applicability, the study examines illustrative cases involving circular, parabolic, and triangular arches subjected to point and distributed loads, calculating their vibration frequencies to assess the influence of transverse load magnitudes on these frequencies. The accurate vibration frequencies obtained serve as benchmark solutions, valuable for validating new analytical formulations and computational models in the vibration analysis of arches.