Dynamic Response Analysis of a Beam–Spring–Arch Coupling Structure under Moving Load/Oscillator

The coupling of beam and arch in bridge engineering introduces intricate dynamic responses. To more efficiently and comprehensively evaluate the coupling dynamic characteristics of arch bridge, this study examines the natural frequencies and dynamic responses of a beam–spring–arch coupling structure under moving loads/oscillators. A mathematical model of the coupling structure is formulated, with the corresponding partial differential equations derived using Hamilton’s principle. The transfer matrix method is employed to establish state vector connections for each segment of the structure, leading to the derivation of a frequency equation to calculate natural frequencies based on specific boundary conditions. Modal functions are determined by transferring the state vectors of each segment, and the Galerkin method is used to discretize the first six-order vibration in the form of ordinary differential equations. The study explores the characteristics of free vibration modes and natural frequencies, and numerically calculates the dynamic responses of the coupling structure under moving loads/oscillators. Responses for the first six modes are superimposed, and the effects of key parameters on the dynamic response are analyzed. The calculated natural frequencies show less than 5% deviation from those obtained via finite element models. The oscillator mass block displacement exhibits an inverted M-shape. Increased structural stiffness raises natural frequencies and induces a curve veering phenomenon. While higher stiffness can reduce oscillator displacement during movement, it does not entirely eliminate member response and may amplify displacement in certain sections. The developed coupling dynamics model and findings provide guidance for the stiffness design of beams, arches, and supporting components, as well as for the vibration reduction of arch bridges.