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Nonlinear Vibration and Resonance Behavior of Semi-Rigid Steel Frames with Second-Order Effects
Dung Bao Trung Le1, Quoc Anh Vu1, Hai Quang Nguyen2,*
1 Faculty of Civil Engineering, Hanoi Architectural University, Hanoi, Vietnam
2 Faculty of Mechanical-Automotive and Civil Engineering, Electric Power University, Hanoi, Vietnam
* Corresponding Author: Hai Quang Nguyen. Email: 
Structural Durability & Health Monitoring https://doi.org/10.32604/sdhm.2026.079036
Received 13 January 2026; Accepted 02 March 2026; Published online 21 April 2026
Abstract
The vibration and resonance behavior of steel frame structures are significantly affected by connection flexibility and geometric nonlinearity. Conventional vibration analyses often assume fully rigid beam-column connections and neglect second-order effects, which can lead to inaccurate predictions of natural frequencies and resonance conditions. This study proposes a finite element-based approach for the vibration analysis of planar steel frames with linear and nonlinear semi-rigid connections, explicitly incorporating geometric nonlinearity. Beam-column connections are modeled using nonlinear moment-rotation relationships, while elastic and geometric stiffness matrices, together with a consistent mass matrix, are integrated into the governing dynamic equations. The time-history response is computed using the Newmark integration scheme. The proposed formulation is validated through benchmark examples and comparisons with published results and commercial finite element software. Numerical results reveal that the combined effects of semi-rigid connections and geometric nonlinearity significantly alter the effective structural stiffness, leading to noticeable variations in natural vibration frequencies. In particular, the fundamental frequency evolves during dynamic response, resulting in resonance shifting and time-dependent resonance behavior. These findings suggest that resonance in steel frames with semi-rigid connections should be regarded as a state-dependent phenomenon rather than a fixed structural property, with important implications for vibration assessment and resonance control in structural design.
Keywords
Semi-rigid connections; steel frames; second-order vibration; resonance behavior; finite element analysis
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