Numerical and experimental investigation on autoparametric resonance of multi-system structures

Abstract

The analysis of dynamic stability in frame structures has always been a critical issue in engineering and mechanical design. Autoparametric resonance instability problems present a more complex dynamic instability mechanism than general parametric resonance, and determining the unstable regions of frame structures with multiple subsystems requires consideration of the coupled vibration of each subsystem. Unfortunately, existing approximate formulas are inadequate to analyze the stable boundary of autoparametric resonance in frame structures. To address this issue, this paper proposes a novel method called the dynamic axial force transfer coefficient (DTC) method to investigate the spatial dynamic instability characteristics of complex frame structures under parametric excitation due to autoparametric resonance. The proposed method, in conjunction with the harmonic balance method and the finite element method (FEM), established the global finite element equation of the frame and derived the stable boundary equation of autoparametric resonance for general frame structures. A complex spatial frame model is built to verify the effectiveness of the DTC method, and a comprehensive parametric analysis is conducted to investigate the dynamic instability mechanism of autoparametric resonance, including structural damping, static load coefficient, connection and boundary conditions of subsystems, and cross-sectional dimensions of subsystems. The results show that autoparametric resonance stability analysis of frame structures should consider the design parameters of each subsystem independently. In addition, strong coupling interaction between subsystems may induce autoparametric internal resonance of structure subjected to dynamic load. An autoparametric resonance test of a Γ-shaped frame is presented to further verify the proposed method. The test reveals the mechanism of the strong coupling effect, which may lead to a high risk of structural failure. More importantly, the DTC method can accurately determine the unstable boundary of multi-system frame structures, which is consistent with conventional methods (EGE) and experimental results, and predict the strong coupling effect of practical structures. The proposed method is simpler and more convenient than the existing methods for stability analysis of the autoparametric resonance of general frame structures, and can provide more effective guidance for structural design.