Modal assurance criterion-guided section selection optimization for increasing the modal frequency of a railway carbody

Abstract

The carbody commonly exhibits a low first-order diamond modal frequency, degrading ride comfort and operational safety of the railway vehicle. Existing optimization methods yield results that are often difficult to implement directly under standardized manufacturing constraints, and discrete dynamic optimization is prone to severe modal exchange during iterations, leading to inaccurate identification of the target mode, and invalid optimization. To address these issues, a mode-consistent discrete section selection framework guided by the Modal Assurance Criterion (MAC) is proposed for enhancing the first-order diamond modal frequency of the carbody. A design space comprising standard sections with discrete orientations is constructed to ensure engineering feasibility, and an eccentric Rayleigh beam formulation is developed to capture the centroid eccentricity, rotary inertia, and bending-torsion coupling of asymmetric sections. A MAC-based mode-tracking constraint is embedded into the optimization loop to maintain the continuity of the diamond mode and eliminate modal exchange. The proposed method is verified against commercial finite element analysis and applied to a full-scale carbody. Results show that the first-order diamond modal frequency increases from 7.18 to 7.64 Hz without modifying the global structural layout. A two-stage scheme that integrates the proposed method with engineering reinforcements further raises the frequency to 8.66 Hz, with the discrete section optimization contributing 31.1% of the total improvement at only half the mass increment of the global reinforcements. Vehicle dynamics simulation confirms that the increased modal frequency effectively suppresses the abnormal elastic vibration and improves the running stability.