Abstract Background/Introduction Coupled composite beam structures exhibit complex dynamic interaction phenomena arising from the interplay between material anisotropy and geometric asymmetry. Theseinteractions manifest as frequency veering, mode veering, and internal resonance, which are known to govern modal energy exchange, vibration localization, and stabilitycharacteristics. Although individual coupling eff ects have been studied, a comprehensive understanding of their combined infl uence on modal interaction mechanisms in materially andgeometrically coupled Timoshenko beams remains incomplete. Purpose The primary objective of this study is to establish a unifi ed and physically interpretable framework for identifying and characterizing frequency veering, mode veering, and internalresonance phenomena in composite Timoshenko beams with simultaneous material and geometric coupling, and to quantify the role of coupling intensity and boundary conditions inshaping modal interaction behavior. Methods An advanced coupled bending–torsion Timoshenko beam model incorporating stiff ness–inertia coupling and elastic–mass axis eccentricity was formulated to capture the essentialphysics of asymmetric composite structures. The Diff erential Transformation Method (DTM) was employed to obtain highly accurate eigensolutions, including natural frequencies, modeshapes, and modal energy-participation ratios. Systematic parametric analyses were conducted over a broad coupling parameter space, and frequency-ratio maps combined withenergy-based interaction metrics were utilized to identify avoided crossings, modal exchange regions, and resonance-prone confi gurations under clamped–free and clamped–clampedboundary conditions. Results The analysis reveals that strong material coupling and negative geometric off sets signifi cantly amplify bending–torsion interaction, producing pronounced frequency veering, clearmode-shape exchange, and substantial modal energy redistribution. In contrast, positive off sets restrict interaction to localized parameter regions. Internal resonance conditions,particularly 1:1 and 2:1 commensurabilities, emerge predominantly in high-coupling regimes and are strongly modulated by boundary constraints. The clamped–clamped confi gurationexhibits earlier onset of modal interaction, sharper spectral clustering, and enhanced coupling-induced energy transfer compared to the clamped–free case. Conclusions The proposed framework provides a robust and physically grounded approach for diagnosing and interpreting modal interaction mechanisms in composite beam systems withsimultaneous material and geometric coupling. The fi ndings advance the fundamental understanding of coupling-induced dynamic phenomena and off er practical guidance forvibration tailoring, resonance avoidance, and stability-oriented design of advanced composite structures in aerospace and high-performance engineering applications.
Aysun Soysal (Sun,) studied this question.