A NEW METHOD FOR SOLVING NATURAL FREQUENCIES OF BEAM STRUCTURES WITH ATTACHMENTS

To address the problems of cumbersome and unsystematic solution methods for frequency equations of beam systems with attachments in vibration mechanics courses, this paper proposes a simplified solution method based on Green’s functions. By equivalently treating the attachment effects as external loads, this approach reduces the mathematical complexity of traditional analytical procedures while maintaining clear physical interpretations. Educational experiments confirm that this approach significantly improves the ability of students to model complex vibration systems while enhancing their systematic thinking in engineering problem solving. The new method provides a novel reference for theoretical instruction and engineering applications in vibration mechanics.