Perspectives on the generalized modeling of six beam theories: A unified dynamic stiffness matrix.

• Unifying six beam theories into a single equation. • Unified dynamic stiffness matrix and transfer matrix. • Frequency-dependent mass and stiffness matrices. • Thorough comparison and scope of different beam theories for curved beams. High-precision, efficient and streamlined methods for the dynamic modeling and analyzing of engineering structures have consistently captured attention of designers and researchers. This paper addressed this increasing demand by presenting a generalized modeling and analyzing method. Specially, a unified model was proposed to integrate six beam theories into a single formula. Upon this model, a unified dynamic stiffness matrix was derived, serving as an elemental building block for formulating the transfer matrix, frequency-dependent mass and stiffness matrices as well as further integrating finite element method, dynamic stiffness matrix method and transfer matrix method. Through this transition, challenges associated with transcendental eigenvalue in dynamic stiffness matrix method and transfer matrix method was effectively resolved and the advantages of transfer matrix method in handling complex structure were maximized. Given the widespread utilization of curved beams in buildings, bridges, robotics and sensors, the proposed method was validated through comparative analysis with other methods, focusing on both curved and straight beams. Furthermore, this study delineated applicability scopes of different beam theories and provided the strategic approach for curved and straight beams. The feasibility of this strategy was demonstrated through an investigation involving a corrugated structure comprising both straight and curved beams. [ABSTRACT FROM AUTHOR]