A consistent rayleigh method-based formulation for analytically determining the dynamically equivalent mass and stiffness parameters of Euler-Bernoulli beams

Abstract This paper introduces a new analytical approach, the Consistent Rayleigh Method-Based Formulation (CRMBF), aimed at developing dynamically equivalent mechanical models of elastic structures. Inspired by the well-known Rayleigh-Ritz technique and the classical modal truncation concept, this study presents an alternative method that employs the Rayleigh approach to effectively derive discrete system models from their continuous versions based on the Euler-Bernoulli beam theory. While well-documented existing strategies for deriving equivalent models rely on static discretization, this research presents a different perspective by introducing a dynamic version of the Rayleigh method that improves the estimation of equivalent mass and stiffness coefficients for continuous systems, thereby simplifying the analysis of complex beam structures. By so doing, the analytical, numerical, and experimental results obtained from the demonstrative examples and the case studies analyzed in this work show that the dynamic version of the Rayleigh method introduced here outperforms its static counterpart, which is conventionally used in the literature. In particular, the critical discussion and the experimental comparison provided in the paper highlight the potential of the proposed dynamic approach, resulting in discrete equivalent models of beam structures that better align with the fields of computational mechanics and structural analysis.