Validation of the stiffness and mass matrices obtained from the two- dimensional equations of motion of curved Timoshenko beams

• Argenis Jesús Bonilla Pinto Universidad de Oriente. Barcelona, Anzoátegui, Venezuela. https://orcid.org/0000-0003-0488-1151
• Carlos José Gomes Ansia Universidad de Oriente. Barcelona, Anzoátegui, Venezuela.  https://orcid.org/0000-0001-8235-4280

DOI: https://doi.org/10.46925//rdluz.39.11

Abstract

In this work, the mass and stiffness matrices for the vibrational behavior, on the plane, of curved Timoshenko’s beams were developed. The mathematical model for the kinetic and elastic potential energy of a two-dimensional curved Timoshenko beam was developed. The energy equations include discrete elements such as translational and rotational inertias, translational and torsional springs. Hamilton's principle was used to obtain the weak finite element formulation and consequently the stiffness and mass matrices. The terms of the matrices were obtained by parametric integration with cubic elements of three degrees of freedom per node. The matrices developed for the curved beam element were validated with case studies presented in previous publications, finding good agreement.

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