Dynamic Analysis of Two Straight and Curved Beams Connected with Intermediate Vertical Beams Made of Functionally Graded Porous Materials
Abstract
This paper presents the dynamic analysis of a complex structure composed of two straight and curved beams connected through intermediate vertical beams, all made of functionally graded porous (FGP) materials. Unlike prior studies, which focused on simpler configurations, this work investigates the free and forced vibration behavior of such a structure for the first time. A novel finite element is developed, and its mass and stiffness matrices are derived to discretize the beams. Continuity conditions at the junctions of straight and curved beams are formulated, facilitating the assembly of the overall mass and stiffness matrices for the entire structure. The proposed method is validated through comparisons with simplified cases from the literature, demonstrating excellent accuracy. The study also explores the effects of various parameters on the dynamic response, offering practical insights for the design of advanced engineering structures such as bridges, roofs, and marine frameworks. By addressing the analysis of a complex structure, this work provides a foundational approach to improve the safety and performance of structural systems in diverse applications.