Free vibrations of spatial frame structures: Analytical modelling and solution

Abstract

This study analytically handles the three-dimensional free vibrations of spatial frames using the initial values method, considering the axial and shear deformations alongside rotary inertias, namely, torsional, in-plane bending and out-of-plane bending. To handle the spatial geometry, the direction cosine matrices are used. Validation is performed with three cases in total, one case available in the literature alongside two numerical examples that are solved analytically and compared to the finite element models. Excellent agreements are found between the analytical results and the results in the literature, as well as those obtained from the finite element models.

Optimization of Motion Parameters and Structural Stiffness of Spatial Four-Bar Weft Insertion Mechanism of Rapier Loom

“…Firstly, the space 4R mechanism was analyzed to establish the relationship between output angle θ0 and input angle θ0. Bar 2 is hypothetically disassembled, combined with the knowledge of space mechanism, and the direction cosine matrix method [3] is adopted to obtain the following relation:…”