Free vibrations of spatial frame structures: Analytical modelling and solution

Genel Ö. E., Tufekci M., Tüfekci E.

JOURNAL OF VIBRATION AND CONTROL, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1177/10775463221122086
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: 3D Timoshenko frame, analytical solution, direction cosine, initial value method, modal analysis, DYNAMIC-ANALYSIS, ELEMENT METHOD, PLANE FRAMES, STIFFNESS, FREQUENCIES, MATRIX, BEAMS
  • Istanbul Technical University Affiliated: Yes


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.