Vibration Analysis of Coupled Extensional/Flexural/Torsional Modes of Curved Beams With Arbitrary Thin-Walled Sections

• Published in: Journal of sound and vibration Vol. 174; no. 2; pp. 261 - 274
• Main Authors: Gendy, A.S., Saleeb, A.F.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 07.07.1994; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Three-dimensional calculations; Mode locking; Variational methods; Warping; Numerical solution; Normal-mode analysis; Mechanical vibrations; Curvature; Thin wall; Beam(mechanics)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1994.1275

A three-dimensional, two-field, variational formulation is employed to derive the differential equations governing the dynamics of stretching, shearing, bending and twisting, as well as warping modes of deformations in a spatially curved beam with arbitrary cross-section. Correspondingly, the finite element discretization was developed for free vibration analysis based on a Timoshenko-Vlasov thin-walled theory, including the effects of flexural-torsional coupling, shear deformations due to flexure as well as torsional warping, and rotary inertia. Attention was given to the significant curvature effects on the results in cases involving unsymmetric cross-sections of the thin-walled type. Several numerical examples are given to demonstrate the high accuracy and effectiveness of the element developed.