On coupled bending and torsional vibration of uniform beams

Use of Generalized Mass in the Interpretation of Dynamic Response of Bending–torsion Coupled Beams

“…The free vibration analysis of such beams has been addressed in the literature [2}4]. In the relatively simpler case when the cross-section of the beam has a single axis of symmetry, the free vibratory modes consist of bending displacements in one plane which are coupled with torsional rotation, and the bending displacements in the other plane which are de-coupled from torsion [5,6]. A high aspect ratio aircraft wing can be idealized as a bending}torsion coupled beam [7,8] for which the torsional coupling occurs only in one of the principal planes of bending.…”

Dynamic Analysis of Bridge Girders Under Moving Loads Considering Warping Effects: Numerical and Analytical Beam Models

“…Since, for a physical problem, the coefficients a, b, c and d are always positive reals, being c less than one, it is possible to show, [10] that all eight roots of the polynomial (19) are…”

Numerical solution for solving special eighth-order linear boundary value problems using Legendre Galerkin method

“…Equations for the equilibrium in terms of components for an orthotropic thin circular cylindrical shell subjected to a load that is symmetric about the shell result in an eighth-order differential equations as shown by Paliwal and Pande [7]. Bishop et al [8] showed that an eighth-order differential equation arises in torsional vibration of uniform beams. Existence and uniqueness of solutions of 2n-th order boundary value problems are discussed by Agarwal [9,10].…”