Coupled Flexural-Torsional Vibration of Laminated Composite Beams Subjected to Axial force and End Moment – A Layerwise Discretization

Abstract- The coupled bending–torsion vibration of layered composite beams, subjected to axial load and end moment, is investigated. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural–torsional vibrations of a slender, prismatic, linearly elastic beam, undergoing coupled linear harmonic vibration, are developed. Considering the lengthwise discretization, and using proper Dynamic (frequency-dependent) interpolation functions in conjunction with the weighted residual method, the element Dynamic Stiffness Matrices (DSM) along the length of each layer are developed. A layer-wise discretization across the thickness is also carried out, where each layer, or laminate with layers stacked at the same fibre angle, is modeled as an equivalent homogenized element. Implementing the elements matrices in a MATLAB-based code, the resulting eigenvalue problem is then solved to determine the natural frequencies and modes of illustrative prestressed beam examples, subjected to various boundary conditions, and exhibiting geometric bending-torsion coupling. The validity and effectiveness of the proposed method are verified against the frequency data obtained from an equivalent system based on overall homogenization, as well as commercial software (ANSYS®). Keywords - ,, , , ,,