Linearised Dynamic Analysis of Bimodular Beams - H. Kurdi, Nahidh (Anbar Journal of Engineering Sciences, 2012)
Linearised dynamic analysis of beams subjected to lateral forces and composed of materials which have different moduli in tension and compression is presented. The position of the neutral surface was rendered independent of the spatial and temporal coordinates by introducing a special assumption which reduced the coupled nonlinear problem of the flexure of such a beam into a linear one. The actual position then became a function of section geometry and the two elastic moduli and was determined by the equivalent section method. The elemental dynamic stiffness matrix was derived using the exact displacement shape functions governed by the governing partial differential equation and the structural stiffness matrix was assembled according to the usual assembling methodology of structural analysis. Symbolic and numerical examples were solved to show the applicability and efficacy of the proposed method.