An investigation into the significance of the non-linear terms in the equations of motion for a cantilevered beam

Abstract

Non-linear beam models can provide accurate and efficient results and are therefore used frequently in the structural dynamic analysis of large-aspect-ratio cantilevered structures. Using a beam model is especially beneficial in aeroelastic applications, which are computationally expensive. This paper investigates the significance of each of the non-linear terms in a third-order non-linear beam model and shows the importance of retaining terms up to the third order. The approach presented in this paper provides an effective method to simplify the non-linear equations of motion by including the most significant non-linear terms. The resulting equations preserve the fidelity of the original equations and are easier to manipulate.