Influence of axial compressive loads on the dynamic behaviour of beams
Beam models are used widely in different areas of engineering to idealise a variety of structures, from power transmission cables to aircraft wings and turbine blades. The rapid advancement of manufacturing technologies and the increase in computer processing capability allow these structures to be highly optimised in order to reduce weight and increase their load bearing capability. As a result, the dynamic behaviour of these structures can be highly complex, and advanced mathematical modelling techniques and numerical simulations are required to understand it. The work presented here examines the lateral vibration of a simple beam subjected to an axial pre-load. Like a guitar string, the presence of a tensile load means the beam vibrates with a higher natural frequency while the opposite is true for a compressive load. Unlike the tensile case, which is limited only by the capability of the beam material to operate within its elastic regime, a compressive loading means we must consider the buckling parameter that comprises cross-sectional geometry and stiffness. To understand this phenomenon, three analytical approaches are applied to the case of a simple beam subject to an axial load and lateral excitation: (1) an analytical model formulated from the Euler-Bernoulli beam theory; (2) a numerical model based on the finite element method as implemented through the Ansys software; (3) an experimental arrangement comprising of a beam loaded compressively along its principal axis and excited laterally. The frequencies and vibration modes of the three models were compared with respect to various axial compressive loads up to and beyond the Euler buckling load.