Influence of axial loads on the dynamic behavior of free-free beams

Abstract

Beam models are used widely in different areas of engineering to idealize a variety of structures. The rapid advancement of manufacturing technologies and the increase in computer processing capability allow these structures to be highly optimized in order to reduce weight and increase their load bearing capability. As a result, the dynamic behavior of these structures can be highly complex. The work presented here examines the lateral vibration of a free-free beam subjected to an axial preload. 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 the buckling parameter must considered. To understand this phenomenon, two analytical approaches are applied to the case of a free-free beam subject to an axial load: an analytical model formulated from the Euler-Bernoulli beam theory and a numerical model based on the finite element method as implemented through a commercial software. The first mode vibration frequencies of the two models were compared under varying axial compressive loads.