Model complexity of a cantilever beam: An energy-based approach

Abstract

The cantilever beam is a component widely used in numerous engineering systems with its geometric and material properties varying depending on the application. Calculating the dynamic behavior of a cantilever beam is a challenging task since the critical physical phenomena and interactions vary significantly based on the geometry of the beam. There exist a number of theories/models that can be used to predict the transverse motion of a cantilever beam of which the two most commonly used are the Timoshenko and Euler-Bernoulli theories. The Euler-Bernoulli theory is simpler and thus preferred, however, depending on the beam's parameters and operating conditions this model can lead to erroneous results and thus the more complex Timoshenko theory must be used. Currently, selecting the theory to use depends on heuristics or rules that are based on experience and the accuracy requirements of the predictions. It is the purpose of this paper to address the model complexity of a cantilever beam through a systematic modeling methodology. The paper presents a new approach for selecting the appropriate theory to use in modeling a cantilever beam. The beam is discretized through the finite segment approach and modeled using the bond graph formulation. The previously developed activity metric is then used to determine which of the inertial and stiffness effects, of the more complex Timoshenko theory, need to be included in the model in order to have accurate predictions of its dynamic behavior. An illustrative example is provided to demonstrate the new methodology.