Numerical Study and Experimental Validation of a Method for Model Updating of Boundary Conditions in Beams

The study of vibrations in beams has been largely addressed by authors and researchers. However, relatively few researchers have considered the case of unknown boundary conditions, as usually it is reasonable to assume the classical cases such as simply supported, clamped or free. Indeed, there are a wide variety of boundary-condition configurations, each one representing a whole different problem with its own modal characteristics. A method for updating experimental beam models to specifically address the issue of unknown boundary conditions is proposed; this methodology takes advantage of vector comparison techniques such as the modal assurance criterion based on the Cauchy-Schwartz inequality to determine the degree of linear relationship between two mode shapes systematically and iteratively until an acceptable parametric match is found. This paper includes the phases of numerical study and experimental validation. A brief introduction with some relevant previous publications is presented, before explaining the methodology derivations and considerations in the numerical study section. A section devoted to demonstrate the methodology with an experimental example is presented in the Experimental validation section, and finally some conclusions and future work.