Theoretical and Experimental Free Vibration Analysis of a Loaded Curved Beam With Moving Boundaries

Abstract

The present article theoretically and experimentally investigates free vibration characteristics of generalized curved beams with moving boundaries. The dynamic behavior is characterized about deformed configuration, attained under different concentrated loads, and rigidly connected to the midpoint of the beam. The coupled static and dynamic analysis of the geometric nonlinear problem is decomposed into two parts: the static problem dealing with large deformed configuration and the dynamic problem dealing with small amplitude free vibration of the deformed configuration beam. The analysis is carried out incrementally in embedded curvilinear coordinate frames using variational principle. The governing equation of the static problem is derived for a combined effect of bending and center line extension. The governing equation for free vibration is derived at the particular configuration of the updated beam geometry, using Hamilton's principle. The comparison between the numerical and experimental results successfully validates the proposed semi-analytical model and leads toward some meaningful observations.