Asymptotic Analysis of The Free In-Plane Vibrations of Beams With Arbitrarily Varying Curvature And Cross-Section

Abstract

An asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross!section[ The effect of splitting the asymptotic limit for eigenvalues into two families is revealed and its connection with boundary conditions is discussed[ The analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams[ The asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are dif_cult to analyse by other means[ The asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature[ An experimental veri_cation of the asymptotic behaviour of mode frequencies is presented Show more