ASYMPTOTIC ANALYSIS OF THE FREE INPLANE VIBRATIONS OF BEAMS WITH ARBITRARILY VARYING CURVATURE AND CROSS-SECTION

An asymptotic analysis is carried out for the equations of free vibrat ions 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. Th e analysis of the properties of the asymptotic solution explains the p henomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams. The as ymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are difficult to analyse by other means. The asymptotic behaviour of the solution i s illustrated numerically for different types of curvature including a ntisymmetric curvature. An experimental verification of the asymptotic behaviour of mode frequencies is presented. (C) 1996 Academic Press L imited