Low-frequency mode transition in the free in-plane vibration of curved beams

The low-frequency mode transition in the free in-plane vibration of beams with varying curvature and cross-section is examined by using perturbation analysis. A simplified zeroth order equation for beam vibration in the region of the mode transition is derived. This equation shows explicitly which modes undergo a transition for a particular type of beam curvature and cross-section. Analytic approximations for frequency and mode shape are derived by the cases of beam curvature represented by symmetric and antisymmetric polynomials and their validity is illustrated by comparison with numerical solutions. Many features of mode transition phenomenon are revealed analytically, including the effect of beam curvature on mode shape during the transition stage. The similarities and distinctions between the low mode and the high mode number transitions are discussed. (C) 1999 Academic Press.