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

The low-frequency mode transition in the free in-plane vibration of beams w ith varying curvature and cross-section is examined by using perturbation a nalysis. A simplified zeroth order equation for beam vibration in the regio n of the mode transition is derived. This equation shows explicitly which m odes 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 p olynomials and their validity is illustrated by comparison with numerical s olutions. Many features of mode transition phenomenon are revealed analytic ally, including the effect of beam curvature on mode shape during the trans ition stage. The similarities and distinctions between the low mode and the high mode number transitions are discussed. (C) 1999 Academic Press.