Jeffry N. Sundermeyer
Richard L. Weaver
Dept. of Theor. and Appl. Mech., Univ. of Illinois, 104 S. Wright St., Urbana, IL 61801
The weakly nonlinear character of a cracked vibrating beam is exploited for the purpose of determining crack location, depth, and opening load. The approach is motivated by examining the response of a bilinear spring-mass system to excitation at two frequencies, such that the difference between the two frequencies is the resonant frequency of the system. The numerically generated steady-state response of the system clearly betrays the presence of the bilinear spring, even if the difference between the compressive and tensile stiffness is very small. The same idea is applied to a cracked beam forced at two frequencies, with the crack providing a local bilinear stiffness in the beam. The numerically generated steady-state response shows the effect of the opening and closing of the crack. The prominence of this nonlinear effect is then correlated with crack position and depth. It is shown that the nonlinear effect is maximized if a static load is also placed on the beam that would cause the crack to be on the verge of opening, thus determining the opening load. A perturbation analysis is applied to the problem, and some preliminary experimental results are discussed. [Work supported by the Army Research Office.]