Quantitative NDE Technique for Assessing Damages in Beam Structures

A physical model using a massless rotational spring to represent the crack‐induced local flexibility is adopted as a basis for developing a quantitative nondestructive evaluation (NDE) technique for assessing the damage in a beam structure. Expressions relating changes in eigenfrequencies of the structure and the quantitative damage index Se are formulated via an influence matrix h. The coefficients in the h matrix can be determined from the knowledge of the modal shapes of the undamaged structure. The damage index matrix Se can be solved by the resulting system of linear algebraic equations using the measured eigenfrequencies of existing structure. Methods of solution for the system of equations are discussed along with special cases where a pseudo‐inverse technique is necessary to solve the system of equations. Series of case studies involving simply supported, cantilevered, and continuous beams are presented to demonstrate the validity of the formulation.