Generalized-order perturbation with explicit coefficient for damage detection of modular beam

A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed. In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile, for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster to the termination criterion.