The paper is divided in two parts. In the first part the effects of structural damage and the complexity level of modal shapes are related together. This helps to introduce damage indices based on several measures of the imaginary content of the complex modal shapes. In the second part a method for the quick and robust identification of complex modal shapes according to conventional tests performed in civil engineering structures is introduced and discussed.

In particular, it is assumed that the structural damage yields changes in the structural matrices (stiffness and/or damping). It is known that these changes involve modifications of the system dynamics in terms of modal quantities. These later exhibit increasing complexity features with increasing damage. This is particularly true for modal shapes that are used to construct indices for damage detection. Four indices proposed in the literature and one new index are compared and their effectiveness is evaluated using theoretical solutions of selected examples. It is found that all indices show a monotonic variation vs. damage and that the new index is more sensitive to changes due to damage.

In order to identify the modal shapes the complex plane representation (CPR) method formerly developed by the authors is used. The CPR method is based on the mapping of the structural vibrations in the complex plane. The mapping operator is provided by the Hilbert transform. The CPR method applies in stationary conditions. When sweep tests are involved, errors are introduced. It is shown by the help of the Bedrossian theorem that the errors are negligible in practical conditions. The case of noise corrupted signals is treated as well and criteria to circumvent the problem are given.

A simulation of field conditions is provided. The CPR method is used to derive the operational complex modal shapes from pseudo-experimental data. The test case is the same as that previously referred for theoretical conditions. The comparison of the proposed damage index between theoretical and pseudo-experimental data shows the reliability and robustness of the CPR method.

The results obtained for the selected test cases are encouraging.

Nevertheless a systematic investigation campaign should be carried out to check the performance of the method in limit conditions.

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