Structural response reconstruction based on the modal superposition method in the presence of closely spaced modes

• Reconstruct structural response in the presence of closely spaced modes.
• Reconstruct structural response with both stochastic and periodic excitation.
• The proposed methods have good performance under relatively high noise levels.
• The proposed methods have the capability of handling high damping ratio case.

An approach for structural response reconstruction based on the modal superposition method in the presence of closely spaced modes is proposed in this paper. In this method, the entire mode-set of a structure is divided into closely spaced modes and the rest of the modes. The rest of the modal responses whose response is known will be separated into individual modal response by using the empirical mode decomposition method with intermittency criteria. Starting from the mode shapes, derived from these modal responses, the rest of the modal responses at the unavailable locations can be acquired. Furthermore, the contribution of the closely spaced modal responses at the unavailable locations can be obtained based on these responses. This proposed method is valid if there is no periodic excitation. However, in practice it is common that a structure might be excited by transient, stochastic, periodic forces or a combination thereof, i.e. hybrid excitations. A hybrid approach for solving the reconstruction problem of hybrid excitations is also developed, which is based on the proposed method and transmissibility concept in response reconstruction. Numerical studies are conducted and compared with theoretical predictions for validation. Effects of background noise level, high damping ratio and multiple forces are investigated in detail.