“…By neglecting the higher modes of vibration, a set of modes of vibration can be selected, where s (≪ N d ) denotes the number of total selected effective modal shapes. The effective mode set can be selected by calculating the contribution coefficient of each mode to the total structural responses, and the details can be found in the study of Hu et al The selected modal set can be expressed as Because of the orthogonality of modal shapes and the proportional damping assumption, Φ T M Φ = I ∈ ℜ s × s , Φ T K Φ = Ω 2 ∈ ℜ s × s , and Φ T C Φ = 2 ΞΩ ∈ ℜ s × s . Thus, the second‐order dynamic equation expressed in the modal coordinate can be obtained as where Ξ ∈ ℜ s × s is the damping ratio matrix and Ω ∈ ℜ s × s is the modal frequency matrix.…”