Engineering structures may be subjected to various vibration sources in service.However,current computational methods have not adequately captured the coupling effects between responses under multiple vibration sources.To address this issue,this study proposed to treat the uncertain vibration sources in practical engineering as stochastic processes and introduces the CQC method,which can accurately consider the coupling responses.Based on the complex mode superposition method and random vibration theory,a generalized CQC method that simultaneously accounts for multiple vibration sources and non-proportional damping structures was proposed,namely,the multi-input complex mode CQC method.Three forms of the formula were provided,including power spectral moment,covariance and matrix multiplication.Theoretical derivation and numerical examples demonstrate that the new approach exhibits broader applicability compared to traditional CQC series methods.The proposed method can also degenerate into the conventional CCQC and CQC methods for scenarios of synchronous inputs or proportional damping.For structures with different degrees of non-proportional damping,the multi-input complex mode CQC method achieves high accuracy and stability.As the degree of non-proportional damping increases,the real mode-based forced decoupling CQC method fails to reflect the true vibrational characteristics of structures,leading to a significant underestimation of responses under multiple excitation sources.
维普
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