Some significant improvements for interval process model and non-random vibration analysis method

Abstract Recently the authors proposed the interval process model for dynamic uncertainty quantification and based on this further developed a kind of non-probabilistic analysis method called ‘non-random vibration analysis method’ to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to become an effective supplement to the traditional random vibration theory. In this paper, some significant improvements are made for the interval process model and the non-random vibration analysis method, making them not only more rigorous in theory but also more practical in engineering. Firstly, the definitions and relevant conceptions of interval process model are further standardized and improved, and in addition some new conceptions such as the interval process vector and the cross-covariance function matrix are complemented. Secondly, this paper proposes the important conceptions of limit and continuity of interval process, based on which the differential and integral of interval process are defined. Thirdly, the analytic formulation of dynamic response bounds is deduced for both of the linear single degree of freedom (SDOF) vibration system and the multiple degree of freedom (MDOF) vibration system, providing an important theoretical basis for non-random vibration analysis. Fourthly, this paper also gives the formulation and corresponding numerical methods of structural dynamic response bounds based on finite element method (FEM) for complex continuum problems, effectively enhancing the applicability of non-random vibration analysis in engineering. Finally, four numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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