Residual Vector Method in Dynamic Analysis of Nuclear Components

Abstract

This paper presents the residual vector method that is employed for improving the accuracy of transient or harmonic multi-degree of freedom dynamic analyses based on the mode-superposition method. In the transient analyses of mechanical systems it is often difficult, for a variety of reasons, to determine the number of natural frequencies that have to be extracted in the initial phase of the dynamic calculation that is the modal analysis. The natural modes of vibration in the higher frequency range are often neglected in order to improve the computational efficiency. The error due to this truncation of the frequency range, and the corresponding mass that depending on the mechanical system configuration may be ignored, can move the accuracy of the computational solution outside the acceptable levels. Typical examples include nuclear piping systems with non-linearities and non-uniform distributions of stiffness, and structures with heavily damped components such as those with viscoelastic layers. In this context, the number of natural frequencies extracted and the resulting accuracy of the computational analysis is dependent on both the spatial characteristic and the frequency content of the forcing function. Forcing functions characterized by impact or shock loading are noted to excite high frequency modes; although these loading conditions are a specific group of applications in which the residual vector method can be employed, they are not within the scope of this paper which instead focuses on the method that can be used when performing analyses involving arbitrarily chosen harmonic and transient loadings. The residual vector method improves the accuracy of the mode-superposition type of dynamic calculation by the application of orthogonalized residual vectors that account for the higher frequency modes not used in the initial solution. Numerical examples are employed to demonstrate the accuracy and the efficiency of this method applied for both harmonic and transient mode superposition calculations.