Seismic Response Analysis of Nuclear Safety-related DCS Cabinet Based on Nonlinear Simplified Beam Element

To enable rapid and accurate seismic response evaluation of nuclear safety-related digital control system (DCS) cabinets in nuclear power plants, this paper proposes a modeling and analysis method based on nonlinear simplified beam elements. Taking the main control cabinet of a DCS platform as the research object, the dynamic characteristics were first obtained through shaking table tests under white noise excitation. The test results show that the first-order natural frequencies in the lateral and longitudinal are 11.5 Hz and 31.33 Hz, respectively, while the vertical fundamental frequency exceeds 60 Hz due to the cantilever beam characteristics and boundary constraints. Based on the experimental data, an Euler-Bernoulli beam element model was established, in which a Duffing-type nonlinear term was introduced into the restoring force to characterize the stiffness softening behavior observed under strong seismic excitations. Modal analysis verifies the dominance of the first vibration mode, which provides the physical basis for nonlinear modal decoupling. Using the linear modal matrix, the nonlinear equations of motion were approximately decoupled, and the system was reduced to an equivalent single-degree-of-freedom Duffing equation. Numerical simulations show that the acceleration time histories obtained from the simplified model agree well with the experimental results, with peak acceleration relative errors at all measurement points within 4%. Further analysis reveals that the acceleration response of the cabinet exhibits a pronounced nonlinear amplification trend along the height direction. The root mean square (RMS) values of acceleration at different heights were fitted with a quadratic polynomial, yielding a coefficient of determination R² of 0.9985, and the top-level RMS exceeds three times that at the bottom. Time-frequency analysis based on wavelet transform indicates that the vibration energy is mainly concentrated in the 10-15 Hz frequency band, which closely matches the first-order natural frequency of 11.26 Hz obtained from the simplified model, confirming the first-mode-dominated response characteristic. The proposed model combines high accuracy with computational efficiency, making it suitable for rapid seismic performance evaluation, margin analysis, and preliminary seismic design of DCS cabinets. Limitations of the current model are also discussed: under strong nonlinear excitations or seismic inputs with significant high-frequency components, the second-order mode may contribute to the top-level response. Future research will focus on developing a reduced-order model incorporating the coupling effects of the first two modes to extend applicability to a wider range of ground motion conditions. This study provides a practical and efficient analytical tool for seismic design and qualification of nuclear safety-related instrumentation and control equipment.