前川 晃

Abstract This paper proposes an improved contactless measurement method for vibration stress of piping systems, by which the measurement time is shorter and the measuring works are more simple. The proposed method includes two processes, in which the bending mode shape of piping vibration is identified by a transmission-type light emitting diode (LED) displacement sensor and the vibration stress is calculated based on beam theory using the approximated curve of the bending mode shape. The proposed method uses one advanced LED displacement sensor to measure the vibration stress in contrast to multiple conventional LED sensors, which must be used in the previous method developed by the authors. Therefore, the measuring system could be reduced in size and a light-weight and portable measurement instrument was developed. The measurement accuracy and reliability of the new method were validated by the vibration experiment using a mockup piping system.

The purpose of this study is to verify the applicability of the proposed noncontact measurement method of vibration stress using multiple laser displacement sensors. In order to demonstrate its applicability, the factors that influence the measurement accuracy were investigated. Since the proposed method has a simple measurement theory and few restrictions on measurement conditions, it can be applied to vibration measurement of various beam-shaped structures such as pipes. However, in actual vibration measurement, it is expected that an inherent error will occur due to the basic principle of the proposed method. Identification and quantitative evaluation of the influential factors that cause the error are important basic findings for determining the practical application of the proposed method. First, based on the basic principle of the proposed method, the influential factors that can occur due to the use of the laser displacement sensor were clarified. Second, the errors caused by the identified influential factors were quantitatively evaluated. Third, a vibration test was performed to verify the identified influential factors and the errors caused by those factors. Finally, from the obtained results, the applicability of the proposed method was demonstrated, and measures for further improving the accuracy were suggested.

This study presents the response mitigation effect of piping systems by inelastic seismic design based on elastic-plastic property of steel pipe supports. The inelastic seismic design to control vibration by absorbing energy using elastic-plastic properties of materials can be one of useful ideas. The design idea to use the elastic-plastic behavior of pipe supports is addressed in Technical Code for Seismic Design of Nuclear Power Plants (JEAC4601) published by the Japan Electric Association in Japan. Here, the component named an elastic-plastic pipe support is proposed as an energy-absorbing element. However, in order to put the inelastic seismic design using the elastic-plastic pipe supports into practical use, it is necessary to accumulate more findings related to the seismic response and the application range. This study aims to investigate the applicability of the inelastic seismic design taking the elastic-plastic pipe supports in the piping systems and to increase the basic findings. In this study, the seismic response analysis using three-dimensional piping system with an elastic-plastic pipe support was conducted. As a result, it was found that the elastic-plastic pipe support affected the seismic response largely. Additionally, the vibration characteristics, the response acceleration, and the load generated in the piping system were discussed relating to the plastic deformation and the plasticity rate of the elastic-plastic pipe support.

This study describes inelastic seismic design of piping systems considering the damping effect caused by elastic-plastic property of a pipe support which is called an elastic-plastic support. Though the elastic-plastic support is proposed as inelastic seismic design framework in the Japan Electric Association code for the seismic design of nuclear power plants (JEAC4601), the seismic responses of the various piping systems with the support are unclear. In this study, the damping coefficient of a piping system is focused on, and the relation between seismic response of the piping system and elastic-plastic behavior of the elastic-plastic support was investigated using nonlinear time history analysis and complex eigenvalue analysis. The analysis results showed that the maximum seismic response acceleration of the piping system decreased largely in the area surrounded by pipe elbows including the elastic-plastic support which allowed plastic deformation. The modal damping coefficient increased a maximum of about sevenfold. Furthermore, the amount of the initial stiffness of the elastic-plastic support made a difference in the increasing tendency of the modal damping coefficient. From the viewpoint of the support model in the inelastic seismic design, the reduction behavior for the seismic response of the piping system was little affected by the 10% variation of the secondary stiffness. These results demonstrated the elastic-plastic support is a useful inelastic seismic design of piping systems on the conditions where the design seismic load is exceeded extremely.

A software system to perform SCC crack propagation analyses for complex and realistically shaped structures consisting of dissimilar materials, such as weld metal, base metal, etc., under weld residual stresses is presented in this paper. The system consists of programs to perform automatic generation of the finite element mesh, weld residual stress mapping to the finite element model with weld residual stresses to carry out fracture analysis and finite element analysis, and evaluating the stress intensity factors and updating crack geometries for crack propagation analysis. The results of stationary crack and crack propagation analyses elucidate the influences of both the residual stress distribution and the crack geometry on the distribution of the stress intensity factors. Their influences on the crack propagation behavior are also clarified. (C) 2017 Elsevier Ltd. All rights reserved.

The vibration-induced fatigue failure of small-bore piping is one of the common causes of failure trouble at nuclear power plants (NPPs). Therefore, the purpose of this study is to develop the measurement methods of vibration-induced stress for the screening to prevent from fatigue failure mechanism of small-bore piping. First, a measurement method using a single-mass model was introduced, and then, a measurement method using a two-mass model developed as an improved calculation model was proposed. These two kinds of models were validated by vibration tests using mock-up with small-bore branch piping. The results showed that the single-mass model could be used as the coarse screening. Additionally, the two-mass model was found to be suitable to the fine screening due to more accurate measurement of vibration-induced stress. Next, for small-bore piping with typical pattern configurations consisting of several masses and supports, the model considering the supports and the center of gravity being out of pipe centerline was developed and put into practical use. Finally, for the more complex small-bore piping with general piping configurations consisting of many bends, branches, or joints, the method based on the finite element analysis and using the measured values was developed. In the developed method, the differences between the natural frequency and the response acceleration obtained by the measurement and those values calculated using the analysis model are optimized to be enough small, and then, the vibration-induced stress is estimated by superposing the vibration modes of the small-bore piping with the static deformation representing the main piping vibration. In this study, the usability of the developed method was confirmed by the comparison with the numerical results without the measurement error, which were assumed to be the true values. The peak stress induced by vibration frequently occurs at the filet weld part between the small-bore piping and the main piping. The developed methods can be used for various weld geometries although the measurement method using strain gauges cannot be used for such weld parts. The failure possibility by vibration-induced fatigue can be evaluated by comparing the nominal stress measured by the methods in this study with the fatigue threshold stress divided by the stress concentration factor appropriate for the weld geometry.

To improve design and troubleshooting techniques of piping systems for operating power plants, it is necessary to investigate, by experiment and simulation, the behavior of fluid inside the piping system in detail. This study was conducted using full-scale piping system under conditions that could seriously threaten the plant operation, by matching pressure pulsations, acoustic resonance, and piping natural frequency. Although piping vibration is reported to influence fluid pressure pulsations, there were no such examples of influence in this experiment. Knowing that the opening ratio of the pressure control valve affects the boundary condition for acoustic resonance, experiment and simulation at different opening ratios were conducted. It has been suggested that the cases in which a valve partially open at 25% or less should not be taken as a closed end. This finding conflicts with such a widespread design assumption.

This study proposes a method to measure pressure pulsations in piping systems easily and directly for their accurate evaluation of occurrence location and pressure amplitude. In the proposed method, the pulsations were estimated by combining the strain measurement result on the pipe outer surface with the calculated formula result for thick-walled cylinders. The proposed method was validated experimentally using a mock-up piping system. It was demonstrated that the method could measure the amplitudes and behavior of pressure pulsations with a practical accuracy. The factors influencing the measurement accuracy of the method were also discussed. The method is expected to contribute to more efficient plant maintenance to prevent fatigue failure of piping and plant components because the pulsations that the method measures are the main cause of vibration fatigue and acoustic noise in piping systems.

Primary water stress corrosion cracking (PWSCC) phenomenon in dissimilar metal welds is one of the safety issues in ageing pressurized water reactor (PWR) piping systems. It is well known that analysis accuracy of cracking propagation due to PWSCC depends on welding residual stress conditions. The U.S. Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute (EPRI) carried out an international round robin validation program to evaluate and quantify welding residual stress analysis accuracy and uncertainty. In this paper, participation results of the authors in the round robin program were reported. The three-dimensional (3D) analysis based on a fast weld simulation using an iterative substructure method (ISM), was shown to provide accurate results in a high-speed computation. Furthermore, the influence of different heat source models on analysis results was investigated. It was demonstrated that the residual stress and distortion calculated using the moving heat source model were more accurate.

This study presents a noncontact measurement method of vibration induced stress (vibration stress) using multiple laser displacement sensors and clarifies its applicability to piping vibration. In the beam structures such as piping, the stress due to bending deformation can be caused by vibration. In the presented method, the vibration displacement in the beam structures induced by the bending deformation is measured at three different locations using laser displacement sensors in a noncontact manner and the vibration stress is estimated by a simple calculation based on the beam theory. First, an applicability validation of the presented method was done by a vibration test using a cantilevered beam plate. This validation was done by comparing measurements by the presented method and the conventional method using strain gauges. Next, an experimental validation was conducted by the vibration test using a pipe specimen, and the applicability to the piping vibration was confirmed. (C) 2015 Elsevier Ltd. All rights reserved.

In this study, two methods to measure bending and torsional vibration stresses of piping systems conveniently and quickly are proposed. The proposed methods are composed of a modeling approach of piping vibration and noncontact measurement techniques. The methods assume the vibration modes as a primary mode within the measuring range without the mode-identification and then estimate the vibration stress by approximating the vibration displacements measured in a noncontact manner as a primary mode. This paper presents the principles and calculation formulas of both methods and shows the measurement techniques for the bending and torsional vibration stresses using laser displacement sensors. Finally the applicability of one method is discussed based on the results of a vibration experiment. (C) 2015 Elsevier Ltd. All rights reserved.

Inherent strain method was employed to measure the distribution of three dimensional welding residual stresses in several multi-pass welded joints of thick pipes and thick cladded plates. Since a function expression approach to the distribution of inherent strains was developed, the measuring efficiency for three dimensional internal welding residual stresses in complicated welded joints was improved a lot. The residual stresses measured by inherent strain method were compared with the high cost stress release method and neutron diffraction method. Furthermore, inherent deformation parameters, which are defined by integrated values of inherent strains on transverse sections, were used for the fast prediction of welding distortion in assembling structures. Based the predicted welding distortion, its mitigation methods such as tack welding and jig constraint were discussed.

An efficient and reliable numerical analysis for three-dimensional (3D) multipass welding simulation is proposed in this paper. A fast analysis method to calculate 3D residual stress distribution in the multipass welds using the iterative substructure method (ISM) was developed and validated using other numerical analysis and measurement results. First, the analysis results by the developed method were compared with those by a conventional method using a commercial finite element analysis code. The comparisons were made for the analysis accuracy and the computational speed of the residual stress analysis in a multipass welded pipe joint. Both sets of analysis results for residual stress agreed well with each other. Furthermore, it was clarified that the developed analysis method could calculate the residual stress in a shorter computing time than the conventional analysis method. Next, the residual stress of the pipe joint computed by the developed analysis method was compared with measurement results obtained using the strain gauge method, and the good analysis accuracy was shown. Consequently, these comparisons demonstrated that the developed method for multipass welding simulation based on the ISM could calculate the residual stress distribution much faster at high analysis accuracy even when the size of the welding problems, such as for multipass welding, was large.

There have been many reports of fatigue failures of small-bore piping systems such as drain piping, vent piping and instrumentation piping in nuclear power plants that arise from vibration sources such as pumps. To prevent the failures, integrity evaluation of piping is conducted by measuring and analyzing vibration stress in the piping. But, a more efficient and economical measurement method is desirable to evaluate the vibration fatigue in small-bore piping. In this study, a non-contacting measurement method was proposed that is based on optical displacement sensors using light emission diodes (LEDs) to measure the vibration stress. The applicability of the method was discussed based on the vibration experiments using pipe elements and a mock-up piping system. From the experimental results, the proposed method was clarified to be sufficiently applicable and practically useful for the vibration measurement and stress evaluation in small-bore piping systems. (C) 2015 Elsevier Ltd. All rights reserved.

In nuclear power plants, vibration stress of piping is frequently measured to prevent the occurrence of fatigue failure. A simpler and more efficient measurement method is desired for rapid integrity evaluation of piping. In this study, a method to measure vibration stress in a noncontact manner using optical displacement sensors is presented and validated. The proposed method estimates vibration-induced stress of small-bore piping directly using noncontact sensors based on a light-emission diode. First, the noncontact measurement method was proposed, and the measurement instrument based on the proposed method was developed for the validation. Next, vibration measurement experiments using the instrument were conducted for a mock-up piping system and an actual piping system. The measurement results were compared with the values measured by the conventional method of known accuracy using strain gauges. From this comparison, the proposed noncontact measurement method was demonstrated to be able to provide sufficient accuracy for practical use.

An iterative substructure method has been proposed as a technique to calculate thermal elastic plastic problems quickly and efficiently. Based on the iterative substructure method, an analysis code for the multipass welding was developed so as to realize accurate residual stress computation using a 3D precise model within a practical time. In the present study, the fast computation performance of the iterative substructure method was considered as a means to improve the original code. Then analysis accuracy and speed of the improved code were investigated. The proper analysis accuracy of the improved code was demonstrated by comparing with residual stress measurements of a multipass butt-welded pipe joint. The analysis speed of the improved code was clarified to be faster than a well-known commercial code in comparison between their computation times. (C) 2014 Elsevier B.V. All rights reserved.

The present paper proposes an efficient contactless measurement method for vibration stress of piping systems, by which the measurement tasks are performed within an extremely short time and the measured stress can be evaluated immediately after the measurement. The proposed method includes two processes, in which the bending shape of a pipe induced by vibration response is identified by a transmission type optical displacement sensor and the vibration stress is calculated based on beam theory using the curvature radius estimated by approximating the bending shape. The proposed method uses only one LED-optical sensor to measure the vibration stress though multiple sensors must be used in the previous method developed by the authors. Therefore, the measuring system could be reduced in size and a light-weight and portable measurement instrument was developed. The measurement accuracy and reliability of the new method were verified by the vibration experiment using a mock-up piping system.

In nuclear power plants, vibration stress of piping is frequently evaluated to prevent fatigue failure. A simple and fast measurement method is attractive to evaluate many piping systems efficiently. In this study, a method to measure the vibration stress using optical contactless displacement sensors was proposed, the prototype instrument was developed, and the instrument practicality for the method was verified. In the proposed method, light emitting diodes (LEDs) were used as measurement sensors and the vibration stress was estimated by measuring the deformation geometry of the piping caused by oscillation, which was measured as the piping curvature radius. The method provided fast and simple vibration estimates for small-bore piping. Its verification and practicality were confirmed by vibration tests using a test pipe and mock-up piping. The stress measured by both the proposed method and an accurate conventional method using strain gauges were in agreement, and it was concluded that the proposed method could be used for actual plant piping systems.

It is necessary to establish properly reliable weld residual stress analysis methods for accurate crack initiation and growth assessment of primary water stress corrosion cracking, which may occur in nickel-based dissimilar metal welds in pressurized water reactors. The US Nuclear Regulatory Commission and the Electric Power Research Institute cooperatively conducted an international round robin for weld residual stress analysis to improve stress analysis methods and to examine the uncertainties involved in the calculated stress values. In this paper, the results from the authors' participation in the round robin were reported. In the round robin, the weld residual stress in a nickel-based dissimilar metal weld of a pressurizer surge nozzle mock-up was computed under various analysis conditions. The residual stress analysis results computed by a welding simulation code currently being developed that uses the iterative substructure method were in good agreement with the measurements. Also, the effect of safe-end length on residual stress distribution was examined as an additional discussion point.

Residual stress caused by welding processes affects characteristics of strength and fracture of equipment and piping in power plants. Numerical thermal elastic-plastic analysis is a powerful tool to evaluate weld residual stress in actual plants. However, the conventional three-dimensional precise analysis for a welding process such as multi-pass welding, machining and thermal treatment requires enormous computation time though it can provide accurate results. In this paper, the finite element analysis code based on the iterative substructure method that was developed to carry out thermal elastic-plastic analysis efficiently, with both high computational speed and accuracy, was proposed to simulate the welding process of plant equipment and piping. Furthermore, optimization of the proposed analysis code was examined and the computational efficiency and accuracy were also evaluated.

This study discussed seismic response of a piping system when the pipe support structure was deformed plastically on being subjected to a much larger seismic load than the designed one. This case is expected as one of the conditions beyond seismic design that should be analyzed. To examine the effect of elastic-plastic deformation of the pipe support structure on seismic response, the effect of various shapes and failure mode of support structures was investigated. Difference of failure modes of the pipe support structure was modeled by change of initial stiffness and secondary stiffness of the load-displacement curve in this study. Seismic response analyses were conducted by using a typical small bore piping system shaped in a three-dimensional arrangement. The investigated change of seismic response behavior generated by plastic deformation of the pipe support structure was clarified based on comparison of seismic responses by using the elastic-fully plastic model and bi-linear model with various initial stiffness and secondary stiffness values. The results showed that the secondary stiffness of the load-displacement curve of the support structure did not affect the decreasing area of the response acceleration and the amount of the decrement significantly. It was concluded that the plastic deformation behavior of the pipe support structure could be modeled by using the elastic-fully plastic model when modeling plastic deformation characteristics of the pipe support structure.

Stress-free lattice spacing d₀ has the most influence on reliability of neutron stress measurements made using an angle dispersive method. However, it is hard to evaluate the lattice spacing of welded structures and ductile materials such as stainless steel accurately. In this study, suitable measurement conditions for d₀ of welded pipe joints of austenitic stainless steel were discussed. The d₀ values derived from {311} and {111} reflections, which are often used in austenitic stainless steel for residual stress measurement, were examined. Comparison of the residual strains and stresses evaluated using the obtained d₀ and the finite element analysis showed that the way the d₀ values were chosen affected the measurement accuracy significantly. The stress measurement accuracy was remarkably improved when the {311} reflection was used and the proper d₀ value was chosen in the respective neutron diffraction measurements. For instance, for the axial diffraction measurements using the {311} reflection, it was recommended that only the axial d₀ value of the {311} reflection be used; the measurements using the {111} reflection were less accurate due to the large Young's modulus. Additionally, a lower diffraction angle was judged to be one of the factors leading to a decrease of the strain measurement accuracy.

Primary water stress corrosion cracking (PWSCC) generated in dissimilar metal welds is one of the safety issues in ageing pressurized water reactor piping systems. It is well known that analysis accuracy of cracking propagation due to PWSCC depends on welding residual stress conditions. The U.S. Nuclear Regulatory Commission carried out an international round robin program for welding residual stress analysis validation to evaluate the accuracy and uncertainty quantitatively. In this study, participation results in the round robin program were reported. The three-dimensional analysis based on a fast weld simulation, using the Iterative Substructure Method was clarified to provide accurate results in a highspeed computation. Furthermore, the influence of different heat source models on analysis results was investigated. It was demonstrated that the residual stress and distortion calculated using the moving heat source model were more accurate.

This study describes inelastic seismic design of piping systems considering the effect of plastic deformation of a pipe support structure. The damping coefficient of a piping system is focused on, and the relation between seismic response of the piping system and elastic-plastic behavior of the support structure was studied using nonlinear time history analysis and complex eigenvalue analysis. The analysis results showed that the maximum seismic response acceleration of the piping system decreased largely in the area surrounded by pipe elbows including the support structure which allowed plastic deformation. Furthermore, modal damping coefficient increased a maximum of about seven-fold. The increase ratio of the modal damping coefficient was proportional to the size of the effective mass ratio, when a relatively large increase was seen in the increase ratio of the modal damping coefficient. On the other hand, the amount of the initial stiffness of the support structure made a difference in the increasing tendency of the modal damping ratio. In the case of relatively small initial stiffness, the modal damping ratio of only one vibration mode increased. The increment of the modal damping ratio was proportional to the effective mass ratio in the case of large initial stiffness. In the viewpoint of the inelastic seismic design, the seismic response of the piping system was little affected by the plastic deformation of the support structure with 10% variation of the secondary stiffness to the initial stiffness. The result suggested that the seismic response of the piping system with, the support structure can be estimated by using only the support model which has the elastic perfectly plastic property even if there are various shapes of steel type of support structures.

In Japanese nuclear power plants, quantitative evaluation for seismic safety margin of the equipment is an important issue. In this study, the seismic safety margin of cylindrical liquid storage tanks used in nuclear power plants was investigated experimentally and analytically using test tanks with water inside. The buckling load of the tanks was examined because buckling was their dominant damage mode. The test tanks were reduced-scale models similar to the large-scale liquid storage tanks used in nuclear power plants. The experimental buckling load was compared with the design value. Furthermore, dynamic and static elastic-plastic buckling simulations by finite element analysis using a three-dimensional model were made and then the simulation results were compared with the experimental and design values. The simulated and experimental results agreed well, showing the values were the nearly-true buckling load, that is, proof stress. The design value was lower than the other values, indicating the difference was the seismic safety margin. The above results illustrated that existing actual tanks would have a bigger seismic safety margin.

An efficient and reliable method for welding residual stress analysis is reported in this paper. The analysis method to calculate the residual stress using the iterative substructure method was developed and compared with a conventional one using a commercial finite element analysis code; comparisons were made for the analysis accuracy and the computational speed of the residual stress in a welded pipe joint. The residual stress distributions obtained by the both methods agreed well with each other. Moreover, it was clarified that the developed method could calculate the residual stress in a shorter computing time and could calculate the residual stress distribution much faster with nearly the same accuracy as the conventional method when the size of the welding structure was large.

To improve condition-based maintenance (CBM) techniques for operating plants, it is necessary to investigate, by experiments and numerical simulations, on the behavior of fluid inside piping system in detail. This study was conducted using the full-scale piping system under conditions that could seriously threaten the plant operation, by matching pressure pulsation, acoustic resonance and piping natural frequency. Although piping vibration is reported to influence fluid pressure pulsation, there were few examples of such influence in the conditions of this experiment. Knowing that the opening ratio of the pressure control valve affects the boundary condition for acoustic resonance, the experiment and numerical simulation at different opening ratios were conducted. It was suggested that there are cases in which a valve partially open at 25% or less shouldn't be taken as a closed end. This finding conflicts with widespread design assumption.

Stress-free lattice spacing d₀ has the most influence on reliability of neutron stress measurements made using an angle dispersive method. However, it is hard to evaluate the lattice spacing of welded structures and ductile materials such as stainless steel accurately. In this study, suitable measurement conditions for d₀ of welded pipe joints of austenitic stainless steel were discussed. The d₀ values derived from {311} and {111} reflections, which are often used in austenitic stainless steel for residual stress measurement, were examined. Comparison of the residual strains and stresses evaluated using the obtained d₀ and the finite element analysis showed that the way the d₀ values were chosen affected the measurement accuracy significantly. The stress measurement accuracy was remarkably improved when the {311} reflection was used and the proper d₀ value was chosen in the respective neutron diffraction measurements. For instance, for the axial diffraction measurements using the {311} reflection, it was recommended that only the axial d₀ value of the {311} reflection be used; the measurements using the {111} reflection were less accurate due to the large Young's modulus. Additionally, a lower diffraction angle was judged to be one of the factors leading to a decrease of the strain measurement accuracy.

In this study, the influence of valve closing and opening operations to change inner pressure during pump operations on the pulsation boundary condition was investigated to improve the prediction accuracy of pressure pulsation. Vibration experiments were conducted by using an actual size mock-up piping system with 40 m long as found in nuclear power facilities. A drastic change in the boundary condition of the acoustic resonance by a slightly different valve opening ratio to set a different inner pressure was seen in the experimental results. The simulation results by using the method of characteristics showed that the boundary condition of the acoustic resonance changed when the valve opening ratio was changed slightly from 10 % to 15 %. This indicated that the boundary condition of the acoustic resonance had a pulsed change and changed even at the small valve opening ratio, which was approximately 15% though the design threshold value was 25 %. It was concluded that the boundary condition of the acoustic resonance was sensitive to a slight change of the valve opening ratio and this was one of the reasons why it is difficult to predict the pressure pulsation behavior including acoustic resonance accurately in actual plants.

This paper describes the results of vibration tests using a 1/10 reduced scale model of large-scale cylindrical water storage tanks to clarify their dynamic behavior under seismic excitation. The thin sidewall of the tanks is not so rigid that the vibration modes (sloshing and bulging) induced by earthquake can affect the distribution of their liquid pressure and seismic load. It is, therefore, important for the seismic design of water storage tanks to consider such elastic deformation theoretically and experimentally. In this study, vibration tests by shaking table are conducted using a reduced scale tank model partially filled with water to investigate the dynamic fluid pressure behavior and seismic-proof safety of the tanks. A small sinusoidal excitation test, large amplitude sinusoidal excitation test and seismic excitation test are conducted. The measured values are compared with the calculated ones by some conventional seismic design methods. The results reveal that the distribution shape and magnitude of the dynamic fluid pressure are different between under positive and negative pressures and depend on the magnitude of input acceleration. Further examination concludes that the oval-type vibration, which is a high-order vibration mode, occurring on the sidewall of the tanks affects the distribution shape and magnitude of dynamic fluid pressure. However, it is demonstrated that the vibration does not act as a seismic load in the conventional evaluation of seismic-proof safety. [DOI: 10.1115/1.4001915]