Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

A Probabilistic Approach for the Assessment of LOC Events in Steel Storage Tanks Under Seismic Loading

The damage states in a storage tank subjected to seismic loading can induce loss of containment (LOC) with possible consequences (fire, explosion, etc..) both for the surrounding units and people. This aspect is particularly crucial for the Quantitative Risk Analysis (QRA) of industrial plants subjected to earthquakes. Classical QRA methodologies are based on standard LOC conditions whose frequency of occurrence is mainly related to technological accident rather than natural events and are thus useless. Therefore, it is evident the necessity of establishing new procedures for the evaluation of the frequencies of occurrence of LOC events in storage tanks when subjected to an earthquake. Consequently, in this work a simple procedure founded on a probabilistic linear regression-based model is proposed, which uses simplified numerical models typically adopted for the seismic response of above ground storage tanks. Based on a set of predetermined LOC events (e.g. damage in the pipes, damage in the nozzles, etc..), whose probabilistic relationship with the local response (stress level, etc..) derives from experimental tests, the probabilistic relationship of selected response parameters with the seismic intensity measure (IM) is established. As result, for each LOC event, the cloud analysis method is used to derive the related fragility curve.

Pipe Ovalization Prediction for the Pipe-Laying Ocean System

This contribution brings a new insight into pipe cross section ovalisation due to plastic deformation during pipe-lying process to the seabed. Firstly, the influence of material model calibration on ovalization prediction is presented on pure bending case including the Prager model, the Chaboche model and the modified Abdel-Karim–Ohno model. The mechanism responsible for cross section ovalisation was identified as the phenomenon of the accumulation of plastic deformation, the so-called ratcheting. The next part of this contribution presents main results of the pipe-laying process simulation. The pipe cross-section behavior during passing the considered pipe-laying system is studied in detail. A macro based solution makes possible to do a parametric study and to easily apply the offshore standard DNV-OS-F101 in technical practice.

On Categorization of Seismic Load As Primary or Secondary for Piping Systems With Hardening Capacity

The concept of primary/secondary categorization is first reviewed and generalized for its application to a non-linear oscillator subjected to a seismic load. Categorizing the seismic load requires calculating the input level associated with the oscillator ultimate capacity and comparing it to the level associated with the plastic yield. To resolve this problem, it is assumed that the non-linear oscillator behaves like a linear equivalent oscillator, with an effective stiffness (or frequency) and an effective damping. However, as it is not a priori possible to predict the equivalent stiffness and damping, a wide range of possibilities is systematically considered. The input motion is represented by its conventional response spectrum. It turns out that key parameters for categorization are i) the “effective stiffness factor” (varying from 0 for perfect damage behaviour to 1 for elastic-perfectly plastic) and the slope of the response spectrum in the vicinity of the natural frequency of the oscillator. Effective damping and spectrum sensitivity to damping play a second order role. A formula is presented that enables the calculation of the primary part of a seismically induced stress as a function of both the oscillator and input spectrum features. The formula is also presented in the form of a diagram. This paper follows-up on a similar paper presented by the author at the PVP 2017 Conference [1]. The new development introduced here is that the oscillator exhibits hardening capacity, while no hardening was assumed in [1]. It appears that the conclusions are slightly modified but the trend is very similar to the non-hardening case. Regarding piping systems, it appears that even when experiencing large plastic strains under beyond design input motions, their observed effective frequency is very close to their natural frequency, decreasing only by a few percents (experimental data from USA, Japan and India are processed). These observations lead to the conclusion that the seismic load, or the seismically induced inertial seismic strains, should basically be regarded as secondary.

Estimation Accuracy of Absolute Maximum Elasto-Plastic Displacements of MDOF Oscillators Based on a Modal Combination Rule With Post-Yielding Modal Properties and Linear Response Spectrum Values

Taniguchi, et al. [1] developed an analytical method for evaluating the absolute maximum elasto-plastic displacements of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. Its essence is that 1) modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded, 2) assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate the absolute maximum elasto-plastic displacement of each mode, 3) the absolute maximum elasto-plastic displacement of the MDOF oscillator is evaluated by the Square Root of Sum of Squares rule (SRSS-rule) by combining the maximum elasto-plastic displacement of each mode approximated by the proposed equivalently linearized system. This study first provides small modification in the equivalently linearized system. Then, employing a couple of MDOF oscillators whose spring at arbitrary storey may yield and an accelerogram, the maximum elasto-plastic displacement of the MDOF oscillator is calculated by the proposed method and is compared with that computed by the time history analysis. Their comparison suggests that the proposed method can reasonably evaluate the absolute maximum elasto-plastic displacement of the MDOF oscillator subjected to earthquake excitation as the conventional SRSS-rule does that for the linear MDOF oscillators.

Seismic Response of a Cylindrical Water Storage Tank of Nuclear Power Plant

It is important in the confirmation of the safety of the nuclear power plant to clarify the response behavior of a vertical cylindrical water storage tank under seismic motion. When a vertical cylindrical tank is shaken by a large earthquake, deformation of side shell due to the elephant foot buckling, the oval vibration etc. may occur. The occurrence of those deformations depends on materials, shapes, stored water level and time history of seismic motion. Then, response behavior was obtained for a condensate storage tank (CST) model under large seismic motion such as standard earthquake Ss multiplied by 2 with the elastic-plastic finite element calculation. In this calculation, dynamic water pressure and elastic-plastic characteristics of the material were taken into account. In this case, the elephant foot bulge did not occur but the oval vibration of side shell became dominant. Based on the result, we estimated the structural integrity of the tank.

Verification of Mainframe Computer Structure Finite Element Model Under Vibration and Seismic Tests

Shorter development design schedules and increasingly dense product designs create difficult challenges in predicting structural performance of a mainframe computer’s structure. To meet certain certification benchmarks such as the Telcordia Technologies Generic Requirements GR-63-CORE seismic zone 4 test profile, a physical test is conducted. This test will occur at an external location at the end of design cycle on a fully functional and loaded mainframe system. The ability to accurately predict the structural performance of a mainframe computer early in the design cycle is critical in shortening its development time. This paper discusses an improved method to verify the finite element analysis results predicting the performance of the mainframe computer’s structure long before the physical test is conducted. Sine sweep and random vibration tests were conducted on the frame structure but due to a limitation of the in-house test capability, only a lightly loaded structure can be tested. Evaluating a structure’s modal stiffness is key to achieving good correlation between a finite element (FE) model and the physical system. This is typically achieved by running an implicit modal analysis in a finite element solver and comparing it to the peak frequencies obtained during physical testing using a sine sweep input. However, a linear, implicit analysis has its limitations. Namely, the inability to assess the internal, nonlinear contact between parts. Thus, a linear implicit analysis may be a good approximation for a single body but not accurate when examining an assembly of bodies where the interaction (nonlinear contact) between the bodies is of significance. In the case of a nonlinear assembly of bodies, one cannot effectively correlate between the test and a linear, implicit finite element model. This paper explores a nonlinear, explicit analysis method of evaluating a structure’s modal stiffness by subjecting the finite element model to a vibration waveform and thereafter post processing its resultant acceleration using Fast Fourier Transformation (FFT) to derive the peak frequencies. This result, which takes into account the nonlinear internal contact between the various parts of the assembly, is in line with the way physical test values are obtained. This is an improved method of verification for comparing sine sweep test data and finite element analysis results. The final verification of the finite element model will be a successful physical seismic test. The tests involve extensive sequential, uniaxial earthquake testing in both raised floor and non-raised floor environments in all three directions. Time domain acceleration at the top of the frame structure will be recorded and compared to the finite element model. Matching the frequency content of these accelerations will be proof of the accuracy of the finite element model. Comparative analysis of the physical test and the modeling results will be used to refine the mainframe’s structural elements for improved dynamic response in the final physical certification test.

Vibration Reduction Mechanism and NPPs Seismic Safety of TMD Shield Building for AP1000 NPPs

Without additional mass, the tuned mass damping (TMD) shield building for AP1000 Nuclear Power Plants (NPPs) was achieved easily by changing the stiffness and damper between parts of shield building. Meanwhile, the new TMD structure combined the structural features of the shield building with TMD technology. The optimal model for the new structure was built and the optimal stiffness and damper of TMD bearing were given on the dynamic characters of the shield building and its parts. The vibration mitigation mechanism and reduction effect were clearly stated by using base shear force transfer function. By comparing with the seismic responses of the traditional model and the base isolation model, the influence factors of the new TMD structure, such as the mechanism of TMD bearing, the gravity liquid tank mass, and the earthquake waves under different sites were studied. The new TMD structure is tested to satisfy the NPPs seismic safety requirements, stable reduction efficiency, anti-seismic robust characteristics and adaptive site.

Appropriate Damping on Seismic Design Analysis for Inelastic Response Assessment of Piping

The current seismic design rule on piping assumes elastic analysis without the effect of response reduction due to plasticity, although some degree of plasticity is allowed in its allowable limits. Damping for the seismic design analysis is conservatively determined depending on the number of supports and thermal insulation conditions. These conservative assumptions lead to large amount of design margin. Based on such recognition, to provide a more rational seismic design method, a new Code Case for seismic design of piping is now under development in the framework of JSME Nuclear Codes and Standards as an alternative rule to the current design rule. The Code Case provides detailed inelastic analysis with using shell or solid FEA models as a more rational method. Simplified analysis with an additional damping taking the response reduction due to plasticity into account is now under consideration to incorporate the convenience in design. In this study, a series of analysis was made to see the adequacy of the simplified inelastic analysis. Design margins contained in the current design analysis method composed of response spectrum analysis and stress factors was quantitatively assessed in the view point of additional damping.

Verification of the Relation Between the Directions of Control Force and Responses in Active Seismic Isolation Device

In this research, the focus is on the energy problem in active vibration control of a seismic isolation device using self-powered active control that regenerates electric power from kinetic energy of vibration system and uses it as control power. In recent years, it is proposed to install semi-active control or active control in an isolated structure to deal with seismic waves of various periods. However, since energy is required for control, there is a problem that the desired response reduction performance cannot be achieved when energy supply is interrupted at the time of a power outage. In our previous device, power is always given to the motor to control, thus power consumption is high. Therefore, the purpose of this research is to propose input method of control force that can reduce control power while keeping base isolation performance by classifying the role of the control force for each control phase and considering various combinations of input control force.