Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

We address a simultaneous optimal design problem of a semi-active control law and design parameters in a vibration control device for civil structures. The Vibration Control Device (VCD) that is being developed by authors is used as the semi-active control device in the present paper. The VCD is composed of a mechanism of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang-bang type semi-active control law referred to as Inverse Lyapunov Approach is proposed as the semi-active control law. In the Inverse Lyapunov Approach the Lyapunov function is searched so that performance measures in structural vibration control are optimized in the premise of the bang-bang type semi-active control based on the Lyapunov function. The design parameters to determine the Lyapunov function and the design parameters of the VCD are optimized for the good performance of the semi-active control system. The Genetic Algorithm is employed for the optimal design.

Critical Section Selection Methodology for the U.S. EPR™ Standard Nuclear Power Plant

This paper presents a three-tier, critical section selection methodology that is used to identify critical sections for the U.S. EPR™ Standard Nuclear Power Plant (NPP). The critical section selection methodology includes three complementary approaches: qualitative, quantitative, and supplementary. These three approaches are applied to Seismic Category I structures in a complementary fashion to identify the most critical portions of the building whose structural integrity needs to be maintained for postulated design basis events and conditions. Once the design of critical sections for a particular Seismic Category I structure is complete, the design for that structure is essentially complete for safety evaluation purposes. Critical sections, taken as a whole, are analytically representative of an “essentially complete” U.S. EPR™ design; their structural design adequacy provides reasonable assurance of overall U.S. EPR™ structural design adequacy.

Analytical Solutions for the Study of Immersed Unanchored Structures Under Seismic Loading

In nuclear power plants, some structures are not anchored and lay directly on the ground. This is the case for fuel storage racks. As a safety issue, one has to evaluate precisely the behavior of this sliding structure, and in particular, the cumulated sliding displacement during a seismic event in order to prevent any impact with other components. During a seismic event, the unanchored structure can slide, rotate and tilt. The aim of this paper is to present analytical solutions to estimate the sliding amplitudes of different simplified systems which represent a given dynamic behavior. These simplified models are: a sliding mass, a sliding spring-masses system and a complex sliding structure defined by its eigenmodes. Each simplified system corresponds to a different set of assumptions made on the flexibility of the structure. Two analytical solutions are presented in this article: single sliding mass and a sliding spring-masses system. The analytical solutions are obtained considering the different phases of the movement and the continuity between each phase. The results are then compared to the values computed with the commercial Finite Element package ANSYS™. The analytical curves show a good fit of the computational results.

Probabilistic Seismic Soil Structure Interaction Analysis of the Mu¨hleberg Nuclear Power Plant Reactor and SUSAN Buildings

Probabilistic seismic soil-structure interaction (SSI) analysis was performed for the Mu¨hleberg Nuclear Power Plant Reactor and SUSAN Buildings in support of the seismic probabilistic saftety assessment of the plant. An efficient hybrid method, employing computer programs SASSI2000 and CLASSI presented in a companion paper, was used in this analysis. The method takes advantage of the capability of SASSI2000 to analyze embedded structures with irregular geometry and the computational efficiency of CLASSI to rapidly perform the SSI response analysis of large structure models. Fixed base finite element models of the buildings were first developed from which the structure geometry, nodal masses, natural frequencies, and mode shapes were extracted. The structure embedments were modeled using SASSI2000. Impedance functions and scattering vectors were calculated by imposing rigid body constraints to the embedded foundation. The fixed base structure dynamic properties and the foundation impedances and scattering functions were input to CLASSI to perform the response analysis. The probabilistic analysis was performed following the Latin Hypercube Simulation (LHS) approach documented in NUREG/CR-2015. Variables defined by probability distributions were sampled according to a stratified sampling approach. The combination of the parameters for each simulation was determined by Latin Hypercube experimental design. Variables in the LHS included the earthquake ground acceleration time histories, structure stiffness and damping, and soil stiffness and damping. Thirty response simulations were performed using CLASSI in which the variable values were randomly selected. The use of CLASSI has the advantage that the response analysis simulations can be executed in a fraction of the time that would be required with SASSI2000 alone. For each simulation, in-structure response spectra (ISRS) were calculated at selected locations in the buildings. Probabilistic distributions, described by the median and 84th percentile response spectra, were calculated from the thirty simulations. The probabilistic ISRS are subsequently used in the seismic fragility evaluations of selected essential equipment.

Seismic Responses of a Building Isolated With Multiple Friction Pendulum System Subjected to Multi-Directional Excitations

In order to prevent a building from earthquake damage, a base isolation system called the multiple friction pendulum system (MFPS) which has numerous concave sliding interfaces is proposed to isolate a building from its foundation. Mathematical formulations have been derived to simulate the characteristic of the MFPS isolation system subjected to multi-directional excitations. By virtue of the derived mathematical formulations, the phenomena of the sliding motions of the MFPS isolator with several concave sliding interfaces under multi-directional earthquakes can be clearly understood. Also, numerical analyses of a building isolated with the MFPS isolator with several sliding interfaces have been conducted in this study to evaluate the efficiency of the proposed system in seismic mitigation. It has been proved through numerical analyses that structural responses have been reduced significantly and that the proposed system is a good tool to insure the safety of structures during earthquakes.

Characteristic and Modeling of Multiple Direction Optimized-Friction Pendulum System With Numerous Sliding Interfaces Subjected to Multi-Directional Excitations

In this paper, a base isolator call the multiple direction optimized-friction pendulum system (Multiple DO-FPS) with numerous sliding interfaces is proposed. For understanding the mechanical behavior of the Multiple DO-PFS isolator under multi-directional excitations, an analytical model called the multiple yield and bounding surfaces model is also proposed. On the basis of the derived mathematical formulations for the simulation of the characteristic of the Multiple DO-FPS isolation bearing, it is revealed that the natural period and damping effect for a Multiple DO-FPS is a function of the sliding displacement and sliding direction. By virtue of the proposed model, the phenomena of the sliding motions of the Multiple DO-FPS isolator with numerous sliding interfaces subjected to multi-directional excitations can be simply understood. Analytical results infer that the natural frequency and damping effect of the Multiple DO-PFS isolator with numerous concave sliding interfaces change continually during earthquakes and are controllable through appropriate designs.

A Study of Elasto-Plastic Response of Single Degree of Freedom System Using Artificial Ground Motions With Given Time-Frequency Characteristics

In this paper, a number of artificial earthquake ground motions compatible with time-frequency characteristics of recorded actual earthquake ground motion as well as the given target response spectrum are generated using wavelet transform. The maximum non-dimensional displacement of elasto-plastic structures excited these artificial earthquake ground motions are calculated numerically. Displacement response, velocity response and cumulative input energy are shown in the case of the ground motion which cause larger displacement response. Under the given design response spectrum, a selection manner of generated artificial earthquake ground motion which causes lager maximum displacement response of elasto-plastic structure are suggested.

Comparison Between Hysteresis Energy and Input Energy for Failure

Many methods for evaluation of seismic resistance have been proposed. Energy balance equation is one of the methods. The main feature of the energy balance equation is that it explains accumulated information of motion. Therefore energy balance is suitable to investigate the influence of cumulative load. We have already conducted some studies that applied the energy balance equation to mechanical structures. In the studies, we confirmed a relationship between input energy and fatigue failure. On the other hand, a relation between fatigue life and hysteresis energy (i.e. area of a hysteresis loop) is well known in the fatigue strength field, and a lot of knowledge has been reported. The input energy of the energy balance equation is essentially equivalent to the hysteresis energy. Therefore it is expected that input energy for failure is equivalent to hysteresis energy for failure. In this paper, two experiments are carried out. One is a fatigue fracture experiment and the other is a vibration experiment that causes fatigue failure to experimental models. Both experiments cause fatigue failure by same bending mode. Finally the input energy and hysteresis energy for failure are compared.

Mathematical Analysis on Two Modelling Techniques for Dynamic Responses of a Structure Subjected to a Ground Acceleration

We considered two kinds of numerical modeling techniques for the dynamic response of a structure subjected to ground acceleration. One of the techniques is based on the equation of motion relative to ground motion, and the other is based on the equation of absolute motion of the structure and the ground. The analytic background of the former is well established while the latter is not yet. The latter is called large mass technique, which allocates an appropriate large mass to the ground so that it can cause the ground to move according to a given acceleration time history. In this paper, employing a single degree-of-freedom spring-mass system, we analyzed the equations of motion of the two techniques and provided some theorems on the large mass technique. Using simple examples, we compared numerical results of two modeling techniques with analytic solutions. We have shown that the theorems give us a clear insight on the large mass technique through numerical tests.

Active Control of Non-Linear System by a Fuzzy-Optimal Control Technique

The purpose of this paper is to estimate the real time vibration control of an actively-controlled nonlinear structure due to non-stationary external loads. When the optimal control theory is adopted as a control law against the concerned task, the derivation of time dependent optimal control gains may be required because of a remarkable non-stationarity of response amplitude. In addition, since the system is nonlinear, it takes more time to calculate those time dependent gains. This means that it is difficult to strictly execute the real time active control with optimal control theory as for the non-stationary and nonlinear system. In this paper, therefore, one approximate technique, coupled fuzzy-optimal control, is proposed in order to realize the real time control of non-stationary and nonlinear system. Finally, results by deterministic analysis based on numerical simulations are compared with those by stochastic analysis using statistical equivalent linearization technique.