Naohiro Nakamura

Basic Study on the Transform Method of Frequency-Dependent Functions into Time Domain: Relation to Duhamel’s Integral and Time-Domain-Transfer Function

The time-domain evaluation of the frequency-dependent dynamic stiffness was studied, and some transform methods were proposed. Although various kinds of stiffness have been well-transformed by these methods, some problems remain. In this paper, the following two problems are studied. First, the relationship between the proposed transform methods and Duhamel’s integral is studied to understand the meaning of the two series of impulse responses obtained by the methods. Next, the time-domain transfer function, obtained by the transform of frequency-domain transfer function, is shown to expand the applicability of the methods. Seismic response values are easily calculated in the time domain using the function without FFT. The efficiency of the function is confirmed with a practical example problem.

Extended Rayleigh Damping Model

In dynamic analysis, frequency domain analysis can be used if the entire structure is linear. However, time history analysis is generally used if nonlinear elements are present. Rayleigh damping has been widely used in time history response analysis. Many articles have reported the problems associated with this damping and suggested remedies. A basic problem is that the frequency area across which the damping ratio is almost constant is too narrow. If the area could be expanded while incurring only a small increase in computational cost, this would provide an appropriate remedy for this problem. In this study, a novel damping model capable of expanding the constant frequency area by more than five times was proposed based on the study of a causal damping model. This model was constructed by adding two terms to the Rayleigh damping model and can be applied to the linear elements in the time history analysis of a nonlinear structure. The accuracy and efficiency of the model were confirmed using example analyses.

Response Analysis and Auto-Regressive Exogenous Modeling of a Steel-Reinforced Concrete High-Rise Building during the 2011 Off the Pacific Coast of Tohoku Earthquake

Many seismic records were obtained during the 2011 off the Pacific coast of Tohoku earthquake. These records can be used to improve the seismic design and disaster prevention capabilities of buildings. In this paper, seismic simulation analyses of a steel-reinforced concrete high-rise building located in the Tokyo Bay area is conducted based on the seismic record of the Tohoku earthquake. A nonlinear sway-rocking model is used in the analysis, and comparisons are drawn between the observed records and analytical results of the pre-shock, main shock and earthquake after 1 month. The analytical results correspond well with the seismic records, and the effect of the nonlinear nature of the main shock is retained in the building. This is an important consideration when conducting response evaluation. An ARX (auto-regressive exogenous) model is used to identify the first and second natural periods, and the damping ratios, of both the records and the analytical results. Although the first and second damping ratios are similar in value to the observed results, the second damping ratio is overestimated in the analytical results because of the stiffness damping model.

Centrifuge Testing and Seismic Response Analysis for Uplift Behavior of Spread Foundation Structures on Rock

The uplift behavior of structures subjected to severe seismic motion has not been clarified. This paper presents experimental and analytical studies conducted for clarifying this problem of spread foundation structures on rock. First, centrifugal loading tests are conducted to determine the uplift behavior of these structures, and the uplift behavior of these structures is confirmed. Then, simulation analyses are performed using a three-dimensional FE model and the accuracy of these analyses is confirmed. A comparison between test and analyses results clarified the important analytical conditions required for maintaining analysis precision and the limit of analysis precision.

Three-Dimensional Energy Transmitting Boundary in the Time Domain

Although the energy transmitting boundary is accurate and efficient for the FEM earthquake response analysis, it could be applied in the frequency domain only. In the previous papers, the author proposed an earthquake response analysis method using the time domain energy transmitting boundary for two dimensional problems. In this paper, this technique is expanded for three dimensional problems. The inner field is supposed to be a hexahedron shape and the approximate time domain boundary is explained, first. Next, two dimensional anti-plane time domain boundary is studied for a part of the approximate three dimensional boundary method. Then, accuracy and efficiency of the proposed method are confirmed by example problems.

3-D SIMULATION ANALYSIS OF FULL SCALE 5-STORY BUILDING WITH STEEL DAMPERS

Recently, vibration control devices are often adopted in Japanese buildings. Then, the seismic behavior of the buildings with them should be seized in the design stage accurately. However, that accuracy is not enough because the test data and analyses of the full-scale building are insufficient. This paper presents the 3 dimensional simulation of the experiment of the full-scale 5-story steel building using steel dampers conducted by E-Defense in 2009. Although the analysis results agreed the test results almost well, some differences were seen. Therefore, additional analyses were performed to study the effect of used models and parameters.