• 한국자동차공학회논문집
• /
• 제11권2호
• /
• pp.172-181
• /
• 2003

In this study, the stress intensity factor of center crack tip is calculated by the superposition method when it is surrounded by symmetrically distributed small cracks. The values of stress intensity factors of center crack tips are compared with those of the center crack tips calculated by the superposition method. These compared errors are influenced by the locations of distributed small cracks. These errors are inspected. When small cracks overlap and approach near the center crack tip, the effect of interaction caused by these cracks becomes noticeable and these errors become larger. In case of multiple distributed small cracks except this case, the stress intensity factor of the center crack tip is easily calculated by the superposition method.

• 한국지진공학회논문집
• /
• 제7권3호
• /
• pp.39-45
• /
• 2003

본 논문에서는 구조물의 효율적인 동적해석을 위한 수정된 Lanczos 벡터중첩법을 제안하였다. 제안방법은 강성행렬에 직교하는 Lanczos 벡터를 생성하는 수정된 Lanczos 알고리즘에 기초하고 있다. 단일입력하중을 받는 구조물의 해석에 있어서 제안한 Lanczos 벡터중첩법은 기존의 Lanczos 벡터중첩법과 동일한 정확도와 효율성을 갖는 반면 다중입력하중을 받는 구조물의 경우 제안방법이 기존의 방법보다 더욱 효율적이다. 수치예제를 통해 제안방법의 효율성을 검증하였다.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
• /
• pp.11-18
• /
• 2003

This paper proposes modified Lanczos vector superposition method for efficient dynamic analysis of structures. Proposed method is based on the modified Lanczos algorithm that generates stiffness-orthonormal Lanczos vectors. Proposed method has better computing efficiency than the conventional Lanczos vector superposition method in the analysis of multi-input-loaded structures. The efficiency of proposed method is verified through numerical examples. Comparison with other vector superposition methods is also presented through numerical examples.

• 한국정밀공학회지
• /
• 제11권4호
• /
• pp.47-57
• /
• 1994

This study investigates the crack propagation behavior to examine the effect of welding residual stress by the superposition method. Especially, as the crack propagation behavior is affected by the applied stress and the stress ratio in compressive residual stress filed, it is studied for three cases as follows; (1) $K_{min}$is smaller than l $K_{r}$l, (2) $K_{min}$ is smaller than l $K_{r}$l in the later stage, (3) $K_{min}$is lager than l $K_{r}$l. The resuslts show that the superposition method is very useful in all the three cases of compressive residual stress field, but is inappropriate in predicting the crack propagation behavior in tensile residual stress field.field.field.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2000년도 춘계학술대회논문집
• /
• pp.549-555
• /
• 2000

The improved mode superposition methods for non-classically damped systems are presented in this paper. Generally, the mode superposition method uses a relatively small subset of the normal modes of structures. The mode acceleration method and the modal truncation augmentation method improve the results of the mode superposition method by considering effects of truncated high modes. For using these methods to analyze non-classically damped systems, the systems are approximated to the classically damped systems and thereby the errors are induced. In this paper, the mode acceleration method and the modal truncation augmentation method are expanded to analyze the non-classically damped systems. The applicability of the expanded methods is verified by closed form solutions and numerical examples. The expanded modal truncation augmentation method is conditionally stable depending on the pattern of the external loading in the non-classically damped systems whereas the expanded mode acceleration method is stable for the all cases of loading. In the stable case, the results are the same with those of the expanded mode acceleration method.

• Structural Engineering and Mechanics
• /
• 제73권3호
• /
• pp.271-286
• /
• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Journal of Mechanical Science and Technology
• /
• 제20권11호
• /
• pp.1950-1960
• /
• 2006

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2010년도 추계학술대회 논문집
• /
• pp.943-944
• /
• 2010

• Earthquakes and Structures
• /
• 제4권4호
• /
• pp.341-363
• /
• 2013

Earthquake response calculation, parametric analysis and seismic parameter optimization of base-isolated structures are some critical issues for seismic design of base-isolated structures. To calculate the earthquake responses for such non-symmetric and non-classical damping linear systems and to implement the earthquake resistant design codes, a modified complex mode superposition design response spectrum method is put forward. Furthermore, to do parameter optimization for base-isolation structures, a graphical approach is proposed by analyzing the relationship between the base shear ratio of a seismic base-isolation floor to non-seismic base-isolation one and frequency ratio-damping ratio, as well as the relationship between the seismic base-isolation floor displacement and frequency ratio-damping ratio. In addition, the influences of mode number and site classification on the seismic base-isolation structure and corresponding optimum parameters are investigated. It is demonstrated that the modified complex mode superposition design response spectrum method is more precise and more convenient to engineering applications for utilizing the damping reduction factors and the design response spectrum, and the proposed graphical approach for parameter optimization of seismic base-isolation structures is compendious and feasible.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
• /
• pp.265-272
• /
• 2005

For bridge-vehicle interaction analysis of cable-supported brides, the superposition method is applied based on the results of 3-dimensional free vibration analysis using General-purpose FEM Software. This study firstly performs the eigenvalue analysis for the free vertical and the torsional vibration of bridges using FEM analysis. Next the equations of motion considering interaction between bridges and vehicles/train are derived from mode superposition method. And then dynamic analysis is performed using the Newmark numericial method. Finally through the numerical examples, the dynamic responses of cable-supported bridges by this study are presented and discussed.