This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The previously developing equation for Power-Law model is a simple ordinary differential type. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Casson model) that continuously flows into a circular tube by surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that the theoretical predictions of the governing equation were in good agreement with the results for considering the Newtonian model.

사용후핵연료 파이로 공정은 전기화학 이론들에 기초하여 개발되고 있다. 공정 모사는 공정 개발과 실험데이터 해석에 주 요한 방법 중 하나로 파이로 공정에서도 필요한 접근 방법 중 하나이다. 현재까지 파이로 공정의 공정 모사는 전해정련 공 정 위주로 진행되어 왔으며 전해환원 공정에 대한 연구는 많지 않았다. 전해환원 공정은 전해정련 공정과 달리 기체 발생과 다공성 전극의 특징을 지니고 있기 때문에 공정 모사를 위한 모델 개발을 위해서는 이를 고려한 수식들이 필요하게 된다. 본 연구에서는 전기화학 셀 해석에 필요한 열역학, 물질전달, 반응공학 이론 중 전해환원 공정 모델 개발에 필요한 개념과 수식 들을 정리하여 제시하였다. 전해환원 셀을 구분하여 각 부분에 적용해야하는 수식들을 나열했으며 각 부분들 연결에 사용되 는 경계조건들 역시 제시하였다. 이들 수식들은 추후 모델 개발에 기초로 사용될 수 있으며 실험데이터와 결합시켜 결정되 어야 하는 매개변수 파악에 활용될 수 있을 것으로 기대된다.

본 논문에서는 단파의 파군이 계단형 지형을 통과할 때 발생하는 2차 장파를 이론적으로 연구하였다. 먼저, 수심 변화에 의한 단파의 회절을 해석하였으며, 다변수 섭동법을 이용하여 2차 장파의 지배방정식을 유도하였다. 2차 장파 방정식을 해석하여 서로 다른 속도로 진행하는 자유장파와 구속장파가 발생함을 보였다.