• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.53-65
• /
• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• Structural Engineering and Mechanics
• /
• 제90권4호
• /
• pp.357-370
• /
• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Advances in nano research
• /
• 제15권3호
• /
• pp.215-224
• /
• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 춘계학술대회논문집A
• /
• pp.254-260
• /
• 2000

The spacer grid is one of the main structural components in fuel assembly, which supports the fuel rods, guides cooling water, and protects the fuel assembly from the external impact load such as earthquakes. The nonlinear dynamic impact analysis is conducted by using the finite element code ABAQUS/Explicit. Boundary condition for dynamic analysis is well applied to the test condition. Simulation results also similarly predict the local buckling phenomena. In addition to the buckling parameter, the local buckling cause is examined by both simulation and test method. It is found to correspond well with the test results. Impact tests are also carried out for some specimens of the spacer grid in order to compare the results between the test and the simulation. This test is accomplished by a free fall dummy weight onto the specimen. From this test, only the uppermost and lowermost layers of the multi-cell are buckled, which implies the local buckling at the weakest point of the grid structure.

• 한국추진공학회지
• /
• 제22권5호
• /
• pp.22-31
• /
• 2018

본 연구에서는 연소실 경계조건 변화에 따른 핀틀 노즐의 동특성을 파악하기 위해 수치해석을 수행하였다. 핀틀의 움직임을 모사하기 위해 노즐과 핀틀의 영역을 분리하여 격자를 생성하고 중첩격자기법을 사용하였다. 연소실의 경계조건은 일정질량유량과 추진제 연소속도 조건을 적용하여 결과를 비교하였다. 일정질량유량조건은 입구에 유입되는 질량유량을 정량적으로 변화시켜 연소실의 압력과 추력 특성을 파악하였다. 추진제 연소속도 조건은 연소실 압력에 의한 연소속도 식을 고려하였다. 추진제 연소속도 조건은 일정질량유량조건과는 다른 비선형적 유량변화를 나타내며, 작은 유량으로도 큰 연소실 압력변화를 가져온다.

• Computers and Concrete
• /
• 제25권3호
• /
• pp.255-266
• /
• 2020

This study presents comparation of fixed and viscos boundary condition effects on three-dimensional earthquake response and performance of a RCC dam considering linear and non-linear response. For this purpose, Cine RCC dam constructed in Aydın, Turkey, is selected in applications. The Drucker-Prager material model is considered for concrete and foundation rock in the nonlinear time-history analyses. Besides, hydrodynamic effect was considered in linear and non-linear dynamic analyses for both conditions. The hydrodynamic pressure of the reservoir water is modeled with the fluid finite elements based on the Lagrangian approach. The contact-target element pairs were used to model the dam-foundation-reservoir interaction system. The interface between dam and foundation is modeled with welded contact for both fixed and viscos boundary conditions. The displacements and principle stress components obtained from the linear and non-linear analyses are compared each other for empty and full reservoir cases. Seismic performance analyses considering demand-capacity ratio criteria were also performed for each case. According to numerical analyses, the total displacements and besides seismic performance of the dam increase by the effect of the viscous boundary conditions. Besides, hydrodynamic pressure obviously decreases the performance of the dam.

• Earthquakes and Structures
• /
• 제13권6호
• /
• pp.573-588
• /
• 2017

The earthquake input is required when the soil-structure interaction (SSI) analysis is performed by the direct finite element method. In this paper, the earthquake is considered as the obliquely incident plane body wave arising from the truncated linearly elastic layered half space. An earthquake input method is developed for the time-domain three-dimensional SSI analysis. It consists of a new site response analysis method for free field and the viscous-spring artificial boundary condition for scattered field. The proposed earthquake input method can be implemented in the process of building finite element model of commercial software. It can result in the highly accurate solution by using a relatively small SSI model. The initial condition is considered for the nonlinear SSI analysis. The Daikai subway station is analyzed as an example. The effectiveness of the proposed earthquake input method is verified. The effect of the obliquely incident earthquake is studied.

• Smart Structures and Systems
• /
• 제18권4호
• /
• pp.787-800
• /
• 2016

The aim of the paper is to analyze nonlinear transverse vibration of an embedded piezoelectric plate reinforced with single walled carbon nanotubes (SWCNTs). The system in rested in a Pasternak foundation. The micro-electro-mechanical model is employed to calculate mechanical and electrical properties of nanocomposite. Using nonlinear strain-displacement relations and considering charge equation for coupling between electrical and mechanical fields, the motion equations are derived based on energy method and Hamilton's principle. These equations can't be solved analytically due to their nonlinear terms. Hence, differential quadrature method (DQM) is employed to solve the governing differential equations for the case when all four ends are clamped supported and free electrical boundary condition. The influences of the elastic medium, volume fraction and orientation angle of the SWCNTs reinforcement and aspect ratio are shown on frequency of structure. The results indicate that with increasing volume fraction of SWCNTs, the frequency increases. This study might be useful for the design and smart control of nano/micro devices such as MEMS and NEMS.

• 대한조선학회논문집
• /
• 제35권1호
• /
• pp.32-39
• /
• 1998

잠수된 원형실린더의 대진폭운동에 대한 수치해석이 제시된다. 방법은 포텐셜이론에 근간을 두고 정현파중에서 2차원 운동은 초기치 문제로 귀결된다. 완전한 비선형자유표면 조건은 수치 계산영역에서 적용되고, 비선형 수치해는 수치계산의 임의의 가정된 경계를 따라 외부영역에서의 선형해로서 부과된다. 잠수된 원형실린더의 대진폭운동의 계산은 직접적으로 시간영역에서 시뮬레이션된다. 계산결과로 부터 물체와 유체입자의 상호 운동은 부양운동과 표류운동에 중요한 효과를 준다.

• 대한조선학회논문집
• /
• 제37권1호
• /
• pp.67-81
• /
• 2000

본 연구에서는 2차원 비선형 방사문제에 대한 정확하고 효과적인 수치기법을 개발하였다. 물체운동에 의해서 생성되는 비선형파계는 이상유체라는 가정에 의하여 기술되고, 라프라스 방정식은 고차경계요소법과 GMRES(Generalized Minimal RESidual) 알고리즘을 이용하여 신속하고 효율적인 풀이가 가능하도록 하였다. 자유표면과 물체면의 교차점에서 발생하는 교차선문제는 불연속 요소를 이용하여 원활하게 해결하였다. 자유표면의 비선형운동을 기술하기 위해서 음해적 사다리꼴 법칙(implicit trapezoidal rule)을 사용하여 시적분하였다. 물체에 의해서 발생한 비선형파가 수직 하류면에서 반사하는 것을 줄이기 위하여 하류면에 수치감쇠항을 도입하였다. 수치계산 결과로부터 본 시적분법 및 수치방사조건이 비선형 방사문제에 매우 적합함을 확인하였다. 시적분 과정에서 자유표면의 격자점들을 재배치함으로써 수치해법의 효율성을 배가하였으며, 교차점근처의 유동 또한 정확하게 기술하였다. 가속도 포텐셜(acceleration potential) 기법을 이용하여 정확하고 안정하게 비선형 방사력을 구하였다. 본 수치계산결과는 다른 수치계산 및 실험결과와 비교하여 볼 때, 좋은 일치를 보인다.