• Journal of Theoretical and Applied Mechanics
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• 제1권1호
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• pp.29-67
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• 1995

A procedure is formulated, in this paper, to compute the bifurcation modes born by the stability change of normal modes, and to compute the forced responses associated with bifurcation modes in inertially and elastically coupled nonlinear oscillators. It is assumed that a saddle-loop is formed in Poincare map at the stability chage of normal modes. In order to test the validity of procedure, it is applied to one-to-one internal resonant systems in which the solutions are guaranteed within the order of a small perturbation parameter. The procedure is also applied to the exact system in which normal modes are written in exact form and the stability of normal modes can be exactly determined. In this system the stability change of normal modes occurs several times so that various types of bifurcation modes are created. A method is described to identify a fixed point on Poincare map as one of bifurcation modes. The limitations and advantage of proposed procedure are discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.609-616
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• 2001

The vibrational characteristics of nonuniform circular rods have been studied theoretically and experimentally in this paper. The differential equation of torsional motion expressed in terms of the angular displacement has been solved exactly and approximately for a stepped circular rod and for a conically-tapered rod. Solutions of the boundary-value problem have yielded the natural frequencies, mode shapes and forced responses of the rods. The theoretical solutions of forced response have been verified by comparing them with experimental ones.

• Structural Engineering and Mechanics
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• 제73권1호
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Steel and Composite Structures
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• 제47권6호
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• 대한기계학회논문집
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• 제14권3호
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• pp.534-546
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• 1990

본 연구에서는 선회 종동자(oscillating follower)를 사용하는 캠 기구(대표 적인 기구중 하나인 자동차용 OHC 형 캠-밸브 기구)에 대해서 동역학적 특성을 고려하 여 종동자 형상과 캠 형상을 동시에 합성하고자 한다.

• 방송공학회논문지
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• 제13권2호
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• pp.214-221
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• 2008

본 논문에서는 두 개의 3차원 메쉬 프레임에서 추출한 운동 성질을 이용하여 형태 특징을 반영하는 3차원 메쉬 에디팅 알고리듬을 제안하였다. 제안하는 알고리듬은 형태적 특징을 유지하는 결과를 얻기 위해서 두 개의 메쉬 프레임으로부터 국부 영역의 표면 특징을 반영하는 운동 특성 벡터를 이용한다. 에디팅 과정에서 사용자는 임의의 꼭지점을 조작 꼭지점(anchor vertex)으로 선택하여 자유롭게 이동시킨다. 조작 꼭지점에는 사용자의 조작에 따라 강제된 운동이 부여되고, 이 운동 특성을 유지하도록 이웃 꼭지점들의 위치가 정해진다. 이 과정을 통해 샘플 메쉬의 특징을 보존하는 에디팅 결과를 얻는다. 모의 실험을 통하여 제안하는 알고리듬이 사용자가 의도한 조작을 충분히 반영하는 동시에 샘플 메쉬 쌍에서 나타나는 운동성을 보존하는 결과를 도출함을 확인하였다.

• Journal of Advanced Research in Ocean Engineering
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• 제3권4호
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• pp.165-173
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• 2017

This study aims at validating simulations of the forced and freely vibrating cylinders at Reynolds number of approximately 500 in order to identify the capability of the CFD code, and to establish the analysis process of the vortex-induced vibration (VIV). The direct numerical and large eddy simulations were employed to resolve the various length scales of the vortices, and the morphing technique was used to consider a motion of the circular cylinder. For the forced vibration case, both in- and anti-phase VIV processes were observed regarding the frequency ratio. Namely, when the frequency ratio approaches to unity, the synchronization/lock-in process occurs, leading to substantial increases in drag and lift coefficients. This is strongly linked with the switch in timing of the vortex formation, and this physical tendency is consistent with that of Blackburn and Henderson (J. Fluid Mech., 1999, 385, 255-286) as well as force coefficients. For the free oscillation case, the mass and damping ratio of 50.8 and 0.0024 were considered based on the study of Blackburn et al. (J. Fluid Struct., 2000, 15, 481-488) to allow the direct comparison of simulation results. The simulation results for a peak amplitude of the cylinder and a shedding mode are reasonably comparable to that of Blackburn et al. (2000). Consequently, based on aforementioned results, it can be concluded that numerical methods were successfully validated and the calculation procedure was well established for VIV analysis with reasonable results.

• 한국구조물진단유지관리공학회 논문집
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• 제8권2호
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• pp.247-258
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• 2004

복합적층 곡선패널의 비감쇠 강제진동문제를 해결하기 위한 쉘 요소를 제안하였다. 본 연구에서는 절점당 6개의 자유도를 갖는 4절점 EAS 쉘요소를 사용하였다. EAS 방법을 이용하여 전단잠김과 면내잠김 현상을 극복하였으며, 전단보정계수를 사용하지 않고 분포형상함수에 의해 두께방향에 따른 전단변형을 포물선으로 분포시킨 수정된 1차전단변형이론을 적용하였다. Newmark 직접적분법이 시간에 관한 운동방정식의 적분과 시간이력을 해결하기 위해 적용되었다. 곡선패널의 기하학적 조건과 화이버 보강각도 및 적층조건 등의 매개변수 변화에 따른 강제진동응답을 분석하였다.

• Coupled systems mechanics
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• 제7권4호
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• pp.485-507
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• 2018

The moving load causes the occurrence of vibrations in civil engineering structures such as bridges, railway lines, bridge cranes and others. A novel engineering method for separation of the variables in the differential equation of the elastic line of Bernoulli-Euler beam has been developed. The method can be utilized in engineering structures, leading to "a beam under moving load model" with generalized boundary conditions. This method has been implemented for analytical study of the dynamic response of the metal structure of a single girder bridge crane due to the telpher movement along the bridge girder. The modeled system includes: a crane bridge girder; a telpher, moving with a constant horizontal velocity; a load, elastically fixed to the telpher. The forced vibrations with their own frequencies and with a forced frequency, due to the telpher movement, have been analyzed. The loading resulting from the telpher uniform movement along the bridge girder is cyclical, which is a prerequisite for nucleation and propagation of fatigue cracks. The concept of "dynamic coefficient" has been introduced, which is defined as a ratio of the dynamic deflection of the bridge girder due to forced vibrations, to the static one. This ratio has been compared with the known from the literature empirical dynamic coefficient, which is due to the telpher track unevenness. The introduced dynamic coefficient shows larger values and has to be taken into account for engineering calculations of the bridge crane metal structure. In order to verify the degree of approximation, the obtained results have been compared with FEM outcomes. An additional comparison has been made with the exact solution, proposed by Timoshenko, for the case of simply supported beam subjected to a moving force. The comparisons show a good agreement.

• Structural Engineering and Mechanics
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• 제88권1호
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• pp.1-12
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• 2023

In this study, forced vibration behavior of a piezo magneto electric sandwich Timoshenko beam is investigated. It is assumed a sandwich beam with porous core and graphene platelet reinforced composite (GPLRC) in facesheets subjected to magneto-electro-elastic and temperature-dependent material properties. The magneto electro platelets are under linear function along with the thickness that includes a cosine function and magnetic and electric constant potentials. The governing equations of motion are derived using modified strain gradient theory for microstructures. The effects of material length scale parameters, temperature change, different distributions of porous, various patterns of graphene platelets, and the core to face sheets thickness ratio on the natural frequency and excited frequency of a sandwich Timoshenko beam are scrutinized. Various size-dependent methods effects such as MSGT, MCST, and CT on the natural frequency is considered. Moreover, the final results affirm that the increase in porosity coefficient and volume fractions lead to an increase in the amount of natural frequency; while vice versa for the increment in the aspect ratio. From forced vibration analysis, it is understood that by increasing the values of volume fraction and the length thickness of GPL, the maximum deflection of a sandwich beam decreases. Also, it is concluded that increasing the temperature, the thickness of GPL, and the initial force leads to a decrease in the maximum deflection of GPL. It is also shown that resonance phenomenon occurs when the natural and excitation frequencies become equal to each other. Outcomes also reveal that the third natural frequency owns the minimum value of both deflection and frequency ratio and the first natural frequency has the maximum.