• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2000년도 춘계학술대회논문집
• /
• pp.1933-1938
• /
• 2000

The partial differential equations for a coil spring derived from Timoshenko beam theory and Frenet formulae. Dynamic stiffness matrix of a coil spring composed of a circular wire is assembled by using dispersion relationship, waves and natural frequencies. Natural frequencies are obtained from maxima in the determinant of inverse of a dynamic stiffness matrix with appropriate boundary conditions. The results of the dynamic stiffness method are compared with those of transfer matrix method, finite element method and test.

• 한국전산구조공학회논문집
• /
• 제15권3호
• /
• pp.463-469
• /
• 2002

탄성지반 위에 놓인 보-기둥 요소의 총포텐셜 에너지로부터 변분원리를 적용하여 지배방정식과 힘-변위 관계식을 유도하였다. 4계 상미분방정식 형태의 지배방정식을 4개의 변위 파라메타를 도입하여 1계 연립미분방정식 형태의 선형 고유치 문제로 전환하고, 힘-변위 관계식을 적용하여 엄밀한 정적, 동적 요소강성행렬을 유도하였다. 직접강성법을 이용하여 구조물 강성행렬을 구하고, 2차원 보-기둥구조의 엄밀한 좌굴하중과 고유진동수를 구하고, 결과를 유한요소해와 비교함으로써 본 연구의 타당성을 검증하였다. 이러한 엄밀한 해석방법은 Hermitian 다항식을 형상함수로 도입하여 요소의 강성행렬을 산정하는 유한요소법과 비교할 때, 요소의 수를 대폭 줄일 수 있는 장점이 있다.

• Structural Engineering and Mechanics
• /
• 제62권6호
• /
• pp.759-769
• /
• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
• /
• pp.435-442
• /
• 2001

Derivation procedures of exact dynamic element stiffness matrix of shear deformable nonsymmetric thin-walled straight beams are rigorously presented for the spatial free vibration analysis. An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The natural frequencies are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• Structural Engineering and Mechanics
• /
• 제38권2호
• /
• pp.195-210
• /
• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• 한국해양공학회지
• /
• 제6권2호
• /
• pp.125-132
• /
• 1992

This paper presents an approach for the derivation of frequency-dependent element matrices for vibration analysis of piping systems containing a moving medium. The dynamic stiffness matrix is deduced from transfer matrix, and, in turn, the frequency-dependent element matrices are derived. Numerical examples show that method gives more accurate results than those obtained using the conventional static shape function based element matrices.

• Architectural research
• /
• 제10권1호
• /
• pp.25-32
• /
• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method to study parametrical instability of lattice dome structures, which is subjected to harmonically pulsating load. We consider elastic stiffness and geometrical stiffness simultaneously during the calculation of stiffness matrix, and adopt consistent mass matrix to make the solution more correct. In order to obtain instability regions, we represent displacements and accelerations in dynamic equation by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability regions eventually. Finally, we take 24-bar star dome and 90-bar lamella dome as examples to investigate dynamic instability phenomena.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 1995년도 춘계학술대회논문집; 전남대학교, 19 May 1995
• /
• pp.367-373
• /
• 1995

터빈 blade에 대해 기존의 stiffness matrix법과 finite element법에 의한 방식을 개선하여 수치계산을 행한 결과 다음의 결론을 얻었다. 1)stiffness matrix법을 적용하기 위해 th.2 order로 방정식을 유도하였으며, 회전시의 원심력의 영향 및 blade의 기하학적 형상이 수식에 고려되었다. 이 방법으로 blade의 여러 parameter의 영향을 간단히 계산할 수 있다. 계산결과는 다른 논문의 결과와 잘 일치함을 보였다. 또한, 원심력의 영향에 있어서는 th.2 order의 계산결과가 기존의 변형된 th.1 order의 결과보다 더 정확한 결과를 얻을 수 있다. 2) FEM 이용시 계산시간을 단축하면서 정확한 결과를 얻기 위해 blade를 간단히 modeling하여, 기하학적인 형상과 회전시의 영향을 고려한 식을 유도하였다. 본 방법의 결과는 타 문헌과 일치하였다.

• Steel and Composite Structures
• /
• 제16권6호
• /
• pp.577-593
• /
• 2014

An exact dynamic stiffness method is introduced for investigating the free vibration characteristics of the steel-concrete composite beams consisting of a reinforced concrete slab and a steel beam which are connected by using the stud connectors. The elementary beam theory is used to define the dynamic behaviors of the two beams and the relative transverse deformation of the connectors is included in the formulation. The dynamic stiffness matrix is formulated from the exact analytical solutions of the governing differential equations of the composite beams in undamped free vibration. The application of the derived dynamic stiffness matrix is illustrated to predict the natural frequencies and mode shapes of the steel-concrete composite beams with seven boundary conditions. The present results are compared to the available solutions in the literature whenever possible.

• 한국공작기계학회:학술대회논문집
• /
• 한국공작기계학회 2004년도 춘계학술대회 논문집
• /
• pp.191-196
• /
• 2004

This study proposed the analysis of mass position detection and modified stiffness due to the change of the mass and stiffness of structure by using the original and modified dynamic characteristics. The method is applied to examples of a cantilever and 3 degree of freedom by modifying the mass. The predicted detection of mass positions and magnitudes are in good agrement with these from the structural reanalysis using the modified mass.