動的應答法을 利用한 多点支持된 連續圓筒셸의 振動特性에 關한 硏究 = (A) study on the vibration characteristics of the continuous circular cylindrical shells with multiple supports by using the receptance method

다국어 초록 (Multilingual Abstract)

This paper presents an useful approach to predict vibrational characteristics of the circular cylindrical shell structures to be used in the high-technology industry such as aircraft, spacecraft, nuclear reactor, submarine including industrial facilities. Such a structure has multiple supports at arbitrary intermediate positions and the structures are always exposed to external vibration sources such as wind, earthquake, shock or power sources and so on. In this study a vibration analysis of the continuous circular cylindrical shell with the multiple supports is conducted to investigate dynamic characteristics and to obtain structural integrity by using analytic, FEM and experimental methods.
To develope the frequency equations of the circular cylindrical shell, the applied linear elastic theory is based on the assumption that the thickness is thin with respect to its radius of curvature and that the deflection is small. The equations are also derived by using the energy method and the Rayliegh-Hitz method. The continuous circular cylindrical shell with multiple supports is regarded as a combined structure, its frequency equation is derived by using the line receptance method and the spring receptance method, including the force equilibrium and the displacement continuity on the intermediate supports. Expecially, the forces acting on the intermediate supports at arbitrary axial positions is defined by the modal expansion method expressed in the Dirac Delta function, displacements of the system are expressed as an infinite series of natural modes. To have a more good reliability for analytical solutions, additionally the finite element analysis(FEA) and the experimental modal analysis are carried out to investigate natural frequencies and mode shapes, the results obtained are compared to the analytical results to verify engineering applications. FE modeling is created by the ANSYS 5.3 program and the modal test is done with an impulse hammer, an accelerometer and FFT analyzer, experimental models and jigs are designed to obtain modal parameters and are fabricated of stainless steel. In this experiment, the time signals which generates during exiting the structure is transformed into the frequency signals including an useful information related to frequency parameters of the system through the FFT Analyzer. The frequency response function(FRF) is obtained from their measured signals and mode shapes are simulated on the display of STAR SYSTEM(Spectral Dynamic Inc.) with respect to their natural frequencies. As a result, the major conclusions of this study are summarized as follows.
1) The frequency equations of circular cylindrical shell is derived using the energy method and Rayleigh-Ritz method from the assumption that the shell is thin and the displacement is small.
2) And then the frequency equation of a continuous circular cylindrical shell is derived using the receptance method, the modal expansion method and the Dirac Delta Function.
3) Analysis of dynamic characteristics for the continuous circular cylindrical shell with multiple supports at the intermediate positions has been performed to get the natural frequency and mode shapes. In this study modal parameters are investigated in considering geometric parameters, and end conditions and the number of intermediate supports.
4) The vibrational characteristics of the continuous circular cylindrical shell may be changed by the end conditions. The natural frequencies of the shell structures without intermediate supports are much affected by the type of constraint conditions at both ends. However, in case that the shell structures have intermediate supports at arbitrary positions along the axial direction, the natural frequencies are not much affected by the constraints at both ends.
5) Investigating the variation of the natural frequency with the intermediate supports, the fundamental frequency of Case V with 3 intermediate supports is about 2.8 times higher than that of Case Ⅱ without intermediate supports in the analytic solution, 2.7 times in the experimental analysis and 3.3 times in the FEM analysis.
6) In order to control the vibrational characteristics for a continuous circular cylindrical shell with multiple supports, it is effective to take advantage of the principle of multiple supports other than geometric parameters or constraint conditions.

목차 (Table of Contents)

• 목차
• Nomenclature = iv
• List of Tables = vii
• List of Figures = ix
• I. 서론 = 1
• 1.1 연구의 배경 및 필요성 = 1
• 1.2 연구동향 = 3
• 1.3 연구목적 및 내용 = 8
• II. 진동수 방정식의 정식화 = 10
• 2.1 원통셀의 진동수 방정식 유도 = 10
• 2.1.1 양단 단순지지 원통셸의 진동수 방정식 = 10
• 2.1.2 고정-단순지지 원통셸의 진동수 방정식 = 18
• 2.2 동적응답의 일반식 = 23
• 2.3 연속원통셸의 진동수 방정식 유도 = 26
• 2.3.1 진동수 방정식 = 26
• 2.3.2 동적응답식 = 31
• 2.4 탄성지지된 연속원통셸의 진동수 방정식 유도 = 37
• 2.4.1 진동수 방정식 = 37
• 2.4.2 N-스팬 연속원통셸의 진동수 방정식 = 42
• III. 수치해석 = 45
• 3.1 원통셸의 수치해석 = 50
• 3.1.1 양단 단순지지 원통셸 = 50
• 3.1.2 고정-단순지지 원통셸 = 51
• 3.2 연속원통셸의 수치해석 = 52
• 3.2.1 동일스팬을 갖는 연속원통셸 = 53
• 3.2.2 비동일스팬을 갖는 연속원통셸 = 54
• 3.3 탄성지지된 연속원통셸의 수치해석 = 55
• 3.4 수렴성의 검증 = 56
• IV. 유한요소 해석 = 58
• 4.1 유한요소 모델링의 생성 = 58
• 4.2 수렴성의 검증 = 64
• 4.3 유한요소의 해 = 66
• V. 실험모드해석 = 67
• 5.1 실험모델 = 67
• 5.2 모델장착 및 실험장치 구성 = 70
• 5.3 진동실험 = 76
• VI. 결과 및 고찰 = 81
• 6.1 원통셸의 동특성 고찰 = 81
• 6.1.1 양단 단순지지 원통셸의 동특성 고찰 = 82
• 6.1.1.1 원주방향 파수 n에 따른 진동특성 = 82
• 6.1.1.2 기하학적 매개변수에 따른 진동특성 = 88
• 6.1.2 고정-단순지지 원통셸의 동특성 고찰 = 100
• 6.1.2.1 원주방향의 파수n에 따른 진동특성 = 100
• 6.1.2.2 기하학적 매개변수에 따른 진동특성 = 105
• 6.2 다점지지된 연속원통셸의 동특성 고찰 = 117
• 6.2.1 구속조건에 따른 다점지지 연속원통셸의 진동특성 = 118
• 6.2.2 기하학적 매개변수에 따른 진동특성 = 122
• 6.2.3 중간지지에 따른 진동특성 = 131
• 6.2.4 탄성지지된 연속원통셸의 진동특성 = 141
• 6.3 모드형상의 비교 검토 = 145
• 6.4 기존의 동적응답법과의 차이 = 157
• VII. 결론 = 159
• 참고문헌 = 161
• Abstract = 167