Effect of natural frequency modes on sloshing phenomenon in a rectangular tank

Jung, Jae Hwan,Yoon, Hyun Sik,Lee, Chang Yeol The Society of Naval Architects of Korea 2015 International Journal of Naval Architecture and Oc Vol.7 No.3

Liquid sloshing in two-dimensional (2-D) and three-dimensional (3-D) rectangular tanks is simulated by using a level set method based on the finite volume method. In order to examine the effect of natural frequency modes on liquid sloshing, we considered a wide range of frequency ratios ($0.5{\leq}fr{\leq}3.2$). The frequency ratio is defined by the ratio of the excitation frequency to the natural frequency of the fluid, and covers natural frequency modes from 1 to 5. When fr = 1, which corresponds to the first mode of the natural frequency, strong liquid sloshing reveals roof impact, and significant forces are generated by the liquid in the tank. The liquid flows are mainly unidirectional. Thus, the strong bulk motion of the fluid contributes to a higher elevation of the free surface. However, at fr = 2, the sloshing is considerably suppressed, resulting in a calm wave with relatively lower elevation of the free surface, since the waves undergo destructive interference. At fr = 2, the lower peak of the free surface elevation occurs. At higher modes of $fr_3$, $fr_4$, and $fr_5$, the free surface reveals irregular deformation with nonlinear waves in every case. However, the deformation of the free surface becomes weaker at higher natural frequency modes. Finally, 3-D simulations confirm our 2-D results.

Effect of natural frequency modes on sloshing phenomenon in a rectangular tank

정재환,윤현식,이창열 대한조선학회 2015 International Journal of Naval Architecture and Oc Vol.7 No.3

Liquid sloshing in two-dimensional (2-D) and three-dimensional (3-D) rectangular tanks is simulated by using a level set method based on the finite volume method. In order to examine the effect of natural frequency modes on liquid sloshing, we considered a wide range of frequency ratios ( 0.5 ≤ fr ≤ 3.2 ). The frequency ratio is defined by the ratio of the excitation frequency to the natural frequency of the fluid, and covers natural frequency modes from 1 to 5. When fr =1 , which corresponds to the first mode of the natural frequency, strong liquid sloshing reveals roof impact, and significant forces are generated by the liquid in the tank. The liquid flows are mainly unidirectional. Thus, the strong bulk motion of the fluid contributes to a higher elevation of the free surface. However, at fr = 2 , the sloshing is considerably suppressed, resulting in a calm wave with relatively lower elevation of the free surface, since the waves undergo destructive interference. At fr = 2 , the lower peak of the free surface elevation occurs. At higher modes of fr3 , fr4 , and fr5 , the free surface reveals irregular deformation with nonlinear waves in every case. However, the deformation of the free surface becomes weaker at higher natural frequency modes. Finally, 3-D simulations confirm our 2-D results.

현악기의 진동특성 연구

정환희(Jung Hwan Hee) 국립국악원 2008 국악원논문집 Vol.18 No.-

본 연구는 전통 현악기의 소리를 결정짓는 요소 중 하나인 울림통의 진동특성을 알아보기 위해서 정악가야금, 산조가야금, 거문고에 대해 모달 분석 (modal analysis)을 실시하였다. 이를 통해 울림통의 앞판과 뒤판의 고유주파수 및 내부의 공명 주파수를 측정하고 주파수별 진통모드를 분류하였다. 실험결과, 세 악기에 대한 휩 모드, 비틀림 모드 및 공기모드의 고유주파수를 각각 2개씩 찾고 악기별 순서대로 분류히였다 산조가야금과 거닐고의 경우 비틀림 모드가 가정 낮은 고유주파수에서 나타난 반면 정악가야금은 비 틀림 모드가 먼저 나타나고 그 다음으로 휩 모드가 나타나는 것으로 측정되었다. 또한 세 악기 모두 휩 모드에서 좌우 비대칭으로 진동하는 형태를 나타냈다. In this study we conducted modal analysis on jeongak gayageum, sanjo gayageum and geomungo to learn the vibrating characteristics of resonant box - one of the major factors that deterrnine the sound of traditional string instruments. Through this test we measured the natural frequency of both sides of resonant box and its internal resonant frequency of each instrument and classified vibration modes (bending, torsion and air modes) according to the frequency. According to the test result, as for sanjo gayageum and geomungo, twisting mode appeared at the lowest natural frequency. However as for jeongak gayageum, twisting mode first appeared and later appeared bending mode. All three instruments commonly showed non-symmetrical frequency type at bending mode.

Steering Wheel Core 진동해석을 통한 최적화 설계에 대한 고찰

채천우(Chunwoo Chae),박동진(Dongjin Park),홍찬호(Chanho Hong),남병찬(ByungChan Nam) 한국자동차공학회 2011 한국자동차공학회 학술대회 및 전시회 Vol.2011 No.11

With rapid change of automotive market, multi-function and complexity in limited shape, cost reduction and weight lightening become more and more popular topic in these days. So it is necessary to study on design optimization. Steering Wheel is one of the parts that drivers touch very often in a car and its main function is steering. Especially, steering wheel vibration and noise becomes one of important quality evaluation criterion. Steering Wheel needs to meet basic strength, resonance by low natural frequency, natural frequency that meets more than optimum level and avoids fatigue fracture. Though steering wheel weight will be increased and natural frequency will be decreased relatively, designers often add rib shape on weak part for strength reinforcement and optimum natural frequency. So those methods do not work effectively. This study focus on the method that improves both of strength and natural frequency by change of geometric moment of inertia through changing cross section shape of spoke (2~4 spoke) and keeping mass at same time.Model of steering wheel core for study was simplified and every model’s rim and base keep its own shape and changed only cross section shape of spoke. Natural frequency of steering wheel core was checked by Nastran FX that used as study solver (Mesh size: 2㎜, node qty: 390,000 ~ 430,000EA, element qty 240,000 ~ 250,000). The study was conducted at same condition of armature mass by every spoke quantity. It is possible to confirm the correlation between cross section size change and its natural frequency of steering wheel core through natural frequency study and it is also possible to apply cross section size change on stress concentrated point occurred for strength reinforcement. As result, it can be judged that cross section change in same mass works on strength reinforcement, high natural frequency and cost reduction.

현이론을 이용한 사장교 케이블 장력산정

박연수,최선민,이병근,김민중 한국방재학회 2009 한국방재학회논문집 Vol.9 No.2

사장교 케이블 장력 산정 방법에는 직접적인 방법과 간접적인 방법이 있는데 직접적인 방법은 정확성에 문제가 있을 뿐만 아니라 제한사항도 많다. 따라서 일반적으로 케이블 장력 추정은 간접적인 방법인 고유진동수를 이용하는 진동법을 사용하고 있다. 최근 시공된 사장교의 케이블에 대해 현이론을 이용한 진동법으로 케이블 장력을 산정해 그 결과를 다중진동모드를 이용한 진동법과 비교했다. 그 결과를 요약하면, 현이론 방법의 오차는 7차이하의 진동모드에서는 2%를 초과하지 않았다. 특히, 3차와 4차 진동모드의 오차는 1%를 초과하지 않았다. 그리고 진동모드의 차수가 증가하고 케이블 단면이 클수록 오차는 증가했고, 장력이 크고 케이블 길이가 길수록 오차는 낮아짐을 알 수 있었다. 즉 7차 이하의 진동모드에서 높은 정밀도를 갖는 다는 것을 알 수 있다. Estimate method of cable tension forces can be classified into direct method and indirect method. Direct method is not accuracy and it has many restrictions. Therefore, in generally Indirect method, vibration method using natural frequency, has been applied to estimate the tension forces. In this study, cable tensions of recently constructed cable-stayed bridge are measured using string vibration method and this result comparing with result of multiple mode method. To put it brief, the error of string vibration method is not exceeding 2% under 7th mode. Specially third and 4th mode error is not exceeding 1%. safety.

고층건물의 자연진동 실험 및 FE 해석모델 향상

조순호 대한건축학회지회연합회 2017 대한건축학회연합논문집 Vol.19 No.1

18층 사무실용도 건물(SIB)의 동적성능을 결정하기 위하여 자연 진동계측 실험을 수행하였다. 해당건물은 기본적으로 철골골조 형식이나, 보다 효율적으로 수평하중을 지지하기 위하여 콘크리트 코아가 추가된 복합 구조형식을 취하고 있다. 계측된 일련의 진동기록에 최신 주파수- 및 시간영역-기반 응답의존 시스템판별법인 FDD, pLSCF 및 SSI를 적용하여 모달계수를 추출하였다. 3방법에 의하여 추출한 결과는 대체로 일치하였으나, 초기 3D-FE 해석결과와 비교하여 저차 3개 고유진동수는 대략 1.1~1.6배 정도의 단단한 거동을 나타냈다. 진동실험 및 FE 해석으로 부터 획득한 고유진동수 및 모드형태와 같은 모달계수의 일치를 위하여 최적화이론에 근거한 자동모델향상을 시도하였다. 자세한 3D-FE모델의 해석결과로부터 매 층 마다 3개의 강성 및 3개의 질량을 변수로 갖는 단순 FE모델을 유도하여 모델향상의 시작모델로 사용하였다. 일치를 시도한 6개의 모드 중 저차 3차 모드까지만 고려한 향상된 FE모델은 자연진동수 및 모드형태에 대하여 우수한 일치를 나타냈다. 모델향상을 수행한 결과에 의하면, 현재의 국내 FE 구조해석 실무는 층강성 및 층질량을 각각 다소 과소 및 과다하게 고려하고 있는 것으로 판단된다. Dynamic response measurements from natural excitation were carried out for a 18-story office building(SIB) to determine its inherent properties. A steel beam-column frame system was adopted as a typical structural form, but a concrete core wall was added to resist the lateral force more effectively, resulting in a mixed configuration. The most advanced operational system identification methods based on frequency- and time-domain like FDD, pLSCF and SSI were used to extract modal parameters form a series of vibration records. The frequencies and mode shapes extracted from different identification methods showed a greater consistency, however the three lower frequencies exhibited 1.1 to 1.6 times as stiff as those obtained using a detailed 3D-FE model. Automatic FE model updating adopting optimization theory was applied to correlate experimental and analytical modal parameters such as natural frequencies and mode shapes. The simplified FE model containing 3 stiffnesses and 3 masses at each story as structural parameters derived from a detailed 3D-FE model was used as a starting one for updating. The excellent match between test and analytical modal parameters was made for the lower three modes out of the six. Based on the updating results, it can be judged that the domestic design practice for FE analysis somewhat underestimates the story stiffness, while overestimating the story mass.

둔턱 진행 차량의 주파수응답 분석

김종도,윤문철 중소기업융합학회 2022 융합정보논문지 Vol.12 No.3

차량의 진행을 근사화한 외부 가진력을 고려한 강제 진동에서의 주파수 특성을 알아보고자 하였고, 다양한 가진 진폭과 주파수를 갖는 외력이 작용하면서 차량이 둔턱을 넘어갈 때에 차량에서 일어나는 주파수 영역의 진동특성을 분석하였다. 응답은 수치해석을 통하여 변위, 속도 및 가속도 등의 응답을 구하였고 이들을 FFT 처리하여 각 시간 응답의 FRF(Frequency response function) 주파수 특성을 분석하였다. 특히, 차량 고유모드와 외부 가진 모드의 발생 위치를 확실하게 비교하여 밝혔고 외부 가진력에 의한 강제진동 모델에서 변위, 속도 및 가속도의 거동과 주파수 응답함수에서의 고유모드의 위치와 주변의 가진 모드 분포 및 파워 스펙트럼, 실수부와 허수부의 FRF도 나타났으며 각 FRF에서 근접 모드 특성도 분석하였다. 외부 가진력으로 정현파의 가진력과 임펄스 가진력에 의한 둔턱 주파수를 고려하여 가정한 근사 모델에서 발생 모드를 구별할 수 있었다. 상당하는 질량, 감쇠 및 강성을 변화하는 여러 시스템에서 강제진동의 응답특성을 체계적으로 다루었다. The purpose of this study was to investigate the frequency characteristics of forced vibration considering the vehicle progress. And the vibration characteristics in frequency domain that occur, when vehicle passes the bump, were analyzed. The responses such as displacement, velocity and acceleration were obtained through numerical analysis, and FFT processing was performed to analyze the frequency response function(FRF) characteristics. In particular, the location of vehicle eigenmodes and external excitation modes was clearly shown and analyzed. In the forced vibration model by external force, the behavior of the eigenmode in power spectrum and real and imaginary parts were also analyzed. The mode characteristics were also analyzed in each FRF. It was approximated by assuming total excitation force by considering the exciting frequency using impulse and sine wave forces, which can give the amplitude and frequencies. The response characteristics of forced oscillations having different mass, damping and stiffness have been systematically discussed.

고속 운영을 위한 능동거니플랩 설계 변경 및 고유진동수 예측

김태주(Taejoo Kim),김도형(Do-Hyung Kim),백승길(Seung-Kil Paek) 한국소음진동공학회 2015 한국소음진동공학회 학술대회논문집 Vol.2015 No.4

Working displacement variation by elastic deformation of Active Gurney Flap which was operated on high frequency was observed. Flap-wise natural frequency was lower than mode analysis result and hinge boundary condition was identified to be the cause through the simple modal test. Design modification for increasing natural frequency was conducted for minimizing the elastic deformation at maximum 35Hz operating condition which was design requirement condition. Brass bushing was applied instead of rotating bearing for gap minimization and Gurney Flap design modification was conducted to increase of the flap-wise natural frequency. Design modification effect was validated by natural frequency comparison with mode analysis result and modal test result of design modification model.

자동차 타이어의 진동특성에 관한 실험적 연구

김병삼,전형주 순천대학교 공업기술연구소 1997 工業技術硏究所論文集 Vol.11 No.-

The vibration characteristics of automobile tire is studied experimentally. In order to obtain the theoretical values of natural frequency and mode shape, the plane vibration of a tire is modeled as a circular beam. Theoretical results are determined by using the Tielking method which considers tension force due to tire inflation pressure, rotational velocity, tangential and radial stiffness. Modal parameters by the inflation pressure, load and rotational velocity are experimentally determined by using frequency response function method. Results show that material property and tire wear are parameters for shift the natural frequency and the increase of sidewall stiffness caused by the load on a tire results in the increase of natural frequency of the tire, and rotational velocity of the tire has no influence on the natural frequency.

모드 추출법을 이용한 무궤도 등반시스템 해석

김홍건,김유신 전주대학교 공학기술종합연구소 2003 전주대학교 공학기술종합연구소 학술논문집 Vol.9 No.1

This paper presents an approach to the analysis of the free wheeled vehicle using various mode extraction methods, and to the investigation of the influence of natural frequency on the structure. For each modal analysis, it is performed so as to investigate the natural frequency. The effectiveness of the bucket is proven itself to operate equally well on the device in the experiments. Furthermore in the rear wheel's analysis, it shows that eigen value in the experiment is numerically 99% convergent and is given a good agreement with the FEM analysis