1st Natural Frequency Research Articles

Propeller Excitation of Longitudinal Vibration Characteristics of Marine Propulsion Shafting System

The submarine experiences longitudinal vibration in the propulsion shafting system throughout most of run. A transfer matrix model of the propulsion shafting system, in which the dynamic characteristics of oil film within thrust bearing are considered, is established to describe the dynamic behavior. Using hydrodynamic lubrication theory and small perturbation method, the axial stiffness and damping of oil film are deduced in great detail, followed by numerical estimation of the foundation stiffness with finite element method. Based upon these values of dynamic parameters, the Campbell diagram describing natural frequencies in terms of shafting rotating speeds is available, and the effect on the 1st natural frequency of considerable variations in thrust bearing stiffness is next investigated. The results indicate that the amplitude of variation of the 1st natural frequency in range of low rotating speeds is great. To reduce off-resonance response without drastic changes in propulsion shafting system architecture, the measure of moving thrust bearing backward is examined. The longitudinal vibration transmission through propulsion shafting system results in subsequent axial excitation of hull; the thrust load acting on hull is particularly concerned. It is observed that the measures of structural modification are of little benefit to minimize thrust load transmitted to hull.

Study on the vibration characteristics of the pre-twisted pillar and beam

For the past several years, large scale earthquakes happened. A lot of industrial facilities were damaged. For example, a lot of power plants were stopped in The 2011 off the Pacific coast of Tohoku Earthquake or The Southern Hyogo prefecture earthquake in 1995. These earthquakes have larger acceleration level than the seismic design level. Therefore, the earthquake proof measures are required. In this study, earthquake proof effect of the beam and the long column having initial twist is focused. The design guidelines for application to the pre-twisted beam structure and the long column structure is proposed. The pre-twisted beam and long column are modelled by FEM and calculated. The natural frequency of the pre-twisted beam and long column are related to the Young's modulus, density, length and cross-sectional area. The tendency of the natural frequency respected to the total twisted angle and the aspect ratio of the cross-section is obtained considering the vibration mode and the natural frequency. Furthermore, when attention is focused on the vibration mode, the influence of the total twisted angle is different for the modal shapes, and the case where the modal shapes are interchanged is shown. The acceleration response to the vibration input is determined by the natural frequency of the primary cross-section, the aspect ratio and boundary conditions. In order to evaluate the response reduction effect, the acceleration amplification respected to the total twisted angle and the 1st natural frequency of the system is analyzed. And the response reduction map is proposed. Using this map, it is possible to estimate the advantage of the pre-twisted effect for the vibration characteristics in a simple manner.

Effects of Bearing Configuration on Spindle Dynamic Characteristics

This article investigates the effects of bearing configuration on the spindle dynamic characteristics. First, an analytical model of spindle is proposed and the bearing sets radial stiffness is calculated. Second, the spindle analytical model is developed to perform modal analysis and harmonic response analysis with ANSYS, and then obtain the natural frequency and FRF under different bearing configurations. The result suggests that bearing configuration has little effect on the natural frequency of spindle system and the FRF amplitude corresponding to the 1st natural frequency under back to back configuration or face to face configuration is relatively small. Finally, the proposed model is validated by modal experiment.

No-Backlash Control System by Two-Motor Drive (3rd. Report, The Analyses and Experiments of Performance Improvement)

A no-backlash drive control technique in which two motors drive a load axis, as one is for a plus direction and another is for a minus direction, has two problems :1) the 1st natural frequency of the drive system may cause a backlash, 2) the drive system has a remarkable power loss. For the former problem, we introduce a notch filter, with its inverse notch filter in some cases, against the 1st natural frequency, which improves the no-backlash drive range, into the simulation. This method is robust, because the 1st natural frequency of the drive system is not related to the load inertia, and related to the motors inertia and the spring stiffness of the drive line. For the latter problem, we employ a torque crossover method, in which a part of torque reference of the drive-side motor gives to the driven-side motor and the resulted torque reference of the driven-side one is reduced. Our experiments showed the total motor current was reduced by half.

성덕대왕신종을 위한 가변형 명동의 설계

본 연구는 성덕대왕신종의 공명효과를 극대화시키기 위하여 계절에 따른 기온의 차이를 보정할 수 있는 가변형 명동의 설계 모델을 제시한다. 성덕대왕신종의 종소리에서는 64 Hz의 1차 고유진동수와 168 Hz의 2차 고유진동수가 가장 중요한 성분이다. 두 주파수 성분을 대상으로 종체 공동, 간극, 명동으로 구성된 내부 음향공동계의 공명조건을 구한다. 이를 위하여 SYSNOISE를 이용한 경계요소해석을 통하여 내부공동의 음향 주파수응답 특성을 구한다. 외적요소로, 계절에 따른 기온 차이는 공명 조건에 크게 영향을 미친다. 그 결과 공명효과를 극대화시키는 명동의 길이는 계절에 따라 달라져야 한다. 이를 고려하여 본 연구에서는 기온 변화에 맞추어 명동의 길이를 종의 설치 현장에서 쉽게 조절할 수 있는 가변형 명동의 설계 모델을 제시한다. This study proposes a design model of the variable type resonator which corrects the temperature variance according to the season, in order to maximize the resonance effect in the Sacred bell of the Great King Seongdeok. In the bell, the 1st natural frequency (64 Hz) and the 2nd natural frequency (168 Hz) are the most important partial tones. Resonance conditions of the two components are determined for the internal acoustic cavity system, which consists of bell body cavity, gap and the resonator. Acoustic frequency response characteristics of the internal cavity are determined by the boundary element analysis using SYSNOISE. As an external factor, temperature variance according to the season largely influences the resonance condition and the length of the resonator should be controlled to maximize the resonance effect. As a measure, this study proposes a design model of the variable type resonator for the Sacred Bell of the Great King Seongdeok, which can control the length at the belfry according to the season.

Effects of using scalloped shape braces on the natural frequencies of a brace-soundboard system

Many prominent musical instrument makers shape their braces into a scalloped profile. Although reasons for this are not well known scientifically, many of these instrument makers attest that scalloped braces can produce superior sounding wooden musical instruments in certain situations. The aim of this paper is to determine a possible reason behind scalloped shaped braces. A simple analytical model consisting of a soundboard section and a scalloped brace is analyzed in order to see the effects that changes in the shape of the brace have on the frequency spectrum of the brace-soundboard system. The results are used to verify the feasibility of adjusting the brace thickness in order to compensate for soundboards having different stiffness in the direction perpendicular to the wood grain. It is shown that scalloping the brace allows an instrument maker to independently control the value of two natural frequencies of a combined brace-soundboard system. This is done by adjusting the brace’s base thickness in order to modify the 1st natural frequency and by adjusting the scalloped peak heights to modify the 3rd natural frequency, both of which are considered along the length of the brace. By scalloping their braces, and thus controlling the value of certain natural frequencies, musical instrument makers can improve the acoustic consistency of their instruments.

Fabrication of carbon nanotubes dispersed woven carbon fiber/epoxy composites and their damping characteristics

Damping characteristics of carbon nanotubes dispersed woven carbon fiber/epoxy composites were investigated. The composites were fabricated by an advanced resin film infusion prepreg manufacturing process based on the calendaring process using three-roll mill. Through this advanced process, well-dispersed nanocomposites containing high weight percent (up to 7 wt%) of carbon nanotubes was achieved. It was confirmed through the scanning electron microscopic images of the carbon nanotubes dispersed composites. Damping characteristics of the specimen were measured by the impact vibration test of the composites beam specimens. Considerable improvement of damping characteristics was observed in the carbon nanotubes dispersed composites, and structural damping increased as the weight percent of carbon nanotubes was increased. Damping ratio was improved up to 12.3% (at the 1st natural frequency) and 16.1% (at the 2nd natural frequency), especially in the 7 wt% carbon nanotubes dispersed specimen. Tensile test was performed to investigate the effects of carbon nanotubes on the tensile properties. The tensile stiffness of carbon nanotubes dispersed composites was similar with the conventional composites; however, tensile strength was degraded.

Behavior of Bridge Bearings for Railway Bridges under Running Vehicle

Open steel plate girder (OPSG) bridges are the most prevalent railroad bridge type in Korea, constituting about 40% of all railroad bridges. Solid steel bearings, known as line type bearings, are placed in most OSPG railway bridges. However, the line type rigid bearings generate several problems with the bridge's dynamic behavior and maintenance in service. To compare and investigate the dynamic behaviors of line type, spherical and disk bearings, the vertical displacements of each bearing, including fixed and expansion type, under running vehicles are measured and analyzed. The displacements of disk and spherical bearings are measured after replacing the line type bearings with spherical and disk bearings. This study also analyzed dynamic behaviors of bridges. Furthermore, the deformation of the PTFE (Polytetrafluoroethylene) plate that is placed inside of expansion type spherical and disk bearings is measured and its effect on the dynamic behavior of the bridges is discussed. The up-lift phenomenon at the bearings installed for the steel bridges is estimated. The vertical displacements at mid-span of the bridges are compared according to the bearing types. Finally, the 1st mode natural frequencies are estimated, and the relationship to the vertical displacement is discussed.

교량받침 형식에 따른 판형교 동적 분석

철도 판형교의 선받침, 스페리칼받침 및 디스크받침의 차량주행에 의한 동적 거동을 측정 분석 하고, 각 받침에 따른 판형교의 동적 거동을 분석하였다. 이를 위해 각 받침은 고정단과 가동단의 형태에 따라 차량주행에 의한 수직변위가 측정되었고, 비교 분석하였다. 또한, 가동단의 스페리칼받침과 디스크받침의 내부에 설치된 PTFE판의 변형 및 이 변형이 교량의 거동에 미치는 영향을 분석하였다. 판형교에 설치된 교량받침에서 들림 현상이 관측되는데, 받침 형태에 따른 들림량을 분석하였다. 중앙 거더의 수직변위를 교량받침 별로 비교하여 교량받침 교체에 의한 교량 수직변위 변화를 분석하였으며, 각 받침에 따른 중앙 거더의 수직변위와 고유진동수의 변화를 상관적으로 분석하여 설명하였다. Dynamic behaviors of line type bearings, spherical bearings and disk bearings which are being used for railway steel bridges are investigated, and that of the bridges is also analyzed. For the purpose, the vertical displacements of the three bearings including fixed and expansion type are measured and analyzed. Also, the deformation of the PTFE plate placed inside of spherical and disk bearings of expansion type is measured and its effect on the dynamic behavior of the bridges is discussed. The up-lift phenomenon at the bearings installed for the steel bridges is estimated. The vertical displacements at mid-span of the bridges are compared according to the bearing types. Finally, the 1st mode natural frequencies are estimated and the relationship to the vertical displacement is discussed.

木造根太床の鉛直振動特性に及ぼす支持条件と偏在荷重の影響に関する研究

Impact hammer tests and analyses by finite element method were conducted to demonstrate the effects of support condition and uneven distributed load on the vertical dynamic characteristics of light frame joist floors with 3.64m-long-span and from 0.91m to 7.82m-wide joist floor consisted of 2" by 8" dimension lumbers and 15 mm-thick plywood subfloor. The results indicate, i) Support condition slightly affects the natural frequencies when the width/span ratios exceed 2; ii) In addition to the mass-ratio of human-load, both the placement and the stand position of persons onto the joist floor give influence on the damping factor of 1st natural frequency; iii) The joist subjected to uneven distributed load generates locally deformed vibrational mode and also determines the 1st natural frequency of the joist floor; iv) Finite element analysis employed the appropriate models is effective to predict the natural frequencies and mode shapes of joist floor subjected to uneven distributed load.

Analysis and Optimization of the Static and Dynamic Characteristics of Head Frame

The head frame is a key component which plays a supportive and accommodative role in the spindle system of CNC machine tool. Improving the static and dynamic characteristics has profound significance to the development of machine tool and product performance. The simplified finite element modal is established with ANSYS to carry out the static and modal analysis. The results showed that the maximum deformation of the head frame was 0.0066mm, the maximum stress was 3.94Mpa, the deformation of most region was no more than 0.0007mm, which all verified that the head frame had a good stiffness and deforming resistance; several improvement measures for dynamic performance were also proposed by analyzing the mode shapes, and the 1st order natural frequency increased 7.33% while the head frame mass only increased 1.58% applying the optimal measure, which improved the dynamic characteristics of the head frame effectively.

High-cycle fatigue life prediction for Pb-free BGA under random vibration loading

This paper develops an assessment methodology based on vibration tests and finite element analysis (FEA) to predict the fatigue life of electronic components under random vibration loading. A specially designed PCB with ball grid array (BGA) packages attached was mounted to the electro-dynamic shaker and was subjected to different vibration excitations at the supports. An event detector monitored the resistance of the daisy chained circuits and recorded the failure time of the electronic components. In addition accelerometers and dynamic signal analyzer were utilized to record the time-history data of both the shaker input and the PCB’s response. The finite element based fatigue life prediction approach consists of two steps: The first step aims at characterizing fatigue properties of the Pb-free solder joint (SAC305/SAC405) by generating the S– N (stress-life) curve. A sinusoidal vibration over a limited frequency band centered at the test vehicle’s 1st natural frequency was applied and the time to failure was recorded. The resulting stress was obtained from the FE model through harmonic analysis in ANSYS. Spectrum analysis specified for random vibration, as the second step, was performed numerically in ANSYS to obtain the response power spectral density (PSD) of the critical solder joint. The volume averaged Von Mises stress PSD was calculated from the FEA results and then was transformed into time-history data through inverse Fourier transform. The rainflow cycle counting was used to estimate cumulative damages of the critical solder joint. The calculated fatigue life based on the rainflow cycle counting results, the S– N curve, and the modified Miner’s rule agreed with actual testing results.

438 内面研削スピンドルの軸形状設計に関する研究(連成振動,設計,OS-18 ロータダイナミクス,総合テーマ「伝統を,未来へ!」)

The aim of this study is presenting a new design method for the internal grinding spindle whose operating range is between 1st and 2nd critical speed. Spindle shape is designed so that the 1st bending natural frequency decreases and the 2nd bending natural frequency increases compare the normally designed spindle which has constant diameter by based on parameter study and optimization calculation using finite element spindle model.

Preliminary evaluation of precise inclination sensor and GPS for monitoring full-scale dynamic response of a tall reinforced concrete building

It is necessary to use different sensors in an integrated manner – GPS, accelerometer, inclination sensor and so on – in order to monitor and identify static, quasi-static and resonant response of tall buildings subjected to wind loading. There are some differences among these sensors with respect to data sampling rate, data quality, and their measurement accuracy. Therefore, using different sensors together for a monitoring project is important because of the complementary nature of each sensor. In this study, the behaviour of a tall reinforced concrete building (30 stories high) under wind load has been monitored using GPS and inclination sensors. This paper assesses the dynamic measurement quality and reliability of inclinometers for building monitoring applications, and discusses the strengths and weaknesses of GPS vis-a-vis the use of inclination sensors for monitoring the dynamic response of tall buildings under wind load. Data collected by these sensors have been analysed in the time and frequency domains. It was found that GPS observations were distorted by multipath caused by a reflecting surface on top of the building. From the analyses in the frequency domain, the 1st mode natural frequencies of the building determined from both sensors agree very well with each other. The discrepancy of this measured 1st mode natural frequency compared to that derived from FEM (Finite Element Model) prediction is 7%.

215 梁の衝突振動 : 高振動数加振時の低次モードの影響(衝突減少・衝突振動,OS-1 振動基礎,総合テーマ「伝統を,未来へ!」)

Impact vibration of beam that has very narrow clearance between beam and impact wall, and that is excited around 2nd natural frequency, was investigated and the followings are made clear. (1) The beam is weakly resonant if excitation frequency is nearly equal to even number times the 1st natural frequency. (2) Even if the excitation frequency is nearly equal to the 2nd natural frequency, the beam is not resonant because 1st mode is dominant the vibration. (3) Those are caused by asymmetric property of the system. Furthermore, the beam is strongly resonant at non natural frequency.

Simple and versatile micro‐cantilever sensors

PurposeThe purpose of this paper is to demonstrate the simplicity and versatility of micro‐cantilever based sensors and to present the influence of added mass and stress on the frequency response of the sensor in order to determine the most suitable sensing domain for a given application.Design/methodology/approachThe frequency response of micro‐cantilevers depends not only on the applied mass and surface stress, but also on the mass position. An interpretation of the theoretical frequency results of the 1st and 2nd natural frequencies, for added mass, identifies a nodal point for the 2nd natural frequency which demonstrates mass invariance. Hence, at this nodal point, the frequency response remains constant regardless of mass and may be used for identifying purely induced surface stress influences on the micro‐cantilever's dynamic response. The Rayleigh‐Ritz energy method is used for the theoretical analysis. Theoretical results are compared with experimental results.FindingsA graph of the 2nd natural frequency of micro‐cantilevers with added mass demonstrates the variability of the frequency with mass position on the micro‐cantilever. Of particular interest is the nodal point at which mass independence is revealed. This nodal point may be exploited to investigate purely stress‐related influences on the dynamic characteristics of micro‐cantilever sensors, thereby eliminating such effects as reactant evaporation from the micro‐cantilever sensor surface. In this regard, the nodal point of the 2nd natural frequency response is used to decouple mass‐stress influences.Research limitations/implicationsOwing to the micro‐scale size of the micro‐cantilevers, it may not be possible to apply mass or stress directly at the nodal point and to concentrate its influence there. Hence, a certain amount of influence due to mass‐stress coupling may remain in the frequency responses observed.Practical implicationsSilicon micro‐cantilevers can be easily shaped and sensitized to a variety of influences. These qualities are highly regarded for sensor applications. The work presented herein, contributes to the optimization of micro‐cantilever sensors' dynamic response as a function of mass and surface stress influences. The main criterion for choosing one or the other is based on the time for the surface reaction to take place between the sensing material and the target material. The results presented contribute to the performance optimization of micro‐cantilever based medical and bio‐sensors.Originality/valueSurface stress effects are generally of much smaller magnitude than mass influences; hence, through an investigation of the stress effects at the nodal point of the 2nd natural frequency it is possible to eliminate the mass influence completely. At this position mass and stress influences are decoupled and the sensor response can be uniquely quantified as a function of the applied stress. This is important for bio‐medical and health monitoring applications in which changes to the applied mass or surface stress on a micro‐cantilever sensor, may be readily observed through changes to the natural frequency response of the micro‐cantilever.

실험계획법을 이용한 인공위성 주반사경 플렉셔 마운트의 최적 설계

The primary mirror system in a satellite camera is an opto-mechanically coupled system for a reason that optical and mechanical behaviors are intricately interactive. In order to enhance the opto-mechanical performance of the primary mirror system, opto-mechanical behaviors should be thoroughly investigated by using various analysis procedures such as elastic, thermo-elastic, optical and eigenvalue analysis. In this paper, optimal design of the bipod flexure mounts for high opto-mechanical performance is performed. Optomechanical performances considered in this paper are RMS wavefront error under the gravity and thermal loading conditions and 1st natural frequency of the mirror system. The procedures of the flexure mounts design based on design of experiments and statistics is as follows. The experiments for opto-mechanical analysis are constructed based on the tables of orthogonal arrays and analysis of each experiment is carried out. In order to deal with the multiple opto-mechanical properties, MADM (Multiple-attribute decision making) is employed. From the analysis results, the critical design variables of the flexure mounts which have dominant influences on opto-mechanical performance are determined through analysis of variance and F-test. The regression model in terms of the critical design variables is constructed based on the response surface analysis. Then the critical design variables are optimized from the regression model by using SQP algorithm. Opto-mechanical performance of the optimal bipod flexure mounts is verified through analysis.

Wheel Load Variation in Coupled Motion Between Wheel and Flexible Track with Short-Wave Irregularity

The decrease of wheel load variation is one of the most important issues which must be solved in railway dynamics. The purpose of this study is to make clear the mechanism of wheel load variation by the numerical simulation by the analytical model which is based on the concept of the multibody dynamics. In this study, we were able to figure out the in-depth mechanism of the wheel load variation, particularly, concerning the phenomenon that the wheel load variation suddenly decreases with more than wheel velocity at which the 1st natural frequency of system consists with the irregularity passing frequency.

Study of Earthquake Isolation System Using Vertically Utilized Coiled Springs (2nd Report, Quasi-Static Tests for Elasto-Plastic Coiled Springs)

This paper describes static loading tests results of elasto-plastic coiled springs and discusses analytical model for hysteretic restoring force. The static loading tests were carried out for two types of elasto-plastic coiled spring in which had a different material SS400 and SWRM17 steel. The elasto-plastic coiled springs were designed to provide a 1 000 kg rated mass with a horizontal 1st natural frequency about 0.74 Hz, yield displacement of about 25 mm and an equivalent damping ratio of 30% or more. The tests results revealed various properties of horizontal stiffness and equivalent damping ratios obtained from the hysteretic restoring force loops. The repeated shear deformation tests showed that the coiled springs could keep their integrity thought the 100-cycle repetition tests. An analytical model for elasto-plastic coiled springs was proposed to express the horizontal hysteretic restoring force, and validity of the analytical model was evaluated.

Mechanics in naturally compliant structures

In this study the mechanics of compliant structures (very light weight structures which do not have bending capability but have axial stiffness (tension)) in particular to spider web has been studied. The orb-web spider has evolved over the last 180 million years [Lin, L.H., Edmonds, D.T., Vollrath, F., 1995. Structural engineering of an orb-spider’s web. Nature 373, 146–148]. This long period of evolution has produced the present spider web, an elegant, natural, lightweight structure to efficiently resist different loads such as wind, insect impact, etc. It can function as a net for catching prey even if any element is broken. Nature has accomplished these tasks by optimizing its form of construction, and by making spider silk a biopolymer with superior elasticity and tensile strength. It is believed that spider webs are the most efficient structures engineered by nature. In this study it is tried to find why spider webs are so efficient. A FE model of an ideal spider web has been created using the FEMAP pre- and post-processing software, and analyzed using the ABAQUS non-linear FE code. Both the static and dynamic problems have been considered, and also the numerical and experimental techniques have been used. It has been tried to look at how stress is redistributed in the face of damage and how the loss of elements affects the dynamic response of the web and how the vibration due to insect impact is damp out. Finally the numerical simulations have been compared to physical experiments. In lieu of actual spider webs, artificial nets have been examined and its 1st natural frequencies for different cases have been measured by laser vibrometer. A FE model of the net has also been created in FEMAP and analyzed by ABAQUS. In both analyses, the same elements have been removed systematically from the center and the 1st natural frequencies have been determined. Prediction matches well with experiment. The results of this study may be used in light structures like cable-stayed bridges [Masura, M., Yokoyama, K., Toshio, M., 1989. Wind-induced cable vibration of cable-stayed bridges in Japan. In: Proceedings of Canada–Japan Workshop on Bridge Aerodynamics, Ottawa, pp. 101–110; Yoshimura, T., Inoue, A., Kaji, K.K., Savage, M.S., 1989. A study on the aerodynamic stability of the Aratsu Bridge. In: Proceedings of Canada–Japan Workshop on Bridge Aerodynamics, Ottawa, pp. 41–50] and space structures.