• Advances in nano research
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• 제8권3호
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• pp.215-228
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• 2020

In this paper, a new method based on the Sander theory is developed for SWCNTs to predict the vibrational behavior of length and ratio of thickness-to-radius according to various end conditions. The motion equation for this system is developed using Rayleigh-Ritz's method. The proposed model shows the vibration frequencies of armchair (5, 5), (7, 7), (9, 9), zigzag (12, 0), (14, 0), (19, 0) and chiral (8, 3), (10, 2), (14, 5) under different support conditions namely; SS-SS, C-F, C-C, and C-SS. The solutions of frequency equations have been given for different boundary condition, which have been given in several graphs. Several parameters of nanotubes with characteristic frequencies are given and vary continuously in length and ratio of thickness-to-radius. It has been illustrated that an enhancing the length of SWCNTs results in decreasing of the frequency range. It was demonstrated by increasing of the height-to-radius ratio of CNTs, the fundamental natural frequency would increase. Moreover, effects of length and ratio of height-to-radius with different boundary conditions have been investigated in detail. It was found that the fundamental frequencies of C-F are always lower than that of other conditions, respectively. In addition, the existence of boundary conditions has a significant impact on the vibration of SWCNTs. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid.

• 대한기계학회논문집
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• 제15권1호
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• pp.366-375
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• 1991

본 연구에서는 보 이론(beam theory)의 변위함수(displacement function)를 도입하고 전달행렬법을 이용하여 각 배관요소의 경계조건에 대한 고유 진동수와 배관 의 불안정성을 일으키는 유체의 임계속도(critical velocity)를 계산 평가하고, 실험 으로 입증된 Blevins의 결과치와 비교하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제35권8호
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• pp.1028-1034
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• 2011

본 논문에서는 파도의 상하운동에너지의 이용효율을 높이기 위해서 부양체와 2 D.O.F.(자유도) 진동발전시스템을 일체로 구성한 파력진동발전시스템을 제안한다. 파도가 갖는 상하운동 주파수 중 속도 에너지가 큰 주요 주파수 ${\omega}_1$, ${\omega}_2$을 선정하고, 2 D.O.F. 파력진동발전시스템의 고유진동수와 선정된 주파수들을 일치시킨다. 그러면 공진효과에 의해 각각의 질량과 권선사이의 상대속도가 파도의 상하운동속도보다 커진다. 또한 2 D.O.F. 진동시스템의 연성효과로 인한 1 D.O.F. 파력진동발전시스템보다 더 많은 전기에너지를 얻을 수 있다. 따라서 본 논문에서 제안한 2 D.O.F. 파력 발전시스템은 파도가 갖는 에너지를 더 많이 이용할 뿐만 아니라 더 많은 전기에너지를 얻을 수 있는 장점을 가짐을 알 수 있었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.297-302
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• 2007

Vibrating test of vehicle component can be possible in lab-based simulators instead of field testing owing to the development of technology in control algorithm as well as computational process. Currently, Multi-Axial Simulation Table(MAST) is recommended as a vibrating equipment, which excites a target component for 3-directional translation and rotation motion simultaneously and hence, vibrational condition can be fully approximated to that of real road test. But, the vibration-free performance of target component is not guaranteed with MAST system, which is only simulator subjective to the operator. Rather, the reliability of multi-axial vibration test is dependent on the quality of input profile which should cover the required severity of vibrating condition on target component. In this paper, multi-axial vibration testing methodology of vehicle component is presented here, from data acquisition of vehicle accelerations to the obtaining the input profile of MAST using severe data at proving ground. To compare the severity of vibration condition, between real road test and proving ground one, energy principle of equivalent damage is proposed to calculate energy matrices of acceleration data and then, it is determined the optimal combination of special events on proving ground which is equivalent to real road test at the aspects of vibration fatigue using sequential searching optimal algorithm. To explain the vibration methodology clearly, seat and door component of vehicle are selected as a example.

• Smart Structures and Systems
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• 제16권2호
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• pp.295-328
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• 2015

In recent years the monitoring of structural behavior through acquisition of vibrational data has become common practice. In addition, recent advances in sensor development have made the collection of diverse dynamic information feasible. Other than the commonly collected acceleration information, Global Position System (GPS) receivers and non-contact, optical techniques have also allowed for the synchronous collection of highly accurate displacement data. The fusion of this heterogeneous information is crucial for the successful monitoring and control of structural systems especially when aiming at real-time estimation. This task is not a straightforward one as measurements are inevitably corrupted with some percentage of noise, often leading to imprecise estimation. Quite commonly, the presence of noise in acceleration signals results in drifting estimates of displacement states, as a result of numerical integration. In this study, a new approach based on a time domain identification method, namely the Unscented Kalman Filter (UKF), is proposed for correcting the "drift effect" in displacement or rotation estimates in an online manner, i.e., on the fly as data is attained. The method relies on the introduction of artificial white noise (WN) observations into the filter equations, which is shown to achieve an online correction of the drift issue, thus yielding highly accurate motion data. The proposed approach is demonstrated for two cases; firstly, the illustrative example of a single degree of freedom linear oscillator is examined, where availability of acceleration measurements is exclusively assumed. Secondly, a field inspired implementation is presented for the torsional identification of a tall tower structure, where acceleration measurements are obtained at a high sampling rate and non-collocated GPS displacement measurements are assumed available at a lower sampling rate. A multi-rate Kalman Filter is incorporated into the analysis in order to successfully fuse data sampled at different rates.

• Wind and Structures
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• 제22권4호
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• pp.429-454
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• 2016

In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

• 한국음향학회지
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• 제24권5호
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• pp.282-293
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• 2005

음향 탄성영상법은 외부 진동을 조직에 인가하고 조직 운동을 측정함으로써 조직의 탄성을 영상화하는 초음파영상기법이다. 본 논문에서는 음향 탄성영상법에서 표면 진동자에 의해 연조직 내에 파동이 발생되는 특성과 모드패턴이암과 같은 병변 검출에 미치는 영향을 조사였다. 이를 위해 반공간, 두께가 일정한 무한평판, 그리고 유한 크기 조직에서 발생된 진동패턴을 이론과 유한요소법으로 계산하고 분석하였다. 유한 너비 진동원에 의해 조직에는 특정한 방향으로 강하게 전달되는 횡파가 발생하였으며, 그 특성은 진동자 너비, 주파수 및 진동자로부터의 거리에 의존하였다. 유한 크기 조직에서 병변의 검출가능성은 변위영상에서는 조직내 모드패턴에 큰 영향을 받았으며, 이에 비해 변형률영상에서는 모드패턴에 덜 민감하고 검출가능성도 아주 높은 것으로 나타났다.

• Steel and Composite Structures
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• 제20권3호
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• Steel and Composite Structures
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• 제37권6호
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• pp.711-731
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• 2020

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

• Steel and Composite Structures
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• 제43권1호
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.