• Title/Summary/Keyword: Elastic wave theory

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Impact of spar-nacelle-blade coupling on the edgewise response of floating offshore wind turbines

  • Dinh, Van-Nguyen;Basu, Biswajit;Nielsen, Soren R.K.
    • Coupled systems mechanics
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    • v.2 no.3
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    • pp.231-253
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    • 2013
  • The impact of spar-nacelle-blade coupling on edgewise dynamic responses of spar-type floating wind turbines (S-FOWT) is investigated in this paper. Currently, this coupling is not considered explicitly by researchers. First of all, a coupled model of edgewise vibration of the S-FOWT considering the aerodynamic properties of the blade, variable mass and stiffness per unit length, gravity, the interactions among the blades, nacelle, spar and mooring system, the hydrodynamic effects, the restoring moment and the buoyancy force is proposed. The aerodynamic loads are combined of a steady wind (including the wind shear) and turbulence. Each blade is modeled as a cantilever beam vibrating in its fundamental mode. The mooring cables are modeled using an extended quasi-static method. The hydrodynamic effects calculated by using Morison's equation and strip theory consist of added mass, fluid inertia and viscous drag forces. The random sea state is simulated by superimposing a number of linear regular waves. The model shows that the vibration of the blades, nacelle, tower, and spar are coupled in all degrees of freedom and in all inertial, dissipative and elastic components. An uncoupled model of the S-FOWT is then formulated in which the blades and the nacelle are not coupled with the spar vibration. A 5MW S-FOWT is analyzed by using the two proposed models. In the no-wave sea, the coupling is found to contribute to spar responses only. When the wave loading is considered, the coupling is significant for the responses of both the nacelle and the spar.

Isogeometric Optimal Design of Kelvin Lattice Structures for Extremal Band Gaps (극대화된 밴드갭을 갖는 켈빈 격자 구조의 아이소-지오메트릭 최적 설계)

  • Choi, Myung-Jin;Oh, Myung-Hoon;Cho, Seonho;Koo, Bonyong
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.4
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    • pp.241-247
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    • 2019
  • A band gap refers to a certain frequency range where the propagation of mechanical waves is prohibited. This work focuses on engineering three-dimensional Kelvin lattices having external band gaps at low audible frequency ranges using a gradient-based design optimization method. Elastic wave propagation in an infinite periodic lattice is investigated by employing the Bloch theorem. We model the ligaments using a shear-deformable beam model obtained by consistent linearization in a geometrically exact beam theory. For a given lattice topology, we enlarge band gap sizes by controlling the configuration of the beam neutral axis and cross-section thickness that are smoothly parameterized by B-spline basis functions within the isogeometric analysis framework.

Laboratory Evaluation of Soil Permeability for Sand Using Biot's Acoustic Wave Propagation Theory (Biot 음향 전파 이론을 이용한 실내 사질 시료의 투수계수 산정)

  • Kim, Jin-Won;Song, Chung-Rak
    • Journal of the Korean Geotechnical Society
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    • v.24 no.8
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    • pp.5-12
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    • 2008
  • Biot proposed the frequency dependent formulation for the propagation of elastic waves in saturated media based on the coupled theory mixtures. Based on Biot theory, a special frequency called 'the characteristic frequency' contains unique information of the permeability of soils. The characteristic frequency is measured from I/Q (inverse quality factor) versus frequency curve by an acoustic sweep test, and the permeability of soils is computed from Biot equation. In this paper, laboratory tests are performed at The University of Mississippi using a large test box. The measured characteristic frequency is consistently obtained at 3500 Hz for mortar sands. The computed permeability of mortar sands based on Biot equation turned out 2.01 $10^{-4}m/sec$, while the permeability from the laboratory constant head test turned out 1.49 $10^{-4}m/sec$. This paper addresses the theoretical background and experimental procedure of this technique.

Small scale computational vibration of double-walled CNTs: Estimation of nonlocal shell model

  • Asghar, Sehar;Khadimallah, Mohamed Amine;Naeem, Muhammad N.;Ghamkhar, Madiha;Khedher, Khaled Mohamed;Hussain, Muzamal;Bouzgarrou, Souhail Mohamed;Ali, Zainab;Iqbal, Zafar;Mahmoud, S.R.;Algarni, Ali;Taj, Muhammad;Tounsi, Abdelouahed
    • Advances in concrete construction
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    • v.10 no.4
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    • pp.345-355
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    • 2020
  • In this paper, vibration characteristics of double-walled carbon nanotubes (CNTs) is studied based upon nonlocal elastic shell theory. The significance of small scale is being perceived by developing nonlocal Love shell model. The wave propagation approach has been utilized to frame the governing equations as eigen value system. The influence of nonlocal parameter subjected to diverse end supports has been overtly analyzed. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of changing mechanical parameter Poisson's ratio has been investigated in detail. The dominance of boundary conditions via nonlocal parameter is shown graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

Extended Slip-Weakening Model and Inference of Rupture Velocity (Slip-Weakening 모델의 확장과 단층 파열속도의 추정)

  • Choi, Hang;Yoon, Byung-Ick
    • Journal of the Earthquake Engineering Society of Korea
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    • v.24 no.5
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    • pp.219-232
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    • 2020
  • The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of fmax given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, fc, and source-controlled cut-off frequency, fmax, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from fmax/fc and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent fmax/fc; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and fmax/fc is quite similar to Kolmogorov's hypothesis on a similarity in the theory of isotropic turbulence.

An Analytical Solution of Dynamic Responses for Seabed under Flow and Standing Wave Coexisting Fields (흐름과 완전중복파와의 공존장하에서 해저지반내 동적응답의 해석해)

  • Lee, Kwang-Ho;Kim, Dong-Wook;Kim, Do-Sam;Kim, Tae-Hyung;Kim, Kyu-Han;Jeon, Jong-Hyeok
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.27 no.2
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    • pp.118-134
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    • 2015
  • An analytical solution of dynamic responses for seabed in shallow, finite and infinite thicknesses has been developed under flow and standing wave coexisting field at a constant water depth condition. To do this, based on the Biot's consolidation theory, the seabed is assumed as a porous elastic media with the assumptions that pore fluid is compressible and Darcy law governs the flow. The developed analytical solution is compared with the previous results and is verified. Using the analytical solution the deformation, pore pressure, effective and shear stresses of seabed are examined under various given values of flow velocity, incident wave period and seabed thickness. From this study, it is confirmed that the seabed response is quite different depending on consideration of flow, which causes changing period and length of incident and reflection waves.

Development of the Predicted Model for the HMA Dynamic Modulus by using the Impact Resonance Testing and Universal Testing Machine (충격공진실험과 만능재료시험기에 의한 아스팔트 공시체의 동탄성계수 예측 모델 개발)

  • Kim, Do Wan;Kim, Dong-Ho;Mun, Sungho
    • International Journal of Highway Engineering
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    • v.16 no.3
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    • pp.43-50
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    • 2014
  • PURPOSES : The dynamic modulus can be determined by applying the various theories from the Impact Resonance Testing(IRT) Method. The objective of this paper is to determine the best theory to produce the dynamic modulus that has the lowest error as the dynamic modulus data obtained from these theories(Complex Wave equation Resonance Method related to either the transmissibility loss or not, Dynamic Stiffness Resonance Method) compared to the results for dynamic modulus determined by using the Universal Testing Machine. The ultimate object is to develop the predictive model for the dynamic modulus of a Linear Visco-Elastic specimen by using the Complex Wave equation Resonance Method(CWRM) came up for an existing study(S. O. Oyadiji; 1985) and the Optimization. METHODS : At the destructive test which uses the Universal Testing Machine, the dynamic modulus results along with the frequency can be used for determining the sigmoidal master curve function related to the reduced frequency by applying Time-Temperature Superposition Principle. RESULTS : The constant to be solved from Eq. (11) is a value of 14.13. The reduced dynamic modulus obtained from the IRT considering the loss factor related to the impact transmissibility has RMSE of 367.7MPa, MPE of 3.7%. When the predictive dynamic modulus model was applied to determine the master curve, the predictive model has RMSE of 583.5MPa, MPE of 3.5% compared to the destructive test results for the dynamic modulus. CONCLUSIONS : Because we considered that the results obtained from the destructive test had the most highest source credibility in this study, the dynamic modulus data obtained respectively from DSRM, CWRM were compared to the results obtained from the destructive test by using th IRT. At the result, the reduced dynamic modulus derived from DSRM has the most lowest error.

A Study on the Ground Input Motion for Seismic Analysis of Structures (구조물의 내진 해석을 위한 지반 입력운동의 산정에 관한 연구)

  • Lee, In-Moo;Song, Tae-Won;Huh, Young
    • Geotechnical Engineering
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    • v.5 no.3
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    • pp.5-18
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    • 1989
  • The ground input motions used for seismic analysis of structures are studied in this paper, The one-dimensional wave propagation theory, the simple transfer function by Elsabee and Morray, and the finite element method that can account for the effect of scattering field, respectively, are used to get the ground input motions, and the results by these methods are compared among others. The responses of structures are also computed by both finite element analysis and elastic half space analysis, using the ground input motions obtained by the different methods mentioned above, and the computed results are analyzed. In addition, the parameteric study Is performed to analyze the effect of the increase of soil stiffness on the response of structures, and on that of the ground input motions. The responses of structures obtained are compared with the results obtained using the Building Code on seismic analysis for structures in Korea. The results of this study show that the ground input motions obtained without considering the effect of scattering field was 2 times larger than those with scattering effect, concluding that the effect of scattering field may not be ignored when obtains the ground input motion.

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Application of Soil Factor on the Aseismic Design (내진 설계시 지반계수의 합리적 적용에 대한 연구)

  • 이인모;임종석
    • Geotechnical Engineering
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    • v.9 no.1
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    • pp.7-20
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    • 1993
  • The first Korean earthquake resistant design code was enacted in 1988. In the code, the soil factor which takes into account both the soil amplification factor and the soil -structare interaction effect is divided into three groups : soil factor, 5 : 1.0, 1.2 and 1.5. In order to assist in choosing the soil factors appropriately in the earthquake resistant design, the local site effects on the based shear force induced by earthquakes are considered in depth for typical soil conditions in Korea. The depth of the alluvial and/or weathered zone is usually not deep and the fresh rock is found at depth shallower than 20 meters, and even at about 10 meters around Seoul. One dimensional wave propagation theory and the elastic half space method are used to obtain the soil -structure interaction effect as well as the soil amplification effect. The kinematic interaction effect due to scattering of waves by pile foundation is also considered. Finally, the soil factor is recommended for each soil condition from loose state to dense, and also from shallow soil depth to deep, so that the designer can choose the factor with-out difficulty.

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Prediction of Driving Stresses in Piles (항타응력 추정)

  • 진병익;황정규
    • Geotechnical Engineering
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    • v.3 no.1
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    • pp.25-38
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    • 1987
  • The prediction of driving stresses in piles is necessary for optimum selection of driving hammers, better design of precast piles, enact assessment of drivabilities and complete description of piling specifications. However, the existing pile-driving formulas based on the theory of Newtonian impact have some defects and shortcomings; the numerical method by the wave equation analysis using electronic computer usually Involves various uncertainties and limitations which can yield erroneous outcomes because it employs soil constants of which the nature is unknown as essential parameters and ignores the effect of residual stresses set up in the pile .after each hammer blow; and the electronic measuring technique needs extra time and expense. The method developed herein is presented for the purpose of giving field engineers a reliable and convenient analytical procedure for the prediction of driving stresses along the full length of pile using the most effetive parameters without resort to electronic computer. This method is based on the fundamental mechanics of stress waves in elastic rods and takes into account the effect of residual stresses induced by reversed friction in piles.

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