• Title/Summary/Keyword: Wave function

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Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation

  • Karami, Behrouz;Janghorban, Maziar;Tounsi, Abdelouahed
    • Structural Engineering and Mechanics
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    • v.70 no.1
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    • pp.55-66
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    • 2019
  • This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories

  • Yi-Wen Zhang;Hao-Xuan Ding;Gui-Lin She;Abdelouahed Tounsi
    • Geomechanics and Engineering
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    • v.33 no.4
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    • pp.381-391
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    • 2023
  • The aim of this work is to analyze and predict the wave propagation behavior of the carbon nanotube reinforced composites (CNTRC) beams within the framework of various higher order shear deformation beam theory. Using the Euler-Lagrange principle, the wave equations for CNTRC beams are derived, where the determining factor is to make the determinant equal to zero. Based on the eigenvalue method, the relationship between wave number and circular frequency is obtained. Furthermore, the phase and group velocities during wave propagation are obtained as a function of wave number, and the material properties of CNTRC beams are estimated by the mixture rule. In this paper, various higher order shear beam theory including Euler beam theory, Timoshenko beam theory and other beam theories are mainly adopted to analyze the wave propagation problem of the CNTRC beams, and by this way, we conduct a comparative analysis to verify the correctness of this paper. The mathematical model provided in this paper is verified numerically by comparing it with some existing results. We further investigate the effects of different enhancement modes of CNTs, volume fraction of CNTs, spring factor and other aspects on the wave propagation behaviors of the CNTRC beams.

Dynamic Behavior Assessment of OC4 Semi-submersible FOWT Platform Through Morison Equation

  • Chungkuk Jin;Ikjae Lee;JeongYong Park;MooHyun Kim
    • Journal of Ocean Engineering and Technology
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    • v.37 no.6
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    • pp.238-246
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    • 2023
  • This paper proposes an effective inertia coefficient (EIC) in the Morison equation for better wave-force calculations. The OC4 semi-submersible floating offshore wind turbine (FOWT) platform was considered to test the feasibility. Large diffraction at large Keulegan-Carpenter (KC) numbers and the interaction between columns can result in errors in estimating the wave force using the Morison equation with a theoretical inertia coefficient, which can be corrected by the EIC as a function of the wave period and direction. The horizontal and vertical wave forces were calculated using the Morison equation and potential theory at each column, wave period, and wave direction. The EICs of each column were then obtained, resulting in a minimal difference between the Morison inertia force and the wave excitation force by the potential theory. The EICs, wave forces, phase angles, and dynamic motions were compared to confirm the feasibility of an EIC concept under regular and random waves.

Inhomogeneous Helmholtz equation for Water Waves on Variable Depth (비균질 Helmholtz 방정식을 이용한 변동 수심에서의 파랑변형)

  • Kim, Hyo-Seob;Jang, Chang-Hwan
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.174-180
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    • 2010
  • The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

Comparison of Tunnel's Deformation by Spatially Variable Ground Motion (공간적으로 변이하는 지진파에 의한 터널의 변형 비교)

  • Kwak, Dong-Yeop;Ahn, Jae-Kwang;Park, Du-Hee
    • 한국방재학회:학술대회논문집
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    • 2008.02a
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    • pp.265-268
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    • 2008
  • The safety of a tunnel under seismic motion is most often evaluated by ovalling deformation of tunnel. This paper research about tunnel's longitudinal deformation. Because of spatial variation of seismic ground motion, the longitudinal structures like tunnel are likely to experience relative displacements along longitudinal direction. The spatially variable ground motion can be estimated by coherency function obtained empirically, and can be considered from different arrival times of ground motion. As a result of estimating tunnel's relative displacements at maximum curvature of tunnel, the displacements and curvatures estimated by coherency function affect the tunnel's safety more than different arrival times. However, if tunnel's displacements by coherency function superpose on displacements by different arrival times, the relative displacements and curvatures of tunnel will be more severe. Therefore, to estimate accurately tunnel's deformation in longitudinal direction has to consider both coherency and wave passage effects.

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Hull-form optimization of a container ship based on bell-shaped modification function

  • Choi, Hee Jong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.7 no.3
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    • pp.478-489
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    • 2015
  • In the present study, a hydrodynamic hull-form optimization algorithm for a container ship was presented in terms of the minimum wave-making resistance. Bell-shaped modification functions were developed to modify the original hull-form and a sequential quadratic programming algorithm was used as an optimizer. The wave-making resistance as an objective function was obtained by the Rankine source panel method in which non-linear free surface conditions and the trim and sinkage of the ship were fully taken into account. Numerical computation was performed to investigate the validity and effectiveness of the proposed hull-form modification algorithm for the container carrier. The computational results were validated by comparing them with the experimental data.

Effects of Extracorporeal Shock Wave Therapy with Myofascial Release Techniques on Pain, Movement, and Function in Patients with Myofascial Pain Syndrome (근막통증 증후군 환자에게 체외충격파와 근막이완술 병행 치료가 통증, 움직임, 기능에 미치는 영향)

  • Choi, Won-Jae;Nam, Eun-Jung;Kim, Hyun-Joong;Lee, Seung-Won
    • PNF and Movement
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    • v.18 no.2
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    • pp.245-254
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    • 2020
  • Purpose: The study investigated the effects of extracorporeal shock wave therapy with myofascial release techniques (ESWT+MFR) on pain, movement, and function in patients with myofascial pain syndrome. Methods: Forty participants with upper trapezius trigger points were recruited and randomly allocated to two groups: an experimental group (n = 20) and a control group (n = 20). The experimental group performed the ESWT+MFR, and the control group performed only myofascial release techniques. Each group was treated for 15 minutes, twice a week for four weeks. Pain was assessed using a visual analogue scale and a pressure pain threshold measure. Movement was assessed by cervical range of motion, and cervical and shoulder function were assessed on the Constant-Murley Scale and the Neck Disability Index before and after treatment. Results: The results indicate statistically significant improvements in the two groups on all parameters after intervention as compared to baseline (p < 0.05). As compared to the control group, the experimental group showed statistically significant improvements on the visual analogue scale and pressure pain threshold, cervical range of motion (except rotation), and on the Neck Disability Index (p < 0.05). Conclusion: The ESWT+MFR is more effective than myofascial release techniques for pain, movement, and function in patients with myofascial pain syndrome and would be clinically useful for physical therapists treating myofascial pain syndrome.

Effects of Extracorporeal Shock Wave Therapy on Ankle Function, Range of Motion, and Dynamic Balance in Patients with Chronic Ankle Instability

  • Lee, Su Bin;Kwon, Jung Won;Yun, Seong Ho
    • The Journal of Korean Physical Therapy
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    • v.34 no.3
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    • pp.91-97
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    • 2022
  • Purpose: This study investigated the short-term effectiveness of extracorporeal shock wave therapy (ESWT) on pain, the ankle instability, the ankle function, dorsiflexion range of motion (ROM), and dynamic balance in patients with chronic ankle instability (CAI). Methods: Eighteen participants were divided into an experimental (n=9) and control group (n=9). The ESWT in the experimental group was applied to the lateral collateral ligament in combination with the tibialis anterior whereas the ESWT was applied to the lateral collateral ligament of the ankle alone in the control group. Pain, the ankle instability, the ankle function, dorsiflexion ROM, and dynamic balance were measured using the Visual analog scale, Cumberland ankle instability tool, American Orthopedic Foot and Ankle Society ankle-hindfoot score, weight-bearing lunge, and Y-balance test, before and after ESWT intervention. Results: Significant interactions (group × time) and time effects were observed in the dorsiflexion ROM and dynamic balance. Bonferroni's post-hoc analysis showed that the experimental group revealed a more significant change in dorsiflexion ROM and dynamic balance than the control group. There was a significant time effect in the pain, the ankle instability, and the ankle function, but no significant interaction (group × time) was observed. Conclusion: The ESWT could improve the pain, ankle instability, ankle function, dorsiflexion ROM, and dynamic balance in patients with CAI. Furthermore, the ESWT combined with lateral ankle ligaments and tibialis anterior more improves the dorsiflexion ROM and dynamic balance.

An Effect of Parent-Child Interactions on Children's Academic Performance: the Mediating Effect of Children's Executive Function Difficulty (부모-아동 상호작용이 아동의 학업수행에 미치는 영향: 아동의 집행기능 곤란의 매개효과)

  • Choi, Hyesun
    • Journal of Korean Home Economics Education Association
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    • v.33 no.1
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    • pp.81-99
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    • 2021
  • The purpose of this study was to examine the effect of parent-child interactions on children's academic performance focusing on the mediating effect of children's executive function difficulty. The data for this study were drawn from the Panel Study on Korean Children(PSKC). The participants were 559 children of elementary school and their families from 8th wave(1st graders), 9th wave(2nd graders), and 10th wave(3rd graders) of PSKC. The data were analyzed with structural equation modeling. The results of this study were as follows. First, mother-child interaction and father-child interaction didn't have a significant direct effect on children's academic performance. Second, mother-child interaction had a significant positive indirect influences on academic performance through children's executive function difficulty. The results of this study indicated that mother-child interaction and children's executive function difficulty are important for children's academic performance.

Is ultrasound wave affected by anisotropy of trabeculae (섬유주의 이방성에 따른 초음파의 파형 변화)

  • Yoon, Won-Sok;Yoon, Young-June
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.4 no.4
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    • pp.236-241
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    • 2011
  • Mechanical properties of cancellous bone with a high porosity and cortical bone with a high fraction of solid are estimated by the measurement of ultrasonic wave propagation. The speed of sound (SOS) in ultrasonic waves is usually measured by two equations, bulk wave equation and bar wave equation. Bulk wave speed has almost same as the fast wave of Biot's theory. In this study, we examine whether the bulk wave speed is influenced by the anisotropy of bone matrix. The SOS when the bone matrix is isotropy is 0.69% faster than that when the bone matrix is transversely isotropy. We also examine if the use of bar equation is adequate for a cortical bone. In the previous paper, the bar wave speed is a function of Young's modulus or elastic coefficient tensor. In the same manner, the effect of bar wave speed to isotropic and anisotropic bone is estimated.