• 제목/요약/키워드: elastic media

검색결과 142건 처리시간 0.026초

Analytical solutions for density functionally gradient magneto-electro-elastic cantilever beams

  • Jian, Aimin;Ding, Haojiang
    • Smart Structures and Systems
    • /
    • 제3권2호
    • /
    • pp.173-188
    • /
    • 2007
  • The general solution for two-dimensional magneto-electro-elastic media in terms of four harmonic displacement functions is proposed analytically. The expressions of specific solutions of magneto-electro-elastic plane problems with specific body forces are derived. Finally, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally gradient media, two kinds of beam problems with body forces depending only on the z or x coordinate are solved by the trial-and-error method.

유한차분법을 이용한 3차원 지진파 전파 모의 (Three-Dimensional Simulation of Seismic Wave Propagation in Elastic Media Using Finite-Difference Method)

  • 강태섭
    • 한국지진공학회:학술대회논문집
    • /
    • 한국지진공학회 2000년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2000
    • /
    • pp.81-88
    • /
    • 2000
  • The elastic wave equation is solved using the finite-difference method in 3D space to simulate the seismic wave propagation. It is based on the velocity-stress formulation of the equation of motion on a staggered grid. The nonreflecting boundary conditions are used to attenuate the wave field close to the numerical boundary. To satisfy the stress-free conditions at the free-surface boundary, a new formulation combining the zero-stress formalism with the vacuum one is applied. The effective media parameters are employed to satisfy the traction continuity condition across the media interface. With use of the moment-tensor components, the wide range of source mechanism parameters can be specified. The numerical experiments are carried out in order to test the applicability and accuracy of this scheme and to understand the fundamental features of the wave propagation under the generalized elastic media structure. Computational results show that the scheme is sufficiently accurate for modeling wave propagation in 3D elastic media and generates all the possible phases appropriately in under the given heterogeneous velocity structure. Also the characteristics of the ground motion in an sedimentary basin such as the amplification, trapping, and focusing of the elastic wave energy are well represented. These results demonstrate the use of this simulation method will be helpful for modeling the ground motion of seismological and engineering purpose like earthquake hazard assessment, seismic design, city planning, and etc..

  • PDF

On the elastic parameters of the strained media

  • Guliyev, Hatam H.
    • Structural Engineering and Mechanics
    • /
    • 제67권1호
    • /
    • pp.53-67
    • /
    • 2018
  • The changes of parameters of pressure and velocity of propagation of elastic pressure and shear waves in uniformly deformed solid compressible media are studied within the nonclassically linearized approach (NLA) of nonlinear elastodynamics to create a new theoretical basis of the geomechanical interpretation of various groups of geophysical observational and experimental data. The cases of small and large deformations are considered while their describing by various elastic potentials, i.e., problems considering the physical and geometric nonlinearity. Convenient analytical formulae are obtained to calculate the indicated parameters in the deformed isotropic media within the nonclassical linear and nonlinear solution in the NLA. Specific numerical experiments are conducted in case of overall compression of various materials. It is shown that the method (generally accepted in the studies of mechanics of standard constructional materials) of additional linearization (relative to the pressure parameter) in the basic correlations of the NLA introduces substantial quantitative and qualitative errors into the results at significant preliminary deformations. The influences of the physical and geometric nonlinearity on the studied characteristics of the medium are large in various materials and differ qualitatively. The contribution of nonlinear components to the values of the considered parameters prevails over linear components at large deformations. When certain critical values of compression deformations in the medium are achieved, elastic waves with actual velocity cannot propagate in it. The values of the critical deformations for pressure and shear waves differ within different elastic potentials and variants of the theory of initial deformations.

Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory

  • Abdelrahman, Alaa A.;Shanab, Rabab A.;Esen, Ismail;Eltaher, Mohamed A.
    • Steel and Composite Structures
    • /
    • 제44권2호
    • /
    • pp.255-270
    • /
    • 2022
  • This manuscript illustrates the dynamic response of nanoscale carbon nanotubes (CNTs) embedded in an elastic media under moving load using doublet mechanics theory, which not considered before. CNTs are modelled by Timoshenko beam theory (TBT) and a bottom to up modelling nano-mechanics is simulated by doublet mechanics theory to capture the size effect of CNTs. To explore the influence of the CNTs configurations on the dynamic behaviour, both armchair and zigzag configurations are considered. The governing equations of motion and the associated boundary conditions are obtained using the Hamiltonian principle. The Navier solution methodology is applied to obtain the solutions for both orientations. Free vibration and forced response under moving loads are considered. The accuracy of the developed procedure is verified by comparing the obtained results with available previous algorithms and good agreement is observed. Parametric studies are conducted to demonstrate effects of doublet length scale, CNTs configurations, moving load velocities as well as the elastic media parameters on the dynamic behaviours of CNTs. The developed procedure is supportive in the design and manufacturing of MEMS/NEMS made from CNTs.

Wave Propagation Analysis in Inhomogeneous Media by Using the Fourier Method

  • Kim, Hyun-Sil;Kim, Jae-Seung;Kang, Hyun-Joo;Kim, Sang-Ryul
    • The Journal of the Acoustical Society of Korea
    • /
    • 제17권3E호
    • /
    • pp.35-42
    • /
    • 1998
  • Transient acoustic and elastic wave propagation in inhomogeneous media are studied by using the Fourier method. It is known that the fourier method has advantages in memory requirements and computing speed over conventional methods such as FDM and FEM, because the Fourier method needs less grid points for achieving the same accuracy. To verify the proposed numerical scheme, several examples having analytic solutions are considered, where two different semi-infinite media are in contact along a plane boundary. The comparisons of numerical results by the Fourier method and analytic solutions show good agreements. In addition, the fourier method is applied to a layered half-plane, in which an elastic semi-infinite medium is covered by an elastic layer of finite thickness. It is showed how to derive the analytic solutions by using the Cagniard-de Hoop method. The numerical solutions are in excellent agreements with analytic results.

  • PDF

이방성 재료에서의 탄성파 전파 과정에 대한 시뮬레이션 (Simulation of Elastic Wave Propagation in Anisotropic Materials)

  • 김영환;이승석
    • 비파괴검사학회지
    • /
    • 제17권4호
    • /
    • pp.227-236
    • /
    • 1997
  • 탄성파 전파 과정의 정량적인 이해와 그 가시화는 결함 탐지는 물론이고, 재료의 물성 평가에 매우 중요하다. 대상 재료가 이방성을 지닐 경우에 탄성파 전파 과정은 복잡해져서 전파 과정의 해석 및 가시화 작업은 탄성파를 이용하는 결함 탐지 및 재질 평가에서는 필수적이다. 이방성 재료에서는 탄성파의 속도가 방향에 따라서 달라짐은 물론이고, 위상 속도와 군 속도의 방향이 어긋나서 파면이 진행하는 방향과 에너지가 진행하는 방향이 달라진다(beam skewing 효과). 특히 복합재료와 같이 이방성이 큰 재료에서는 이 효과가 매우 크게 나타나므로 탄성파를 이용한 시험 결과를 해석하고자 할 때에는 반드시 전파 과정을 이해해야 한다. 이방성 재료에 대해 해석적인 접근에는 한계가 있어서 유한차분법(finite difference method: FDM)과 같은 수치 해석 방법이 유용하게 사용되고 있다. 본 연구에서는 탄성파 전파 과정을 해석할 수 있는 2차원 FDM 프로그램을 개발하고, 이를 이용하여 이방성 재료에서의 탄성파 전파에 대한 전산 시뮬레이션 결과를 비교 분석한다.

  • PDF

Effect of fractional order on energy ratios at the boundary surface of elastic-piezothermoelastic media

  • Kumar, Rajneesh;Sharma, Poonam
    • Coupled systems mechanics
    • /
    • 제6권2호
    • /
    • pp.157-174
    • /
    • 2017
  • In the present investigation reflection and transmission of plane waves at an elastic half space and piezothermoelastic solid half space with fractional order derivative is discussed. The piezothermoelastic solid half space is assumed to have 6 mm type symmetry and assumed to be loaded with an elastic half space. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and Cadmium Selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy across the interface is verified. Some cases of interest are also deduced from the present investigation.

彈性支持를 받는 四角多孔板의 荷重分布係數에 관한 연구 (A Study on the Load Distribution Factor in the Perforated Square Plate with Elastic Support at Four Corners)

  • 임정식;이영신
    • 대한기계학회논문집
    • /
    • 제13권4호
    • /
    • pp.563-571
    • /
    • 1989
  • 본 연구에서는 이들 무시된 영향을 고려하여 하중작용점에서의 하중분포계수 를 구하여, 이 하중분포계수에 의해 위치에 따라 실제와 가까운 하중을 가하므로서 보다 엄밀한 판의 해석을 할 수 있도록 제시하였다.

Axisymmetric analysis of multi-layered transversely isotropic elastic media with general interlayer and support conditions

  • Lee, J.S.;Jiang, L.Z.
    • Structural Engineering and Mechanics
    • /
    • 제2권1호
    • /
    • pp.49-62
    • /
    • 1994
  • Based on the transfer matrix approach and integral transforms, a solution method is developed for the stress analysis of axisymmetrically loaded transversely isotropic elastic media with generalized interlayer and support conditions. Transfer functions (Green's functions in the transformed domain) are obtained in explicit integral form. For several problems of practical interest with different loading and support conditions, solutions are worked out in detail. For the inversion operation, an efficient technique is introduced to remedy the slow convergence of numerical integrals involving oscillating functions. Several illustrative examples are considered and numerical results are presented.

Fourier 방법을 이용한 지진파 전달해석 (An Analysis of Seismic Wave Propagation by Using the Fourier Method)

  • 김현실
    • 한국지진공학회:학술대회논문집
    • /
    • 한국지진공학회 1998년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Spring 1998
    • /
    • pp.399-406
    • /
    • 1998
  • Transient acoustic and elastic wave propagation in inhomogeneous media are studied by using the Fourier method. To verify the proposed numerical scheme, several examples having analytic solutions are considered, where two different semi-infinite media are in contact along a plane boundary. The comparisons of numerical results by the Fourier method and analytic solutions show good agreements. In addition, the Fourier method is applied to a layered half-plane, in which an elastic semi-infinite medium is covered by an elastic layer of finite thickness. It is showed how to derive the analytic solutions by using the Cagniard-de Hoop method. The numerical solutions are in excellent agreements with analytic results.

  • PDF