• 제목/요약/키워드: Elastic Field

검색결과 822건 처리시간 0.031초

장파장 산란 근사를 이용한 구형 개재물 문제의 유효 탄성적 성질 (Long Wavelength Scattering Approximations for the Effective Elastic Parameters of Spherical Inclusion Problems)

  • 정현조;김진호
    • 대한기계학회논문집A
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    • 제23권6호
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    • pp.968-978
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    • 1999
  • The effective elastic properties of materials containing spherical inclusions were calculated by the elastic wave scattering theory. In the formulation additional scattering fields by the presence of random multiple scatterers that affects the effective properties were found by the single scattering approximation. In calculating the scattering fields the ensemble average on the displacements and strains inside the scatterer was found from the static approximation at long wavelength limit. The displacements were assumed to be equal to the incident field, while the strains were calculated by Eshelby's equivalent inclusion principle on the single inclusion problem. Four different models were considered and they reflected different degrees of multiple scattering effects based on the approximation introduced in the process of embedding the inclusion in the matrix. The expressions for the effective elastic constants were given in each model, and their relations to the results obtained from other scattering theory and elasticity theory were discussed. The theoretical predictions were compared with experimental results on the epoxy matrix composites containing tungsten particles of different sizes and volume fractions

Inspection of Ceramic Coatings Using Nanoindentation and Frequency Domain Photoacoustic Microscopy

  • Steen, T.L.;Basu, S.N.;Sarin, V.K.;Murray, T.W.
    • 비파괴검사학회지
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    • 제26권6호
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    • pp.390-402
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    • 2006
  • The elastic properties and thickness of mullite environmental barrier coatings grown through chemical vapor deposition (CVD) on silicon carbide substrates were measured using frequency domain photoacoustic microscopy. In this technique, extremely narrow bandwidth surface acoustic waves are generated with an amplitude modulated laser source. A photorefractive crystal based interferometer is used to detect the resulting surface displacement. The complex displacement field is mapped as a function of source-to-receiver distance in order to extract the wavelength of the surface acoustic wave at a given excitation frequency, and the phase velocity is determined. The coatings tested exhibited spatial variations in thickness and mechanical properties. The measured surface wave dispersion curves were used to extract an effective value for the elastic modulus and the coating thickness. Nanoindentation was used to validate the measurements of the effective elastic modulus. The average elastic modulus measured through the coating thickness using nanoindentation is compared to the effective modulus found using the photoacoustic system. Optical microscopy is used to validate the thickness measurements. The results indicate that the photoacoustic microscopy technique can be used to estimate the effective elastic properties in coatings exhibiting spatial inhomogeneities, potentially providing valuable feedback for the optimization of the CVD growth process.

TA-ESPI에 의한 외팔보의 탄성계수 측정 (Evaluation of Young's Modulus of a Cantilever Beam by TA-ESPI)

  • 이항서;김경석;강기수;정현철;양승필
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 2005년도 춘계학술대회 논문집
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    • pp.1115-1119
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    • 2005
  • The paper proposes the elastic modulus evaluation technique of a cantilever beam by vibration analysis based on time-average electronic speckle pattern interferometry (TA-ESPI) with non-contact and nondestructive and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of thin film are Nano indentation test, Bulge test and Micro-tensile test and so on. They each have strength and weakness in the preparation of test specimen and the analysis of experimental result. ESPI has been developed as a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at a resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI is a clue to find the resonance frequency at each vibration mode shape. And the elastic modules of test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique is able to give the elastic modulus of materials through the simple processing of preparation and analysis.

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Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory

  • Bouderba, Bachir
    • Steel and Composite Structures
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    • 제27권3호
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    • pp.311-325
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    • 2018
  • This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

An investigation of the thermodynamic effect on the response of FG beam on elastic foundation

  • Bouiadjra, Rabbab Bachir;Bachiri, Attia;Benyoucef, Samir;Fahsi, Bouazza;Bernard, Fabrice
    • Structural Engineering and Mechanics
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    • 제76권1호
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    • pp.115-127
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    • 2020
  • This study presents an analytical approach to investigate the thermodynamic behavior of functionally graded beam resting on elastic foundations. The formulation is based on a refined deformation theory taking into consideration the stretching effect and the type of elastic foundation. The displacement field used in the present refined theory contains undetermined integral forms and involves only three unknowns to derive. The mechanical characteristics of the beam are assumed to be varied across the thickness according to a simple exponential law distribution. The beam is supposed simply supported and therefore the Navier solution is used to derive analytical solution. Verification examples demonstrate that the developed theory is very accurate in describing the response of FG beams subjected to thermodynamic loading. Numerical results are carried out to show the effects of the thermodynamic loading on the response of FG beams resting on elastic foundation.

굽힘 압전 복합재료 작동기의 하중 특성 (Load Capability in a Bending Piezoelectric Composite Actuator with a Thin Sandwiched PZT Plate)

  • 우성충;구남서
    • 대한기계학회논문집A
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    • 제31권8호
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    • pp.880-888
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    • 2007
  • This article describes the load capability of bending piezoelectric actuators with a thin sandwiched PZT plate in association with the stored elastic energy induced by an increased dome height after a curing process. The stored elastic energy within the actuators is obtained via a flexural mechanical bending test. The load capability is evaluated indirectly in terms of an actuating displacement with a load of mass at simply supported and fixed-free boundary conditions. Additionally, a free displacement under no load of mass is measured for a comparison with an actuating displacement. The results reveal that an actuator with a top layer having a high elastic modulus and a low coefficient of thermal expansion exhibits a better performance than the rest of actuators in terms of free displacement as well as actuating displacement due to the formation of the large stored elastic energy within the actuator system. When actuators are excited at AC voltage, the actuating displacement is rather higher than the free displacement for the same actuating conditions. In addition, the effect of PZT ceramic softening results in a slight reduction in the resonance frequency of each actuator as the applied electric field increases. It is thus suggested that the static and dynamic actuating characteristics of bending piezoelectric composite actuators with a thin sandwiched PZT plate should be simultaneously considered in controlling the performance.

자기장과 온도장으로 재하된 강자성 판의 좌굴 (Buckling of Ferromagnetic Plates in Thermal and Magnetic Fields)

  • 이종세;왕성철
    • 한국전산구조공학회논문집
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    • 제15권4호
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    • pp.727-739
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    • 2002
  • 강자성 판의 자기-열-탄성 상호작용을 고찰하기 위하여 자기-열-탄성에 관한 일반화된 변분원리에 기초한 이론적인 모델이 제안되었다. 자탄성 선형화이론과 섭동법을 사용하여, 온도장과 자기장으로 재하된 단순지지 강자성 평판의자-탄성 좌굴과 자기-열-탄성 좌굴거동을 해석하였다. 또한 해석적인 고찰이 어려운 보다 복잡한 강자성 판의 자기-열-탄성 거동을 모사하기 위하여 비선형 유한요소 모형을 개발하였다. 이 유한요소모형을 이용하여 유한한 강자성 판의 자기-열-탄성 ?과 좌굴거동 그리고, 이에대한 온도장과 자기장의 영향에 대하여 고찰하였다.

Thermo-elastic analysis of rotating functionally graded micro-discs incorporating surface and nonlocal effects

  • Ebrahimi, Farzad;Heidar, Ebrahim
    • Advances in aircraft and spacecraft science
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    • 제5권3호
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    • pp.295-318
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    • 2018
  • This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).

Limit speeds and stresses in power law functionally graded rotating disks

  • Madan, Royal;Saha, Kashinath;Bhowmick, Shubhankar
    • Advances in materials Research
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    • 제9권2호
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    • pp.115-131
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    • 2020
  • Limit elastic speed analysis of Al/SiC-based functionally graded annular disk of uniform thickness has been carried out for two cases, namely: metal-rich and ceramic rich. In the present study, the unknown field variable for radial displacement is solved using variational method wherein the solution was obtained by Galerkin's error minimization principle. One of the objectives was to identify the variation of induced stress in a functionally graded disk of uniform thickness at limit elastic speed using modified rule of mixture by comparing the induced von-Mises stress with the yield stress along the disk radius, thereby locating the yield initiation. Furthermore, limit elastic speed has been reported for a combination of varying grading index (n) and aspect ratios (a/b).Results indicate, limit elastic speed increases with an increase in grading indices. In case of an increase in aspect ratio, limit elastic speed increases up to a critical value beyond which it recedes. Also, the objective was to look at the variation of yield stress corresponding to volume fraction variation within the disk which later helps in material tailoring. The study reveals the qualitative variation of yield stress for FG disk with volume fraction, resulting in the possibility of material tailoring from the processing standpoint, in practice.

Correcting the Elastic-modulus Error of Quartz Glass Using Digital Speckle-pattern Interferometry

  • Ziyang Song;Weixian Li;Sijin Wu;Lianxiang Yang
    • Current Optics and Photonics
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    • 제7권4호
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    • pp.337-344
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    • 2023
  • Three-point bending is the main method for measuring the elastic modulus of a thin plate. Although various displacement transducers may be used to measure the bending, these are single-point measurements, and it is difficult to eliminate the error caused by eccentric load and shear force. Error-correction models for the elastic modulus of quartz glass using digital speckle interferometry are proposed for eccentric load and shear force. First, the positional misalignment between maximum deflection and load is analyzed, and the error caused by eccentric load is corrected. Then, the additional displacement caused by shear force at different positions of the quartz glass plate is explored. The effect of shear deformation is also corrected, by measuring two points. Since digital speckle interferometry has the advantage of full-field measurement, it can simultaneously obtain deflection data for multiple points to realize error correction. Experimental results are presented to demonstrate that the proposed model can effectively correct the measurement error of the elastic modulus.