• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1875-1882
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• 1993

Variable thickness plates are commonly used as structural members in the majority of industrial sectors. Previous fracture mechanics researches on variable thickness plates were limited to mode I loading cases. In practice, however, cracks are usually located inclined to the loading direction. In this respect, combined mode(mode I/II) stress intensity factors $K_{I}$ and $K_{II}$ at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a slant edge crack were chosen. The parameters used in this study were dimensionless crack $length{\lambda}$, slant $angle{\alpha}$, thickness $ratio{\beta}$ and width ratio{\omega}$. Stress intensity factors were calculated by crack opening displacement(COD) and crack sliding displacement(CSD)method proposed by Ingraffea and Manu.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.701-713
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• 2012

Results pertaining to 3D investigations on the effect of the thickness on the stress fields at the crack front are presented. A 3D finite element analysis is performed using a modified single edge-notched tension specimen configuration, with an inclined crack to include mixed mode I-II. A technique to mesh the crack front (3D) with singular finite elements in ANSYS without using third party software is introduced and used in this study. The effect of the specimen thickness is explicitly investigated for six thicknesses ranging from 1 to 32 mm. In addition, three crack inclination angles, including pure Mode-I, are used to study the effect of mixed-mode I-II fracture. An attempt is made to correlate the extent of a particular stress state along the crack front to thickness. In addition, ${\sigma}_{zz}/{\nu}({\sigma}_{xx}+{\sigma}_{yy})$ contours at the crack front are presented as a useful means to analyze the stress state.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.20 no.9
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• pp.771-775
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• 2007

In this study, in order to develop low temperature sintering ceramics for thickness vibration mode multilayer piezoelectric transformer, $PbTiO_3$ system ceramics were fabricated using $Na_2CO_3,\;Li_2CO_3,\;MnO_2\;and\;Bi_2O_3$ as sintering aids and their dielectric and piezoeletric properties were investigated according to the amount of $Bi_2O_3$ addition. At the sintering temperature of $900^{\circ}C\;and\;Bi_2O_3$ addition of 0.1 wt%, density, grain size, thickness vibration mode eletromechanical coupling factor($k_t$), thickness vibration mode mechanical quality factor($Q_{mt}$) and dielecteic constant(${\varepsilon}_r$) showed the optimum value of $6.94g/cm^3,\;2.413{\mu}m$, 0.497, 3,162 and 209, respectively, for thickness vibration mode multilayer piezoelectric transformer application.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.335-342
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• 2005

Using higher order Mindlin plates and piezoelectric materials, eigenvalue problems are considered. Since piezoelectric crystal resonators produce a proper amount of electric signal for a thickness-shear frequency, the objective is to decouple the thickness-shear mode from the others. Design variables are the bulk material densities corresponding to the mass of masking plates for electrodes. The design sensitivity expressions for the thickness-shear frequency and mode shape vector are derived using direct differentiation method(DDM). Using the developed design sensitivity analysis (DSA) method, we formulate a topology optimization problem whose objective function is to maximize the thickness-shear component of strain energy density at the thickness-shear mode. Constraints are the allowable volume and area of masking plate. Numerical examples show that the optimal design yields an improved mode shape and thickness-shear energy.

• Journal of the korean Society of Automotive Engineers
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• v.15 no.2
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• pp.112-120
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• 1993

Variable thickness plates are commonly encountered in the majority of mechanical/structural components of industrial applications. And, as a result of the unsymmetry of the structure or the load and the anisoptropy of the materials, the cracks in engineering structures are generally subjected to combined stresses. In spite of considerable practical interest, however, a few fracture mechanics study on combined mode crack in a variable thickness plate have carried out. In this respect, combined mode 1/3 stress intensity factors $K_{1}$ and $K_{3}$ at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a central slant crack were chosen. the parameters used in this study were dimensionless crack length .lambda. crack slant angle .alpha, thickness ratio .betha. and width ratio .omega. Stress intensity factors were calculated by crack opening displacement(COD) and crack tearing displacement(CTD) method proposed by Ingraffea and Manu. The effect of thickness ratio .betha. on $K_{1}$ is relatively great in comparison to $K_{3}$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.2
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• pp.198-203
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• 2010

In this paper, study on the mode characteristics analysis of the SH-EMAT (shear horizontal, electromagnetic acoustic transducer) waves for evaluating the thickness reduction in plates such as corrosion and friction is presented. Noncontact methods for ultrasonic wave generation and detection have been a great concern and highly demanded due to their capability of wave generation and reception on surface of high temperature or on rough surface. Mode identification of the SH-EMAT wave is carried out in an aluminum plate with thinning defects using time frequency analysis method such as wavelet transform, compared with theoretically calculated group velocity dispersion curve. The changes of various wave features such as the amplitude and the time-of-flight have been observed and the correlations with the thickness reduction have been investigated. Firstly, experiments have been conducted to confirm that it is possible to selectively generate and receive specific desired SH modes. These modes have then been analyzed to select the parameters that are sensitive to the thickness change. The results show that the mode cutoff and the time-of-flight changes are feasible as key parameters to evaluate the thickness reduction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2541-2549
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• 2002

In order to study the vibration characteristics of fluid-structure interaction problem, two rectangular plates coupled with bounded fluid were investigated. Experimental modal analyses were carried out to extract the modal parameters of the system. Additionally. finite element modal analyses performed using a commercial computer code, ANSYS. The FEM solutions were compared with the experimental solutions to verify the finite element model. As a result, the comparison between the experiment and FEM results showed excellent agreement. The transverse vibration modes, in-phase and out-of-phase, were observed alternately in the fluid-coupled system. The thickness effect of the plates on the fluid-coupled natural frequencies and mode shapes was investigated for two different cases with the identical thickness and the unequal thickness. It was found that the coupled natural frequencies increase with the thickness for the identical plates regardless of the mode phase. The experimental and the finite element analysis results showed that the out-of-phase mode shapes were deviated from the symmetrical mode shapes in the plate transverse direction fur the unequal plate thickness case.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.11 no.10
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• pp.855-860
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• 1998

This paper presents a new structure for a piezoelectric transformer, operating in thickness extensional vibration mode. Modified $PbTiO_3$ family ceramics were used for the piezoelectric transformer, because it was a material with large anisotropy between elecromechanical coupling factors $K_t$ and $K_p$ . The size of piezoelectric transformer was 20mn long, 20mm wide and 3.1mm thick. The second harmonic resonant frequency of thickness extensional vibration mode was 0.72MHz at loading resistance 100[$\omega$], And Voltage gin of piezoelectric ceramics showed 0.53 at resonant frequency of sencond thickness extensional vibration mode.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.1
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• pp.8-14
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• 2000

In this paper, three adaptive sliding mode control algorithms, which self-tune both the sliding mode gain and the boundary layer thickness, are proposed. The first algorithm uses a gain adaptation rule is combined with the boundary layer thickness adaptatioin rule to satisfy the sliding condition. In the third algorithm, the computation burden of the second algorithm is reduced further, and therefore no extra cost is required for real-time implementation. Due to the mixed sliding mode gain and the boundary layer thickness adaptation scheme, the tracking error and the chattering of the control input can be reduced greatly.

• Journal of the Optical Society of Korea
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• v.12 no.2
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• pp.112-117
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• 2008

Single-mode propagation conditions of X-ray waveguides are investigated by numerical calculations in order to understand the importance of waveguide design parameters, such as core thickness and the optical constants of waveguide materials, on the transmission and coherence properties of the waveguide. The simulation code for mode analyzing is developed based on a numerical solution of the parabolic wave equation. The initial boundary value problem is solved numerically using a finite-difference scheme based on the Crank-Nicolson scheme. The E-field intensities in a core layer are calculated at an X-ray energy of 8.0 keV for air and beryllium(Be) core waveguides with different cladding layers such as Pt, Au, W, Ni and Si to determine the dependence on waveguide materials. The highest E-field intensity radiated at the exit of the waveguide is obtained from the Pt cladded beryllium core with a thickness of 20 nm. However, the intensity from the air core waveguide with Pt cladding reaches 64% of the Be-Pt waveguide. The dependence on the core thickness, which is the major parameter used to generate a single mode in the waveguide, is investigated for the air-Pt, and Be-Pt waveguides at an X-ray energy of 8.0 keV. The mode profiles at the exit are shown for the single mode at a thickness of up to 20 nm for the air-Pt and the Be-Pt waveguides.