• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.2
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• pp.208-216
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• 2009

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.4
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• pp.39-48
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• 2021

In this paper, an in-plane deformation measuring system using a dual-beam shear interferometer was constructed to measure the in-plane deformation of the measuring object. The in-plane deformation of the object was quantitatively measured according to the load and surface treatment conditions of the object. We also verified the reliability of the proposed technique by simultaneously performing the technique with an electronic speckle pattern interferometry system (ESPI), which is another laser application measurement technology. Digital shearography directly measures the deformation gradient or strain components and has the advantages of being full-field, noncontact, highly sensitive, and robust. It offers a much higher measurement sensitivity compared with noncoherent measurement methods and is more robust and applicable to in-field tests.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.247-269
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• 2020

A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.5
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• pp.793-800
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• 2006

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Transactions of Materials Processing
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• v.3 no.2
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• pp.229-242
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• 1994

An approximate procedure based on a combination micro-macroscopic theories of plasticity for predicting the crystallographic texture during the plane strain forming of fcc metals has been developed. This procedure is divided into two steps. Firstly, we extract the history of the deformation gradient at all deformed elements with a elasto-plastic finite element method using isotropic plasticity model. Secondly, we use this deformation gradient history to predict the crystallographic deformation texture based on the Bishop-Hill theory. Renouard and Wintenberger' method is chosen for selecting the active slip systems. The predicted results have been compared with reported experimental results. The calculated results are in good agreement with their results.

• Steel and Composite Structures
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• v.21 no.4
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• pp.949-962
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• 2016

The braking hose in the automotive hydraulic braking system exhibits the complicated anisotropic large deformation while its movable end is moving along the cyclic path according to the steering and bump/rebound motions of vehicle. The complicated large deformation may cause not only the interference with other adjacent automotive parts but also the durability problem resulting in the fatal microcraking. In this regard, the design of high-durable braking hose with the interference-free layout becomes a hot issue in the automotive industry. However, since it has been traditionally relied on the cost-/time-consuming trial and error experiments, the cost- and time-effective optimum design method that can replace the experiment is highly desirable. Meanwhile, the hose deformed configuration and fatigue life are different for different hose cyclic paths, so that their characteristic investigation becomes an important preliminary research subject. As a preliminary step for developing the optimum design methodology, we in this study investigate the hose deformed configuration and the fatigue life for four representative hose cyclic paths.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.1107-1124
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• 2016

Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

• Journal of Magnetics
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• v.16 no.3
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• pp.220-224
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• 2011

Die-upset magnets from a mechanically-milled Pr(Co,In)$_5$-type alloy are known to have a peculiar texture; the easy magnetization axis (c-axis) is perpendicular to the pressing direction. This peculiar texture is thought to be linked closely to the anisotropic mechanical properties of Pr(Co,In)$_5$-type hexagonal compounds. The hardness of the Pr(Co,In)$_5$-type crystal was measured using selectively grown grains in an annealed $Pr_{17}Co_{82}In_1$ alloy button, and the crystallographic orientation was determined by observing the magnetic domain image. The hardness (549 VHN) on the plane with a 'cogwheel'-type domain image was significantly higher than that (510 VHN) on the plane with a 'cigar'-type domain image, indicating that the inter-layer bonding force between the (000l) basal planes is stronger than that between the (hki0) planes. This suggests that the most probable slip plane is the (hki0) plane parallel to the c-axis. During die-upsetting of the Pr(Co,In)$_5$-type alloys the deformation proceeds by (hki0) plane slip, and the c-axis rotates to ultimately become oriented perpendicular to the pressing direction. It is proposed that the peculiar texture in the die-upset Pr(Co,In)$_5$-type magnets is probably developed by slip deformation of the (hki0) plane of the Pr(Co,In)$_5$-type grains.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.27-28
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• 2006

This study performs to investigate deformation of wall thinning pipe and to find out the position of the internal thinning defect by shearography. Shearography is one of optical methods those have applied to nondestructive testing (NDT) and the strain/stress analysis. This technique has the merit of the directly measuring the first derivative of displacement, sensitivity of which can be adjusted by the handling of optical component in interferometer. In this paper, we tested carbon steel pipe locally wall thinned and loaded internal pressure and developed the nondestructive out-of-plane deformation analysis technique fur internal thinning defect of elbow by shearography. From the results, it was confirmed that this technique is proper to the practical application on the pipe line system with internal defect.