• Structural Engineering and Mechanics
• /
• v.88 no.2
• /
• pp.189-200
• /
• 2023

Silicate glass is usually a brittle and plate-like material, and it is difficult to measure the elastic modulus by the traditional method. This paper develops a test method for the glass elastic modulus based on the fundamental frequency of the cantilever beam with an elastic support and a free end. The method installs the beam-type specimen on a semi-rigid support to form an elastic support-free end beam. The analytic solution of the stiffness coefficients of the elastic support is developed by the fundamental frequency of the two specimens with known elastic modulus. Then, the glass elastic modulus is measured by the fundamental frequency of the specimens. The method significantly improves the measurement accuracy and is suitable for the elastic modulus with the beam-type specimen whether the glass is homogeneous or not. Several tests on the elastic modulus measurement are conducted to demonstrate the reliability and validity of the test method.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.647-655
• /
• 2006

We consider the applications of modulus to the boundary behavior of meromorphic functions in connection with the singularities. The proofs are based on the method of modulus. The relations between the moduli and the logarithmic capacities shall be introduced and we have shown that the conformal capacity is related to the modulus.

• Structural Engineering and Mechanics
• /
• v.77 no.1
• /
• pp.137-149
• /
• 2021

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.16 no.11 s.116
• /
• pp.1158-1164
• /
• 2006

For the description of the elastic properties of linear objects a convenient parameter is the ratio of the stress to the strain, a parameter called the Young's modulus of the material. Young's modulus can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material. Conventional method for estimating Young's modulus measured the ratio of stress to corresponding strain below the proportional limit of a material using a tensile testing machine. But the method needs precision specimens and expensive equipment. In this paper, we proposed method for estimating Young's modulus using accelerometer. The basic idea comes from that the wave velocity is different as the Young's modulus. To obtain Young's modulus, a group velocity is obtained. It is difficult to measure group velocity. This is because plate medium has a dispersive characteristics which has different wave speed as frequency. In this paper, we used Wigner-Ville distribution to measure group velocity. To verify the proposed method, steel and acryl plate experiments have been performed. Experimental results show that the proposed method is powerful for estimating Young's modulus.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.1027-1032
• /
• 2007

For the description of the elastic properties of linear objects a convenient parameter is the ratio of the stress to the strain, a parameter called the Young's modulus of the material. Young's modulus can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material. Conventional method for estimating Young's modulus measured the ratio of stress to corresponding strain below the proportional limit of a material using a tensile testing machine. But the method needs precision specimens and expensive equipment. In this paper, we proposed method for estimating Young's modulus using accelerometer. The basic idea comes from that the wave velocity is different as the Young's modulus. To obtain Young's modulus, a group velocity is obtained. It is difficult to measure group velocity. This is because plate medium has a dispersive characteristics which has different wave speed as frequency. In this paper, we used Wigner-Ville distribution to measure group velocity. To verify the proposed method, steel and acryl plate experiments have been performed. Experimental results show that the proposed method is powerful for estimating Young's modulus.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2010.09a
• /
• pp.1190-1200
• /
• 2010

A method was developed to determine resilient modulus for crushed rock-soil mixtures whose usage has been increased recently without engineering specifications. The method is based on the subtle different modulus called nonlinear dynamic modulus and was lately implemented in residual soils and engineered crushed-stones. Hereby. the same method was expanded to crushed rock-soil mixtures containing as large grain diameter as 300mm. The method utilize field direct-arival tests for the determination of maximum Young's modulus, and a large scale free-free resonant column test, which is recently developed to is capable to test as large grain diameter as 25mm, for modulus reduction curves. The prediction model of resilient modulus was evaluated for crushed rock-soil mixtures of a highway construction site at Gimcheon, Korea.

• Smart Structures and Systems
• /
• v.20 no.4
• /
• pp.473-481
• /
• 2017

This study suggests a simple, convenient and non-destructive method for investigation of the Young's modulus detection in stepped shafts which only utilizes the first-order resonant frequency in flexural mode and dimensions of structures. The method is based on the impulse excitation technique (IET) to pick up the fundamental resonant frequencies. The standard Young's modulus detection formulas for rectangular and circular cross-sections are well investigated in literatures. However, the Young's modulus of stepped shafts can not be directly detected using the formula for a beam with rectangular or circular cross-section. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formula to detect Young's modulus of stepped shafts. The numerical simulation performed by finite element method (FEM) to obtain enough simulation data for RSM analysis. After analysis and calculation, the relationship of flexural resonant frequencies, dimensions of stepped shafts and Young's modulus is obtained. Numerical simulations and experimental investigations show that the IET method can be used to investigate Young's modulus in stepped shafts, and the FEM simulation and RSM based IET formula proposed in this paper is applicable to calculate the Young's modulus in stepped shaft. The method can be further developed to detect mechanical parameters of more complicated structures using the combination of FEM simulation and RSM.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.769-784
• /
• 2013

We consider the modulus-based successive overrelaxation method for the linear complementarity problems from the discretization of Black-Scholes American options model. The $H_+$-matrix property of the system matrix discretized from American option pricing which guarantees the convergence of the proposed method for the linear complementarity problem is analyzed. Numerical experiments confirm the theoretical analysis, and further show that the modulus-based successive overrelaxation method is superior to the classical projected successive overrelaxation method with optimal parameter.

• The Journal of the Acoustical Society of Korea
• /
• v.31 no.6
• /
• pp.399-409
• /
• 2012

In this paper we propose a method for measuring the shear modulus of an ultrasound soft tissue phantom using an acoustic radiation force. The proposed method quantitatively determines the shear modulus based on the rise time of a displacement induced by an acoustic radiation force at the focal point of a focused ultrasound beam. The shear wave speed and shear modulus obtained from the proposed method and a shear wave propagation method were compared to verify the validity of the proposed method. In the shear wave propagation method, the shear modulus is first computed by measuring the propagating speed of a shear wave induced in a phantom by a limited-diffraction transmit field, and then was compared to that obtained with the proposed method in an ultrasound data acquisition system calibrated based on the first computed shear modulus. The relative errors between the two methods were found to be 4% for shear wave speed and less than 9% for shear modulus, confirming the usefulness of the proposed method.

• Structural Engineering and Mechanics
• /
• v.26 no.5
• /
• pp.499-516
• /
• 2007

An experimental method denoted as Impulse Method is proposed as a cost-effective non-destructive technique for the on-site evaluation of concrete elastic modulus in existing structures: on the basis of Hertz's quasi-static theory of elastic impact and with the aid of a simple portable testing equipment, it makes it possible to collect series of local measurements of the elastic modulus in an easy way and in a very short time. A Hypothesis Testing procedure is developed in order to provide a statistical tool for processing the data collected by means of the Impulse Method and assessing the possible occurrence of significant variations in the elastic modulus without exceeding some prescribed error probabilities. It is based on a particular formulation of the renowned sequential probability ratio test and reveals to be optimal with respect to the error probabilities and the required number of observations, thus further improving the time-effectiveness of the Impulse Method. The results of an experimental investigation on different types of plain concrete prove the validity of the Impulse Method in estimating the unknown value of the elastic modulus and attest the effectiveness of the proposed Hypothesis Testing procedure in identifying significant variations in the elastic modulus.