• Journal of KSNVE
• /
• v.2 no.2
• /
• pp.99-106
• /
• 1992

The complex Young's modulus of a viscoelastic material can be obtained as a function of frequency from the measurements of relative motion between the two ends of a bar-type specimen. Non-resonance method is usually used to obtain the complex Young's modulus over wide range of frequency including resonance points, while in resonance method information at resonance frequencies only is used. However, the complex Young's modulus obtained by the non-resonance method is often unreliable in the anti-resonance frequency regions because of the measurement noise problems. In this study, the effects of the random measurement errors on estimating the complex Young's modulus are studied in the aspect of sensitivity, and how to obtain the reliable frequency region for a given measurement error level is shown. The usable frequency regions in determining the complex Young's modulus are represented by a non-dimensional parameter formed with the wave length and specimen length.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.1
• /
• pp.9-17
• /
• 2011

In this paper, the general equation of motion of damped sandwich beam with multi-viscoelastic material layer was derived based on the equation presented by Mead and Markus. The viscoelastic layer, which has characteristics of complex shear modulus, was assumed to be dominantly under shear deformation. The equation of motion of n-layered damped sandwich beam in bending could be represented by (n+3)th order ordinary differential equation. Finite element model for the n-layered damped sandwich beam was formulated and programmed using higher order shape functions. Several numerical examples were implemented to show the effects of damped material.

• Structural Engineering and Mechanics
• /
• v.43 no.1
• /
• pp.15-30
• /
• 2012

A damped Timoshenko beam element is introduced for the DOF-efficient forced vibration analysis of beam-like structures coated with viscoelastic damping layers. The rotary inertia as well as the shear deformation is considered, and the damping effect of viscoelastic layers is modeled as an imaginary loss factor in the complex shear modulus. A complex composite cross-section of structures is replaced with a homogeneous one by means of the transformed section approach in order to construct an equivalent single-layer finite element model capable of employing the standard $C^{0}$-continuity basis functions. The numerical reliability and the DOF-efficiency are explored through the comparative numerical experiments.

• Steel and Composite Structures
• /
• v.53 no.1
• /
• pp.91-101
• /
• 2024

A cost-effective fabrication method suitable for research purposes is proposed in this study. The elastic modulus of the fabricated functionally graded materials is evaluated and compared using two experimental methods: the three-point bending test and the tensile test, with a focus on the fiber volume fraction of the FGM layers. New methods for computing the elastic modulus are introduced, which are based on Castigliano's theorem and the secant modulus concept, incorporating the non-linear behavior of the material. Additionally, the mode I fracture toughness of the FGM layers is measured accurately using the three-point bending test and finite element analysis, and the influence of varying fiber volume fractions on this parameter is investigated through statistical analysis. Results indicate that while an increase in fiber volume fraction correlates with a rise in elastic modulus, it does not necessarily lead to an enhancement in mode I fracture toughness, highlighting the complex interactions between material composition and mechanical properties.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2006.05a
• /
• pp.411-414
• /
• 2006

In this paper, the forced vibration of damped composite beam with arbitrary section was analyzed. The damping material was assumed to have either complex shear modulus or complex Young???smodulus. Damped composite beam could be modeled using beam elements with less D.O.F. rather than solid elements. Finite element method for these methods was formulated and programmed using complex values. The results of frequency responses revealed good agreement with those of NASTRAN in several beam structures.

• Structural Engineering and Mechanics
• /
• v.51 no.2
• /
• pp.249-265
• /
• 2014

The mechanical characteristics of materials are very essential in structural analysis for the accuracy of structural calculations. The estimation modulus of elasticity of concrete ($E_c$), one of the most important mechanical characteristics, is a very complex area in terms of analytical models. Many attempts have been made to model the modulus of elasticity through the use of experimental data. In this study, the neuro-fuzzy (NF) technique was investigated in estimating modulus of elasticity of concrete and a new simple NF model by implementing a different NF system approach was proposed. A large experimental database was used during the development stage. Then, NF model results were compared with various experimental data and results from several models available in related research literature. Several statistic measuring parameters were used to evaluate the performance of the NF model comparing to other models. Consequently, it has been observed that NF technique can be successfully used in estimating modulus of elasticity of concrete. It was also discovered that NF model results correlated strongly with experimental data and indicated more reliable outcomes in comparison to the other models.

• Structural Engineering and Mechanics
• /
• v.64 no.1
• /
• pp.81-92
• /
• 2017

Many materials in engineering exhibit different modulus in tension and compression, which are known as bi-modulus materials. Based on the bi-modulus elastic theory, a modified semi-analytical model, by introducing a stress function, is established in this paper to study the mechanical response of a bi-modulus cylinder placed in an axisymmetric temperature field. Meanwhile, a numerical procedure to calculate the temperature stresses in bi-modulus structures is developed. It is proved that the bi-modulus solution can be degenerated to the classical same modulus solution, and is in great accordance with the solutions calculated by the semi-analytical model proposed by Kamiya (1977) and the numerical solutions calculated both by the procedure complied in this paper and by the finite element software ABAQUS, which demonstrates that the semi-analytical model and the numerical procedure are accurate and reliable. The result shows that the modified semi-analytical model simplifies the calculation process and improves the speed of computation. And the numerical procedure simplifies the modeling process and can be extended to study the stress field of bi-modulus structures with complex geometry and boundary conditions. Besides, the necessity to introduce the bi-modulus theory is discussed and some suggestions for the qualitative analysis and the quantitative calculation of such structure are proposed.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.1
• /
• pp.1-7
• /
• 2007

In this paper, the necessary and sufficient conditions for strict positive realness of the rational transfer functions directly from basic definitions in the frequency domain are studied. A new frequency domain approach is used to check if a rational transfer function is a strictly positive real or not. This approach is based on the Taylor expansion and the Maximum Modulus Principle which are the fundamental tools in the complex functions analysis. Four related common statements in the strict positive realness literature which is appeared in the control theory are discussed. The drawback of these common statements is analyzed through some counter examples. Moreover a new necessary condition for strict positive realness is obtained from high frequency behavior of the Nyquist diagram of the transfer function. Finally a more simplified and completed conditions for strict positive realness of single-input single-output linear time-invariant systems are presented based on the complex functions analysis approach.

• The Journal of the Acoustical Society of Korea
• /
• v.10 no.1
• /
• pp.30-36
• /
• 1991

Since the Complex Young's Modulus of acoustic materials is a function of frequency under a static load, a cylindrical specimen modelled by rod-like one with losses is used to determine the dynamic characteristics of materials. The specimen is excited into longitudinal vibration at its one end by shaker and at the other end, loaded by a mass corresponding to the desired static load and thus the transfer function of specimen is measured. This transfer function method is analyzed theoretically and experimentally over a frequency range of 50 Hz to 20 KHz. The analysis includes the measurability of the transfer function, the frequency range of the method and lateral motion effect.

• Korean Journal of Materials Research
• /
• v.32 no.4
• /
• pp.181-185
• /
• 2022

In this study, phase-pure titanium dioxide TiO₂ ceramics are sintered using standard high-temperature solid-state reaction technique at different temperatures (1,000, 1,100, 1,200, 1,300, 1,400 ℃). The effect of sintering temperature on the densification and impedance properties of TiO₂ ceramics is investigated. The bulk density and average grain size increase with the increase of sintering temperature. Impedance spectroscopy analysis (complex impedance Z^* and complex modulus M^*), performed in a broad frequency range from 100 Hz to 10 MHz, indicates that the TiO₂ ceramics are dielectrically heterogeneous, consisting of grains and grain boundaries. The complex impedance Z^* -plane indicates the resistance of grains of the TiO₂ ceramics increases with increasing sintering temperature, while that of grain boundaries develops in the opposing direction. The complex modulus M^*-plane shows a grain capacitance that seems to be independent of the sintering temperature, while that of the grain boundaries decreases with increasing sintering temperature. These results suggest that different sintering temperatures have effects on the microstructure, leading to changes in the impedance properties of TiO₂ ceramics.