• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.1
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• pp.9-17
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• 2016

The elastic modulus of a 3D-printed Kelvin foam plate is investigated by measuring the acoustic wave velocity of 1 MHz ultrasound. An isotropic tetrakaidecahedron foam with 3 mm unit cell is designed and printed layer upon layer to fabricate a Kelvin foam plate of 14 mm thickness with a 3D CAD/printer using ABS plastic. The Kelvin foam plate is completely filled with paraffin wax for impedance matching, so that the acoustic wave may propagate through the porous foam plate. The acoustic wave velocity of the foam plate is measured using the time-of-flight (TOF) method and is used to calculate the elastic modulus of the Kelvin foam plate based on acousto-elasticity. Finite element method (FEM) and micromechanics is applied to the Kelvin foam plate to calculate the theoretical elastic modulus using a non-isotropic tetrakaidecahedron model. The predicted elastic modulus of the Kelvin foam plate from FEM and micromechanics model is similar, which is only 3-4% of the bulk material. The experimental value of the elastic modulus from the ultrasonic method is approximately twice as that of the numerical and theoretical methods because of the flexural deformation of the cell edges neglected in the ultrasonic method.

• Advances in concrete construction
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• v.9 no.3
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• pp.301-312
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• 2020

This research deals with the study of the orthotropic vibrational features of single-walled carbon nanotubes according to Kelvin's model and to check the accuracy of the models, the results have been compared with earlier modeling/simulations. Obtaining rough approximations of the natural frequencies of CNTs using continuum equations are still a common procedure, even at high harmonics. The effects of different physical and material parameters on the fundamental frequencies are investigated for zigzag and chiral single-walled carbon nanotubes invoking Kelvin's theory. By using nonlocal Kelvin's model, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes (SWCNTs) have been calculated. The influence of frequencies with nonlocal parameters and bending rigidity are investigated in detail for these tubes. Computer software MATLAB is utilized for the frequencies of SWCNTs and current results shows a good stability with comparison of other studies.

• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.6
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• pp.474-482
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• 2016

A Kelvin foam plate - widely used in the energy and transport industries as a lightweight structural material - was examined to estimate its Young's modulus using ultrasound. An isotropic tetrakaidecahedron foam structure was designed in SolidWorks and printed using 3D printer with an ABS plastic material. The 3D printed foam structure was used to build a foam plate with a 14 mm thickness ($50mm{\times}100mm$ in size) for the ultrasonic test. The Kelvin foam plate, a significantly porous medium, was completely filled with paraffin wax to enable the ultrasound to penetrate through the porous medium. The acoustic wave velocity of the wax-filled Kelvin foam was measured using the time of flight (TOF) method. Furthermore, the elastic modulus of the Kelvin foam was estimated based on an elastic structural model developed in this study. The Young's modulus of the produced Kelvin foam was observed to be approximately 3.4% of the bulk value of the constituent material (ABS plastic). This finding is consistent with experimental and theoretical results reported by previous studies.

• Coupled systems mechanics
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• v.7 no.2
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• pp.141-162
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• 2018

This work presents a novel model for analysis of the loading rate influence onto structure response. The model is based on the principles of nonlinear system dynamics, i.e., consists of a system of nonlinear differential equations. In contrast to classical linearized models, this one comprises mass and loading as integral parts of the model. Application of the Kelvin and the Maxwell material models relates the novel formulation to the existing material formulations. All the analysis is performed on a proprietary computer program based on Wolfram Mathematica. This work can be considered as an extended proof of concept for the application of the nonlinear solid model in material response to dynamic loading.

• East Asian mathematical journal
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• v.32 no.3
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• pp.355-364
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• 2016

In this paper, we study exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Kang [3]. Energy decay rate are obtained by the exponential stability of solutions by using multiplier technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.2
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• pp.85-91
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Gannesh C. Gorain [1]. Energy decay rates are obtained by the exponential stability of solutions by using multiplier technique.

• Advances in nano research
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• v.8 no.4
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• pp.307-322
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• 2020

In this article, free vibration of double-walled carbon nanotubes (DWNT) based on nonlocal Kelvin's model have been investigated. For this purpose, a nonlocal Kelvin's model is established to observe the small scale effect. The wave propagation is employed to frame the governing equations as eigenvalue system. The influence of nonlocal parameter subjected to different end supports has been overtly examined. The new set of inner and outer tubes radii investigated in detail against aspect ratio. The influence of boundary conditions via nonlocal parameter is shown graphically. Due to small scale effect fundamental frequency ratio decreases as length to diameter ratio increases. Small scale effect becomes negligible on all end supports for the higher values of aspect ratio. With the smaller inner tube radius double-walled CNT behaves more sensitive towards nonlocal parameter. The results generated furnish the evidence regarding applicability of nonlocal model and also verified by earlier published literature.

• Steel and Composite Structures
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• v.47 no.6
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• pp.743-757
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• 2023

In this paper, the dynamic response of a simply-supported composite sandwich plate with a viscoelastic core based on the Golla-Hughes-McTavish (GHM) viscoelastic model is investigated analytically. The formulation is developed using the three-layered sandwich panel theory. Hamilton's principle has been employed to derive the equations of motion. Since classical models, like kelvin-voigt and Maxwell models, cannot express a comprehensive description of the dynamic behavior of viscoelastic material, the GHM method is used to model the viscoelastic core of the plate in this research. The main advantage of the GHM model in comparison with classical models is the consideration of the frequency-dependent characteristic of viscoelastic material. Identification of the material parameters of GHM mini-oscillator terms is an essential procedure in applying the GHM model. In this study, the focus of viscoelastic modeling is on the development of GHM parameters identification. For this purpose, a new method is proposed to find these constants which express frequency-dependent behavior characterization of viscoelastic material. Natural frequencies and loss factors of the sandwich panel based on ESL and three-layered theories in different geometrics are described at 30℃ and 90℃; also, the comparisons show that obtained natural frequencies are grossly overestimated by ESL theory. The argumentations of differences in natural frequencies are also illustrated in detail. The obtained results show that the GHM model presents a more accurate description of the plate's dynamic response by considering the frequency dependency behavior of the viscoelastic core.

• 유체기계공업학회:학술대회논문집
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• 2005.12a
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• pp.825-828
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• 2005

Experimental and numerical study was done to confirm the effect of the flexible tube in pipeline on transient flow oscillation. Experiment was made for a pipeline with and without deformable flexible tube using a single pumping system of main stainless pipe. The wave speeds of main pipe and flexible tube were calculated from the pipe material properties, structures, and boundary conditions. Time dependent pressure fluctuations were calculated for the pipeline using the simple and the Kelvin-Voigt viscoelastic models for the deformation of main pipe and flexible tube. Pressure calculated by the Kelvin-Voigt viscoelastic model showed better agreement with measured one than pressure by the simple model. Experimental and numerical results show that the maximum pressure as well as amplitude of pressure oscillation was decreased by inserting short flexible tube in pipeline. Hence, inserted short flexible tube to pipeline was found to be effective for the suppression of strong pressure oscillation. Moreover, the wave speed in pipe was discussed based on numerical and experimental results.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.305-320
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• 2024

We consider a mathematical model which describes the quasistatic contact of electro-viscoelastic rod with an obstacle. We use a modified Kelvin-Voigt viscoelastic constitutive law in which the elasticity operator is nonlinear and locally Lipschitz continuous, taking into account the piezoelectric effect of the material. We model the contact with a general damped response condition. We establish a local existence and uniqueness result of the solution by using arguments of time-dependent nonlinear equations and Schauder's fixed-point theorem and obtain a global existence for small enough data.