• Advances in aircraft and spacecraft science
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• v.2 no.1
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.63-74
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• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Advances in nano research
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• v.7 no.2
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• pp.89-98
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• 2019

In this work, the thermal buckling characteristics of zigzag single-walled boron nitride (SWBNNT) embedded in a one-parameter elastic medium modeled as Winkler-type foundation are investigated using a nonlocal first-order shear deformation theory (NFSDT). This model can take into account the small scale effect as well as the transverse shear deformation effects of nanotubes. A closed-form solution for nondimensional critical buckling temperature is obtained in this investigation. Further the effect of nonlocal parameter, Winkler elastic foundation modulus, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia on the critical buckling temperature are being investigated and discussed. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of boron nitride nanotubes.

• Journal of the Korean Society of Radiology
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• v.82 no.6
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• pp.1556-1564
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• 2021

Purpose This study aimed to apply MR elastography (MRE) to achieve in vivo evaluation of the elastic properties of thigh muscles and validate the feasibility of quantifying the elasticity of normal thigh muscles using MRE. Materials and Methods This prospective study included 10 volunteer subjects [mean age, 32.5 years, (range, 23-45 years)] who reported normal activities of daily living and underwent both T2-weighted axial images and MRE of thigh muscles on the same day. A sequence with a motion-encoding gradient was used in the MRE to map the propagating shear waves in the muscle. Elastic properties were quantified as the shear modulus of the following four thigh muscles at rest; the vastus medialis, vastus lateralis, adductor magnus, and biceps femoris. Results The mean shear modulus was 0.98 ± 0.32 kPa and 1.00 ± 0.33 kPa for the vastus medialis, 1.10 ± 0.46 kPa and 1.07 ± 0.43 kPa for the vastus lateralis, 0.91 ± 0.41 kPa and 0.93 ± 0.47 kPa for the adductor magnus, and 0.99 ± 0.37 kPa and 0.94 ± 0.32 kPa for the biceps femoris, with reader 1 and 2, respectively. No significant difference was observed in the shear modulus based on sex (p < 0.05). Aging consistently showed a statistically significant negative correlation (p < 0.05) with the shear modulus of the thigh muscles, except for the vastus medialis (p = 0.194 for reader 1 and p = 0.355 for reader 2). Conclusion MRE is a quantitative technique used to measure the elastic properties of individual muscles with excellent inter-observer agreement. Age was consistently significantly negatively correlated with the shear stiffness of muscles, except for the vastus medialis.

• Journal of Ocean Engineering and Technology
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• v.36 no.4
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• pp.217-231
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• 2022

Reinforced polyurethane foam (R-PUF), a material for liquefied natural gas cargo containment systems, is expected to have different mechanical properties depending on its stacking position of foaming as the glass fiber reinforcement of R-PUF sinks inside R-PUF under the influence of gravity. In addition, since R-PUF is not a homogeneous material, it is also expected that the coordinate direction within this material has a great correlation with the mechanical properties. So, this study was conducted to confirm this correlation with the one between the mechanical properties and the stacking position. In particular, in this study, R-PUF of 3 different densities (130, 170, and 210 kg/m³) was used, and tensile, compression, and shear tests of this material were performed under 5 temperatures. As a result of the tests, it was confirmed that the strength and modulus of elasticity of the material increased as the temperature decreased. Specifically, the strength and modulus of elasticity in the Z direction, which was the lamination direction, tended to be lower than those in the other directions. Finally, the strength and elastic modulus of different specimens of the material found at the bottom of their lamination compared to the specimens with these properties found at positions other than their lamination bottom were evaluated. Further analysis confirmed that as the temperature decreased, hardening of R-PUF occurred, indicating that the strength and modulus of elasticity increased. On the other hand, as the density of R-PUF increased, a sharp increase in strength and elastic modulus of R-PUF was observed.

• Steel and Composite Structures
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• v.48 no.2
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• pp.131-143
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• 2023

The CFRP bar was used to achieve more ductile and durable headed-stud shear connectors in composite components. Three series of push-out tests were firstly conducted, including specimens reinforced with pure steel fibers, steel and CFRP bars. The distributed stress was measured by the commercial PPP-BOTDA (Pre-Pump-Pulse Brillouin optical time domain analysis) optical fiber sensor with high spatial resolution. A series of numerical analyses using non-linear FE models were also made to study the shear force transfer mechanism and crack response based on the test results. Test results show that the CFRP bar increases the shear strength and stiffness of the large diameter headed-stud shear connection, and it has equivalent reinforcing effects on the stud shear capacity as the commonly used steel bar. The embedded CFRP bar can also largely improve the shear force transfer mechanism and decrease the tensile stress in the transverse direction. The parametric study shows that low content steel fibers could delay the crack initiation of slab around the large diameter stud, and the CFRP bar with normal elastic modulus and the standard reinforcement ratio has good resistance to splitting crack growth in headed stud shear connectors.

• Steel and Composite Structures
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• v.39 no.1
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• pp.95-107
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• 2021

In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.1-18
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• 2020

Present research is aimed to investigate the free vibration behavior of functionally graded (FG) nanocomposite conical panel reinforced by graphene platelets (GPLs) on the elastic foundation. Winkler-Pasternak elastic foundation surrounds the mentioned shell. For each ply, graphaene platelets are randomly oriented and uniformly dispersed in an isotropic matrix. It is assumed that the Volume fraction of GPLs reainforcement could be different from layer to layer according to a functionally graded pattern. The effective elastic modulus of the conical panel is estimated according to the modified Halpin-Tsai rule in this manuscript. Cone is modeled based on the first order shear deformation theory (FSDT). Hamilton's principle and generalized differential quadrature (GDQ) approach are also used to derive and discrete the equations of motion. Some evaluations are provided to compare the natural frequencies between current study and some experimental and theoretical investigations. After validation of the accuracy of the present formulation and method, natural frequencies and the corresponding mode shapes of FG-GPLRC conical panel are developed for different parameters such as boundary conditions, GPLs volume fraction, types of functionally graded and elastic foundation coefficients.

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.4
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• pp.295-306
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• 2010

Contrary to an intact rock, the jointed rock mass shows strain-dependent deformation characteristics (elastic modulus and damping ratio). The maximum elastic modulus of a rock mass can be obtained from an elastic wave-based exploration in a small strain level and applied to seismic analyses. However, the assessment and application of the non-linear characteristics of rock masses in a small to medium strain level ($10^{-4}{\sim}0.5%$) have not been carried out yet. A non-linear dynamic analysis module is newly developed for FLAC3D to simulate strain-dependent shear modulus degradation and damping ratio amplification characteristics. The developed module is verified by analyzing the change of the Ricker wave propagation. Strain-dependent non-linear characteristics are obtained from disks of cored samples using a rock mass dynamic testing apparatus which can evaluate wave propagation characteristics in a jointed rock column. Using the experimental results and the developed non-linear dynamic module, seismic analyses are performed for the intersection of a shaft and an inclined tunnel. The numerical results show that vertical and horizontal displacements of non-linear analyses are larger than those of linear analyses. Also, non-linear analyses induce bigger bending compressive stresses acting on the lining. The bending compressive stress concentrates at the intersection part. The fundamental understanding of a strain-dependent jointed rock mass behavior is achieved in this study and the analytical procedure suggested can be effectively applied to field designs and analyses.

• Composites Research
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• v.31 no.5
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• pp.276-281
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• 2018

In this paper, elastic behavior of woven fabric composites with various fiber yarn structure were predicted through a theoretical calculation model. A representative volume elements (RVE) that can represent the mechanical properties of the woven composites were selected and crimp angle of the weave yarn was defined by several sinusoidal functions. The effective material properties of the woven composite such as young's modulus, shear modulus and poisson's ratio was predicted by classical laminate theory (CLT). The fiber volume fractions were calculated according to the shape and pattern (plain, twill weave) of the fiber yarn, and the elastic behavior of each woven composite was obtained through a theoretical calculation model. Also, to verify the theoretical predictions, woven composite specimens of plain and twill weave were fabricated by vacuum assisted resin transfer molding (VARTM) process and then mechanical test was conducted. As a results, a good correlation between theoretical and experimental results for the elastic behavior of woven composites could be achieved.