• Structural Engineering and Mechanics
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• v.28 no.5
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• pp.549-570
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• 2008

Numerical integration is an efficient approach for nonlinear dynamic analysis. In this paper, general category of the implicit integration errors will be discussed. In order to decrease the errors, Dynamic Relaxation method with modified time step (MFT) will be used. This procedure leads to an alternative algorithm which is very general and can be utilized with any implicit integration scheme. For numerical verification of the proposed technique, some single and multi degrees of freedom nonlinear dynamic systems will be analyzed. Moreover, results are compared with both exact and other available solutions. Suitable accuracy, high efficiency, simplicity, vector operations and automatic procedures are the main merits of the new algorithm in solving nonlinear dynamic problems.

• Electrical & Electronic Materials
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• v.11 no.10
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• pp.1-5
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• 1998

Complex dynamic relaxation processes of mechanical as well as dielectric character in polymeric anelastic solids are closely related through the movement of molecular chain segment in morphological structure, and the morphology can easily be modified by the treatments such as mechanical drawing or irradiation, those of which result, in turn, the complicated change on the appearance of the observed complex relaxation peak. In order to extract any meaningful understanding from the modified appearance of the peak, the relaxation peak must be resolved into the sum of the dynamic single relaxation peaks, each of which can be characterized respectively by three factors such as activation energy, magnitude of peak height and peak point temperature on the temperature dependent characteristics.

• Structural Engineering and Mechanics
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• v.34 no.1
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• pp.109-133
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• 2010

This paper addresses the modified Dynamic Relaxation algorithm, called mdDR by minimizing displacement error between two successive iterations. In the mdDR method, new relationships for fictitious mass and damping are presented. The results obtained from linear and nonlinear structural analysis, either by finite element or finite difference techniques; demonstrate the potential ability of the proposed scheme compared to the conventional DR algorithm. It is shown that the mdDR improves the convergence rate of Dynamic Relaxation method without any additional calculations, so that, the cost and computational time are decreased. Simplicity, high efficiency and automatic operations are the main merits of the proposed technique.

• Computers and Concrete
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• v.1 no.4
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• pp.371-388
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• 2004

Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.51-58
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• 2000

Dynamic relaxation method is a shape finding analysis method for flexible structures by introducing the dynamic equilibrium equation. However, it is difficult for shape finding to estimate the most appropriate values for the mass and damping on each shape because the values are random one. In this study, the unit mass, the unit damping and the principal direction stiffness are utilized to avoid the random values, and the Newmarks assumption is introduced during the dynamic analysis. By introducing variant time increment method presented, the convergence time is reduced, that is, it can be reduced the total times for analysis.

• Journal of the Korean Chemical Society
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• v.19 no.3
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• pp.149-155
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• 1975

Pivalic acid, which has a globular shape and is a plastic crystal, has been examined by means of temperature-dependent with-line proton magnetic resonance spectroscopy. Results of temperature-dependent line width, second moment, and spin-lattice relaxation time studies of pivalic acid were interpreted in terms of dynamic behavior and hydrogen bonding. The dynamic behavior consists of superimposed reorientation of the methyl groups about their three-fold axes$(C_3) and of the molecule about the central C-C bond(C_3'),$ general molecular reorientation about the center of gravity, and molecular self-diffusion. Activation energies for the motional processes have been obtained from line width measurements using the modified Bloembergen, Purcell, and Pound theory and from spin-lattice relaxation time measurements. The results were compared with the Pople-Karasz theory of fusion and the agreement was found to be poor. The discrepancy was interpreted in terms of hydrogen bonding in this molecule.

• Advances in nano research
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• v.16 no.4
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• pp.413-426
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• 2024

This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.

• Bulletin of the Korean Chemical Society
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• v.22 no.4
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• pp.337-348
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• 2001

This article gives an overview of a recently developed channel system, frit-inlet asymmetrical flow field-flow fractionation (FI-AFlFFF), which can be applied for the separation of nanoparticles, proteins, and water soluble polymers. A conventiona l asymmetrical flow FFF channel has been modified into a frit-inlet asymmetrical type by introducing a small inlet frit near the injection point and the system operation of the FI-AFlFFF channel can be made with a great convenience. Since sample components injected into the FI-AFlFFF channel are hydrodynamically relaxed, sample injection and separation processes proceed without interruption of the migration flow. Therefore in FI-AFlFFF, there is no requirement for a valve operation to switch the direction of the migration flow that is normally achieved during the focusing/relaxation process in a conventional asymmetrical channel. In this report, principles of the hydrodynamic relaxation in FI-AFlFFF channel are described with equations to predict the retention time and to calculate the complicated flow variations in the developed channel. The retention and resolving power of FI-AFlFFF system are demonstrated with standard nanospheres and protreins. An attempt to elucidate the capability of FI-AFlFFF system for the separation and size characterization of nanoparticles is made with a fumed silica particle sample. In FI-AFlFFF, field programming can be easily applied to improve separation speed and resolution for a highly retaining component (very large MW) by using flow circulation method. Programmed FI-AFlFFF separations are demonstrated with polystyrene sulfonate standards and pululans and the dynamic separation range of molecular weight is successfully expanded.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.5
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• pp.204-209
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• 2003

An elastomeric bushing is a device used in automotive suspension systems to reduce the load transmitted from the wheel to the frame of the vehicle. A bushing is an elastomeric hollow cylinder which is bonded to a solid steel shaft at its inner surface and a steel sleeve at its outer surface. The relation between the load applied to the shaft or sleeve and the relative deformation of elastomeric bushing is nonlinear and exhibits features of viscoelasticity. A load-displacement relation for elastomeric bushing is important for dynamic numerical simulations. A boundary value problem for the bushing response leads to the load-displacement relation which requires complex calculations. Therefore, by modifying the constitutive equation fur a nonlinear viscoelastic incompressible material developed by Lianis, the data fur the elastomeric bushing material was obtained and this data was used to derive the new load-displacement relation for radial response of the bushing. After the load relaxation function for the bushing is obtained from the step displacement control test, Pipkin-Rogers model was developed, Solutions were allowed fur comparison between the results of Modified Lianis model and those of the proposed model. It is shown that the proposed Pipkin-Rogers model is in very good agreement with Modified Lianis model.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.415-419
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• 2003

An elastomeric bushing is a device used in automotive suspension systems to reduce the load transmitted from the wheel to the frame of the vehicle. A bushing is an elastomeric hollow cylinder which is bonded to a solid steel shaft at its inner surface and a steel sleeve at its outer surface. The relation between the load applied to the shaft or sleeve and the relative deformation of elastomeric bushing is nonlinear and exhibits features of viscoelasticity. A load-displacement relation for elastomeric bushing is important for dynamic numerical simulations. A boundary value problem for the bushing response leads to the load-displacement relation which requires complex calculations. Therefore, by modifying the constitutive equation for a nonlinear viscoelastic incompressible material developed by Lianis, the data for the elastomeric bushing material was obtained and this data was used to derive the new load-displacement for radial response of the bushing. After the load relaxation function for the bushing is obtained from the step displacement control test, Pipkin-Rogers model was developed. Solutions were allowed for comparison between the results of Modified Lianis model and those of the proposed model. It is shown that the proposed Pipkin-Rogers model is in very good agreement with Modified Lianis model.