• 충청수학회지
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• 제31권1호
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• pp.137-149
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• 2018

In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.

• Structural Engineering and Mechanics
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• 제23권2호
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• International Journal of Ocean System Engineering
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• 제1권1호
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.607-614
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• 2019

The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.

• Coupled systems mechanics
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• 제8권1호
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• pp.39-53
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• 2019

Here in this investigation, a two-dimensional thermoelastic problem of thick circular plate of finite thickness under fractional order theory of thermoelastic diffusion has been considered in frequency domain. The effect of frequency in the axisymmetric thick circular plate has been depicted. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature change and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect frequency has been shown on the various components.

• Coupled systems mechanics
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• 제9권6호
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• pp.521-538
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• 2020

The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solid with new modified couple stress theory without energy dissipation and with two temperatures in frequency domain. The time harmonic sources and Hankel transform technique have been employed to find the general solution to the field equations.Concentrated normal force, normal force over the circular region, thermal point source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of angular frequency on the resulted quantities.

• Structural Engineering and Mechanics
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• 제82권2호
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• pp.225-232
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• 2022

In this paper, the physical neutral surface concept is applied to study the wave propagation of functionally graded (FG) circular plate, the wave equation is derived by Hamiltonian variational principle and the first-order shear deformation plate model. Then, we convert the equations to dimensionless equations. The exact solution of wave propagation problem is obtained by Laplace integral transformation, the first order Hankel integral transformation and the zero order Hankel integral transformation. The results obtained by the current model are very close to those obtained in the existing literature, which indicates the correctness and reliability of this study. Moreover, the effects of the functionally graded index parameters and pore volume fraction on the wave propagation are also discussed in detail.

• Coupled systems mechanics
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• 제11권3호
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• pp.199-215
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• 2022

The present paper deals with the axisymmetric deformation in homogeneousisotropic thermoelastic solid with two temperatures, with and without energy dissipation using modified couple stresstheory. The effect of energy dissipation and two temperature isstudied due to the concentrated normalforce, normalforce overthe circularregion, thermal pointsource and thermalsource over the circular region. The Laplace and Hankel transform techniques have been used to find the solution to the problem. The displacement components, conductive temperature distribution, stress components and couple stress are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. Effects of two temperature and energy dissipation on the conductive temperature,stress components and couple stress are depicted graphically.

• 대한수학회보
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• 제60권5호
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• pp.1253-1263
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• 2023

Let 𝓤⁺ be the class of analytic functions f such that ${\frac{z}{f(z)}}$ has real and positive coefficients and f^-1 be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for f, as well as, sharp estimates of the second and the third Hankel determinant for f and f^-1. We also show that the Zalcman conjecture holds for functions f from 𝓤⁺.

• Coupled systems mechanics
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• 제12권3호
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• pp.261-276
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• 2023

This article is an application of new modified couple stress thermoelasticity without energy dissipation in association with two-temperature theory. The upper and lower surfaces of the plate are subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform techniques. The analytical expressions of displacement components, conductive temperature, stress components and couple stress are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of two temperature is shown on the various components.