• Steel and Composite Structures
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• 제48권3호
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Korea-Australia Rheology Journal
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• 제19권4호
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• pp.211-219
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• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

• Structural Engineering and Mechanics
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• 제62권5호
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• pp.607-618
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• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• 한국전산구조공학회논문집
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• 제18권3호
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• pp.321-332
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• 2005

본 논문에서는 축대칭 형상의 점탄성 구조물이 정적 하중을 받을 때에 대한 시간영역에서의 유한요소해법의 정식화 과정을 제시한다. 또한, 여러 가지 경계조건을 갖는 점탄성 중공구나 원통 문제들의 변위나 응력 이론해들을 탄성-점탄성 상응원리를 이용하여 유도하고 제시한다. 이때 점탄성 재료는 부피변형이 탄성적이고 전단변형은 3요소로 구성된 표준선형 고체처럼 거동한다고 가정한다. 구대칭, 축대칭 및 평면변형률 유한요소모텔을 이용한 수치결과들을 유도된 이론해들과 비교하여 제시된 유한요소해법과 이론해들의 타당성과 정확성을 보인다.

• Structural Engineering and Mechanics
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• 제40권6호
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• 한국소음진동공학회논문집
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• 제21권5호
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• pp.430-436
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• 2011

The purpose of this study is to analyze the vibration and sound generation characteristics of the sandwich panel. Two thick panels were assumed to be separated by a compliant viscoelastic core. The transverse vibration induced by an external impact was analyzed using the Rayleigh-Ritz method. For applying arbitrary boundary condition of the panels, the edges were assumed to be supported by the translational and rotational springs. The beam functions were used as the trial functions. The effect of the boundary condition and viscoelastic core on the resulting vibration characteristics was investigated. The radiated sound power was analyzed using the proposed numerical model and the Rayleigh integral. The dynamic properties of the core and the mass-stiffness-mass resonance frequency had significant influence on the impact sound.

• 한국전산구조공학회논문집
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• 제13권1호
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• pp.97-103
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• 2000

이 논문에서는, 반도체 칩과 리드프레임을 결합하는 과정에서 점탄성 접착제층에 발생하는 잔류응력 문제를 다루고 있다. 접착제층은 “열유동단순”거동을 한다고 가정하였다. 접착제층에서의 응력들은 경계요소법을 사용하여 조사하였다. 매우 큰 응력 구배가 계면 모서리에서 발생하는데, 그러한 응력들은 국부 항복을 일으키거나, 칩과 리드프레임의 박리를 야기시킬 수 있음을 보여주고 있다.

• 반도체디스플레이기술학회지
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• 제9권3호
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• pp.35-39
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• 2010

Interfacial stress singularity induced in an analysis model consisting of the polymeric thin film and the elastic substrate has been investigated using the boundary element method. The interfacial singular stresses between the viscoelastic thin film and the elastic substrate subjected to a uniform moisture ingression are investigated for the case of a small interfacial edge crack. It is assumed that moisture effects are assumed to be analogous to thermal effects. Then, the overall stress intensity factor for the case of a small interfacial edge crack is computed. The numerical procedure does not permit calculation of the limiting case for which the edge crack length vanishes.

• 대한수학회논문집
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• 제38권3호
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Structural Engineering and Mechanics
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• 제5권6호
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• pp.705-713
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• 1997

The residual thermal stresses at the interface corner between the elastic fiber and the viscoelastic matrix of a two-dimensional unidirectional laminate due to cooling from cure temperature down to room temperature were studied. The matrix material was assumed to be thermorheologically simple. The time-domain boundary element method was employed to investigate the nature of stresses on the interface. Numerical results show that very large stress gradients are present at the interface corner and this stress singularity might lead to local yielding or fiber-matrix debonding.