• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Computers and Concrete
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• v.24 no.5
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• pp.423-436
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• 2019

Design equations to evaluate the bursting force in a post-tensioned anchorage zone have been introduced in many design codes, and one equation in AASHTO LRFD is widely used. However, this equation may not determine the bursting force exactly because it was designed on the basis of two-dimensional numerical analyses without considering various design parameters such as the duct hole and shape of the bearing plate. To improve the design equation, modification of the AASHTO LRFD design equation was considered. The behavior of the anchorage zone was investigated using three-dimensional linear elastic finite element analysis with design parameters such as bearing plate size and diameter of sheath hole. Upon the suggestion of a modified design equation for evaluating the bursting force in an anchorage block with a rectangular anchorage plate (Kim and Kwak 2018), additional influences of design parameters that could affect the evaluation of bursting force were investigated. An improved equation was introduced for determining the bursting force in an anchorage block with a circular anchorage plate, using the same procedure introduced in the design equation for an anchorage block with a rectangular anchorage plate. The validity of the introduced design equation was confirmed by comparison with AASHTO LRFD.

• Architectural research
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• v.13 no.1
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• pp.17-24
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• 2011

Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

• International Journal of Korean Welding Society
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• v.1 no.2
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• pp.18-22
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• 2001

The stress intensity factor has been calculated theoretically for the cracked plate subjected to remote normal stress and reinforced with a plate by symmetric seam welding. The singular integral equation was derived based on displacement compatibility condition between the cracked plate and the reinforcement plate, and solved by means of Erdogan and Gupta's method. The results from the derived equation for stress intensity factor were compared with FEM solutions and seems to be reasonable. The reinforcement effect gets better as welding line is closer to the crack and the stiffness ratio of the cracked plate and the reinforcement plate becomes larger.

• Transactions of the Korean Society of Automotive Engineers
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• v.20 no.1
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• pp.141-146
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• 2012

Aluminum alloys have been used with various thicknesses suitable for light weight of structure. It is known that the thickness effect of material is an important factor affecting fatigue crack propagation under constant fatigue stress condition. In this work, we presented the behavior of fatigue crack propagation in thin plate compared to thick plate Al 2024-T3 alloy with referred thickness effect in a correlative equation determined by the shape factor and the loading factor. We chose two factors that are used in the correlative equation with considering that the experiments were carried out under a constant fatigue stress condition. The thickness ratio of thin plate compared to thick plate and the equivalent effective stress intensity factor ratio depending on thickness were chosen as shape and loading factors. A correlative equation is utilized to determine the equivalent effective stress intensity factor range of thin plate and identify the degree of increasing phenomenon of fatigue life in thin plate compared to thick plate.

• Wind and Structures
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• v.25 no.1
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• pp.25-38
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• 2017

This study investigates the dynamic analysis of a transversely isotropic thin plate. The plate is made of hyperelastic John's material and its constitutive law is obtained by taken the Frechect derivative of the highlighted energy function with respect to the geometry of deformation. The three-dimensional equation governing the motion of the plate is expressed in terms of first Piola-Kirchhoff's stress tensor. In the reduction to an equivalent two-dimensional plate equation, the obtained model generalizes the classical plate equation of motion. It is obtained that the plate under consideration exhibits harmonic force within its planes whereas this force varnishes in the classical plate model. The presence of harmonic forces within the planes of the considered plate increases the natural and resonance frequencies of the plate in free and forced vibrations respectively. Further, the parameter characterizing the transversely isotropic structure of the plate is observed to increase the plate flexural rigidity which in turn increases both the natural and resonance frequencies. Finally, this study reinforces the view that non-classical models of problems in elasticity provide ample opportunity to reveal important phenomena which classical models often fail to apprehend.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.321-338
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• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Journal of Advanced Marine Engineering and Technology
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• v.26 no.1
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• pp.48-58
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• 2002

There is a purpose of this study for the proposal of the optimum technique utilized for the vibration design initial step. The stiffened plate structure for the ship hull is made for analysis model. To begin with, dynamic characteristics of stiffened plate structure is analysed using FEM. Main vibrational mode of the structure is decided in the analytical result of FEM. The simplified equation on the natural frequency of the main vibrational mode is induced. Next, sensitivity analysis is carried out using the simplified equation, and rate of change of dynamic characteristics is calculated. Then, amount of design variable is calculated using this sensitivity value and optimum structural modification method. The change of natural frequency is made to be an objective function. Thickness of panel, cross section moment of stiffener and girder become a design variable. The validity of the optimization method using simplified equation is examined. It is shown that the result effective in the optimum modification for natural frequency of the stiffened plate structure.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.731-738
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• 2001

The conventional techniques for the prediction of natural frequency are often used to estimate the floor vibration. However. the predicted frequency differs significantly from the measured one since the predicted equation is not able to proper1y treat various material type. Transformation of slab section is necessary to predict natural frequency of composite deck plate, and this effort is complicated due to the various shape of each deck plate. In this study, a new simplified methodology to transform slab section is proposed, which treats effective depth as the distance from the top of a concrete topping to neutral axis of each deck plate. Finally proposed equation with fairly reasonable result compared to the measured values is obtained. based on the modification of vibration equation from LRFD theory. This efforts enhance errors in predicting frequency up to 15％.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.