• Journal of the Society of Naval Architects of Korea
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• v.33 no.2
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• pp.85-95
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• 1996

An iterative Kantorovich method is presented for the vibration analysis of rectangular isotopic and orthotropic thick plates. Mindlin plate characteristic functions are derived in general forms by the Kantorovich method initially starting with Timoshenko beam functions consistent with the boundary conditions of the plate. Through numerical calculations of natural pairs, i.e. natural frequencies and corresponding modes, and dynamic responses of appropriate models, it has been confirmed that the presented method is superior to the Rayleigh-Ritz analysis or the FEM analysis in accuracy and computational efficiency.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.7 s.100
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• pp.836-842
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• 2005

Nonlinear dynamic characteristics of active piezolaminated plates are investigated with respect to the thermopiezoelastic behaviors. For largely deformed structures with small strain, the incremental total Lagrangian formulation is presented based on the virtual work principles. A multi-field layer-wise finite shell element is proposed for assuring high accuracy and non-linearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap-through phenomena, the implicit Newmark's scheme with the Newton-Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. The bifurcate thermal buckling of symmetric structural models is first investigated and the characteristics of piezoelectric active responses are studied for finding snap-through piezoelectric potentials and the load-path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap-through phenomena with several attractors are proved using the nonlinear time responses for various initial conditions and damping loss factors. Present results show that thermopiezoelastic snap-through phenomena can result in the difficulty of buckling and postbuckling control of intelligent structures.

• Geomechanics and Engineering
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• v.16 no.2
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Computational Structural Engineering
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• v.11 no.1
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• pp.227-235
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• 1998

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross-sections and with arbitrary boundary conditions was developed and reported by D. H. Kim in 1974. This method has been developed for two-dimensional problems including the laminated composite plates and was proved to be very effective for the plates with arbitrary boundary conditions and irregular sections. In this paper, the result of application of this method to the building slabs with passive and active control devices is presented. Finite difference method is used to obtain the deflection influence surfaces needed for this vibration analysis in this paper. The influence of the modulus of the foundation on the natural frequency is thoroughly studied.

• Journal of the Society of Naval Architects of Korea
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• v.46 no.2
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• pp.155-164
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• 2009

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.1
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• pp.18-24
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• 2003

A three node triangular element with drilling rotations incorporating improved higher-order zig-zag theory(HZZT) is developed to analyze the vibration of pretwisted composite plates with embedded damping layer. Shear force matching conditions are enforced along the interfaces between the embedded damping patch and the border patch by matching the shear forces of the embedded damping patch to the shear forces of the adjacent border patch. The natural frequencies and modal loss factors are calculated for cantilevered pretwisted composite blade with damping core with the present triangular element, and compared to experiments and MSC/NASTRAN using a layered combination of plate and solid elements.

• Smart Structures and Systems
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• v.29 no.3
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• pp.395-420
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• 2022

A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.

• Coupled systems mechanics
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• v.13 no.2
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• pp.95-113
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• 2024

In this paper, we will analyse the thermo-elastic behavior of the plate element of a structure arranged in a climatically aggressive environment (extreme temperature), we use a refined four-variable thick plate theory to take the shear effect into consideration, the proposed theory less computationally expensive and more accurate so that it incorporates the shear effect into the formulation. The plate is assumed to be simply supported on its four edges, so exact (closed-form) solutions are found according to the Navier expansion, and the governing stability equations and associated boundary conditions of the problem are obtained via the virtual works principle. The plate studied ismade of laminated composite materials, so a parametric study is needed to see the effect of different types of parameters and coupling on the critical temperature value causing thermo-elastic instability of the plate and also on the natural frequency of free vibration, as well as for other parameters such as anisotropy, slenderness and aspect ratio of the plate and finally the lamination angle. Numerical results are obtained for specially orthotropic and antisymmetrical plates and are compared with those obtained by othertheoriesin the literature to validate the analysis approach used.

• Wind and Structures
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• v.38 no.2
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• pp.93-107
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• 2024

A π-shaped composite deck in the form of an open section is a type of blunt body that is highly susceptible to wind loads. To investigate its vortex-induced vibration (VIV) performance, a large-scale (1/20) section model of a cable-stayed bridge with a main span of 650 m was tested in a wind tunnel. The vibration suppression mechanism of the countermeasures was analyzed using computational fluid dynamic. Experimental results demonstrate that the vertical and torsional VIVs of the original section can be suppressed by combining guide plates with a tilt angle of 35° and bottom central stabilizing plates as aerodynamic countermeasures. Numerical results indicate that the large-scale vortex under the deck separates into smaller vortices, resulting in the disappearance of the von Kármán vortex street in the wake zone because the countermeasures effectively suppress the VIVs. Furthermore, a full-bridge aeroelastic model with a scale of 1/100 was constructed and tested to evaluate the wind resistance performance and validate the effectiveness of the proposed countermeasures.

• Steel and Composite Structures
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• v.52 no.1
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• pp.89-107
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• 2024

This article focuses on the static and dynamic analysis and optimization of an anisogrid lattice plate subjected to axial compressive load with simply supported boundary conditions. The lattice plate includes diagonal and transverse ribs and is modeled as an orthotropic plate with effective stiffness properties. The study employs the first-order shear deformation theory and the Ritz method with a Legendre approximation function. In the realm of optimization, the Non-dominated Sorting Genetic Algorithm-II is utilized as an evolutionary multi-objective algorithm to optimize. The research findings are validated through finite element analysis. Notably, this study addresses the less-explored areas of optimizing the geometric parameters of the plate by maximizing the buckling load and natural frequency while minimizing mass. Furthermore, this study attempts to fill the gap related to the analysis of the post-buckling behavior of lattice plates, which has been conspicuously overlooked in previous research. This has been accomplished by conducting nonlinear analyses and scrutinizing post-buckling diagrams of this type of lattice structure. The efficacy of the continuous methods for analyzing the natural frequency, buckling, and post-buckling of these lattice plates demonstrates that while a degree of accuracy is compromised, it provides a significant amount of computational efficiency.