• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1062-1073
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. In developing a TS equation, it is assumed that the radiated pressure is known and the re-radiated intensity is unknown. This research provides a TS equation for polygonal plates, which is applicable to near field acoustics. In this research, Helmholtz-Kirchhoff formula is used as the primary equation for solving the re-radiated pressure field; the primary equation contains a surface (double) integral representation. The double integral representation can be reduced to a closed form, which involves only a line (single) integral representation of the boundary of the surface area by applying Stoke's theorem. Use of such line integral representations can reduce the cost of numerical calculation. Also Kirchhoff approximation is used to solve the surface values such as pressure and particle velocity. Finally, a generalized definition of Sonar Cross Section (SCS) that is applicable to near field is suggested. The TS equation for polygonal plates in near field is developed using the three prescribed statements; the redection to line integral representation, Kirchhoff approximation and a generalized definition of SCS. The equation developed in this research is applicable to near field, and therefore, no approximations are allowed except the Kirchhoff approximation. However, examinations with various types of models for reliability show that the equation has good performance in its applications. To analyze a general shape of model, a submarine type model was selected and successfully analyzed.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.3
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• pp.279-293
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• 2004

The analysis of linear static and free vibration problems of isotropic and laminated composite plates and shells is performed by the improved 9-node shell element with the new strain displacement relationship. In that relationship, the effect of new additional terms between the bending strain and displacement has been investigated in the warping problem. Natural co ordinate based strains, stresses and constitutive equations are used. The assumed natural strain method is used to alleviate both membrane and shear locking behavior from the element. The Lanczos method is employed in the calculation of the eigenvalues of laminated composite structures and the Gauss integration rule is adopted to evaluate the mass matrix. The numerical examples are compared with the analytical solutions to validate the current formulation and the results presented could be useful for the understanding of the behaviour of laminates under free vibration conditions.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.6
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• pp.615-630
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• 2016

Complex stress distributions often exist in ocean engineering structures. This stress influences structural vibrations. Finite Element Methods exhibit some shortcomings for solving non-uniform stress problems, such as an unclear physical interpretation, complicated operation, and large number of computations. Analytical methods research considers mainly uniform stress problems, and often, their methods cannot be applied in practical marine structures with non-uniform stress. In this paper, an analytical method is proposed to solve the vibration of plates with general stress distributions. Non-uniform stress is expressed as a special series, and the stress influence is inserted into a vibration equation that is solved through decoupling to obtain an analytical solution. This method has been verified using numerical examples and can be used in arbitrary stress distribution cases. This method requires fewer computations and it provides a clearer physical interpretation, so it has advantages in some qualitative research.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.10
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• pp.3173-3185
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• 1996

Multi-model vibration control of laminated composites plates for various fiver orientations has been carried out by making use of piezolectric materials(PZT) as sensors and actuators. Cantilever plate is used as a specimen to test multi-modal vibration supression under random exitation. Impulse technique is applied to determine the natural frequency, the damping ratio(.zeta.) and the modal damping(2.zeta..omega.) of the first bending and the trosion modes. Two independent controllers are implemented to control the two modes simultaneously and established digitally on the basis of the direct negative velocity feedback control with collocated sensor/actuator. Experimental results for various fiber orientations and feedback gains are compared with finite element analysis considering stiffnesses and dampings of piezoeletiric sensors, actuators and bonding layer.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.674-680
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• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Advances in materials Research
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• v.12 no.1
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• pp.43-65
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• 2023

Free vibration analysis of power law and sigmoidal sandwich plates made up of functionally graded materials (FGMs) has been carried out using finite element based higher-order zigzag theory. The present model satisfies all-important conditions such as transverse shear stress-free conditions at the plate's top and bottom surface along with continuity condition for transverse stresses at the interface. A Nine-noded C0 finite element having eleven degrees of freedom per node is used during the study. The present model is free from the requirement of any penalty function or post-processing technique and hence is computationally efficient. The present model's effectiveness is demonstrated by comparing the present results with available results in the literature. Several new results have been proposed in the present work, which will serve as a benchmark for future works. It has been observed that the material variation law, power-law exponent, skew angle, and boundary condition of the plate widely determines the free vibration behavior of sandwich functionally graded (FG) plate.

• Structural Engineering and Mechanics
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• v.85 no.4
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• pp.445-459
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• 2023

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs) in thermal environment. Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine the influence of various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio, thermal environment, and boundary conditions of the plate, on its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.2
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• pp.1109-1117
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• 2014

We study free vibration analysis of sigmoid functionally graded materials(S-FGM) nano-scale plates, using a nonlocal elasticity theory of Eringen in this paper. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Numerical solutions of S-FGM nano-scale plate are presented using this theory to illustrate the effect of nonlocal theory on natural frequency of the S-FGM nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index (ii) nonlocal parameters, (iii) elastic modulus ratio and (iv) thickness and aspect ratios on nondimensional frequencies are investigated. In order to validate the present solutions, the reference solutions are compared and discussed. The results of S-FGM nano-scale plates using the nonlocal theory may be the benchmark test for the free vibration analysis.