• Earthquakes and Structures
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• 제22권5호
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• pp.527-538
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• 2022

In this paper the free vibration frequencies of tri-directional functionally graded materials imperfect plate is investigated for Several plate geometries with two types of porosity (even and uneven) and different type of material configuration. The effect of several parameters such as power law index and boundary conditions have been investigated. For this purpose, an efficient computational method is developed and written under Matlab environment, based on a three-dimensional modeling and the isogeometric method is used for the discretization of the structure based on NURBS (Nonuniform rational B-spline) basis functions. The results obtained by the present method are validated by the comparison with the results given by several authors in the literature.

• Structural Engineering and Mechanics
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• 제73권4호
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• pp.407-426
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• 2020

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.788-793
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• 2004

The main purpose of this paper is to Investigate the free vibrations of circular curved members resting on nonhomogeneous elastic foundations. The governing differential equations derived in a previous paper are used. The governing equations are solved numerically to obtain frequencies. Hinged-hinged end constraint is considered in numerical examples. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the foundation rested ratio, the foundation parameter, the horizontal rise to span length ratio, the slenderness ratio, and the width ratio of the contact area between the member and the foundation.

• Smart Structures and Systems
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• 제17권2호
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• pp.257-274
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• 2016

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

• Wind and Structures
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• 제29권5호
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• pp.361-369
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• 2019

The modal frequency responses of adhesive bonded T-joint structure have been analyzed numerically and verified with own experimental data. For this purpose, the damped free frequencies of the bonded joint have been computed using a three-dimensional finite element model via ANSYS parametric design language (APDL) code. The practical relevance of the joint structure analysis has been established by comparing the simulation data with the in-house experimental values. Additionally, the influences of various geometrical and material parameters on the damped free frequency responses of the joint structure have been investigated and final inferences discussed in details. It is observed that the natural frequency values increase for the higher aspect ratios of the joint structure. Also, the joint made up of Glass fiber/epoxy with quasi-isotropic fiber orientation indicates more resistance towards free vibration.

• Structural Engineering and Mechanics
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• 제85권4호
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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.

• Structural Engineering and Mechanics
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• 제55권2호
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• pp.245-261
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of eccentric hemi-spherical shells of revolution with variable thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\Theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Potential and kinetic energies of eccentric hemi-spherical shells with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactitude is demonstrated for the first five frequencies of the shells. Numerical results are presented for a variety of eccentric hemi-spherical shells with variable thickness.

• Structural Engineering and Mechanics
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• 제40권5호
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• pp.665-688
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• 2011

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

• 한국공간구조학회논문집
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• 제4권4호
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• 한국구조물진단유지관리공학회 논문집
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• 제16권4호
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• pp.60-68
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• 2012

본 연구에서는 미국 뉴욕주 로체스터시 소재 강합성 데크 트러스 보도교를 대상으로 사용성을 평가하기 위한 상시진동 실험(ambient vibration test)을 수행하였고 이를 해석적 방법에 의한 결과와 비교하였다. 교량전체에 대한 상시진동실험은 수치모델 작성 시 도입되는 여러 가정들에 대한 타당성을 평가하는데 있어서 유용한 방법이며, 교량의 고유진동수나 모드형상과 같이 구조 동력학에서 중요한 구조적인 변수를 결정하는데 있어 중요한 역할을 한다. 본 연구에서는 교량의 수직방향 및 수평방향 진동 특성과 변위를 측정하기 위하여 실제 교량에서 보행자에 의해 발생하는 진동을 입력하중으로 사용하였다. 교량 구조물에 대한 모델링을 위하여 3차원 유한 요소법을 사용하여 해석을 수행하였으며, 이를 통하여 현장실험 결과와의 유효성을 입증하였다.