• Structural Engineering and Mechanics
• /
• 제90권1호
• /
• pp.83-96
• /
• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• 한국지반공학회지:지반
• /
• 제11권2호
• /
• pp.139-156
• /
• 1995

지반진동특성의 지진공학적인 정밀측정의 일환으로 지반진동의 탁월주기와 지반진동의 거리에 따른 감쇠특성을 현장실험을 통하여 조사하였다. 이 조사는 세가지 부분의 실험을 통하여 결과를 얻었다. 첫째, 지반의 탁월주기는 고감도 디지탈 속도지진계-3축성분 속도계를 이용하는 Seismometer와 디지탈 Seismograph를 이용하여 지반과 건물에서 일정한 주기를 가진 연속적인 미소진동으로 부터 지반 및 건물진동의 탁월주기를 계측하였다. 지반에서의 탁월주기는 0.18~0.23 sec, 건물2층의 탁월주기는 0.26~0.31 sec였다. 둘째, 지반 구조조사는 디지탈 탄성파탐사기를 이용하여 굴절법을 이용한 탄성파탐사를 실시하였다. 실험장소인 한양대학교 안산캠퍼스의 지층구조는 상부층(표토층: surface layer)은 저속도층으로서 662m1s, 하부층(지반층: base ground)은 2210m/s의 P파 속도를 갖고, 주시곡선도로부터 표토층의 두께는 약 7m로 검측되었다. 이것은 7m두깨의 표토층(top soil)과 그 하부에 사질 점토성의 지반층(base ground)이 존재함을 암시한다. 셋째, Seisgun을 이용하여 인공적인 탄성파 에너지원을 만들어 지반의 진동 감쇠특성을 조사 하였다. 거리 감쇠상수(spatial attenuation conf$\ulcorner$icient) Y는 거리에 따른 진폭 을 계산하여 Z-성분(vertical)은 0.0137, X-성분(longitudinal)은 0.0025, Y-성분(transverse)은 0.0290이고 Spatial QP의 값은 각각 5.913~7.575, 32.371 ~41.452, 2.794~3.579의 값이 산출되었었다. 이 결과 다른 두성분에 비해서 종방향(z-성분, longitudinal)성분은 감쇠경향이 낮음을 알 수 있다. 그러므로 이 경우에 구조물 설계시 종방향(x-성분, longitudinal)성분에 대 한 내진설계가 고려 되어야 할 것이다.

• 한국지진공학회논문집
• /
• 제3권1호
• /
• pp.9-20
• /
• 1999

본 논문에서는 고정 또는 자유 연단 조건의 모든 조합을 고려한 마름모꼴 평판의 휨 진동에 대한 엄밀한 해석방법을 제시한다. 본 논문의 주된 관점은 마름모꼴 평판 둔각 모서리의 경계조건이 고정 또는 자유일 때 휨응력의 특이도를 엄밀히 고려하여 해석하는 것이다. 고정 또는 자유인 모서리 응력 특이도의 중대한 영향력이 이해 될 수 있도록 충분히 큰 165。 둔각모서리를 갖는 마름모꼴 평판에 대하며 엄밀한 무차원 진동수와 수직 변동변위의 전형적인 등고선을 제시하였다.

• Journal of Theoretical and Applied Mechanics
• /
• 제2권1호
• /
• pp.1-14
• /
• 1996

In this paper, breaking waves are generated in a 2-D wave tank and simulated by using a higher-order boundary element method. A piston-type wavemaker is operated by signals composed of elementary waves. The phase of elementary waves is determined by the linear theory such that they are focused to a prescribed position. Calculated plunging waves coincide well with experiment. A steel box with different plate thicknesses is installed at a predetermined position in the tank. Measured impulsive pressures due to breaking waves are found to be 0.8-1.2$\rho$C2, where $\rho$ corresponds to water density and C to wave celerity. The transverse displacement of the plate is described in terms of modal eigenfunctions. The natural frequencies measured by impact tests in air for thin plate coincide with the computational and theoretical values. The radiationpotential due to plate vibration is derived and the radiation force is expressed in terms of hydroelastic added mass and damping forces. Comparison of natural frequencies of plate in water proves that hydroelastic added mass and damping are properly considered. The measured strain due to regular waves supports the calculated one, but there are apparent discrepancies between theory and experiment in the impulsive case.

• Earthquakes and Structures
• /
• 제12권4호
• /
• pp.409-423
• /
• 2017

This paper proposes a quick and simplified method to describe masonry vaults in global seismic analyses of buildings. An equivalent macro-element constituted by a set of six trusses, two for each transverse, longitudinal and diagonal direction, is introduced. The equivalent trusses, whose stiffness is calculated by fully modeled vaults of different geometry, mechanical properties and boundary conditions, simulate the vault in both global analysis and local analysis, such as kinematic or rocking approaches. A parametric study was carried out to investigate the influence of geometrical characteristics and mechanical features on the equivalent stiffness values. The method was numerically validated by performing modal and transient analysis on a three naves-church in the elastic range. Vibration modes and displacement time-histories were compared showing satisfying agreement between the complete and the simplified models. This procedure is particularly useful in engineering practice because it allows to assess, in a simplified way, the effectiveness of strengthening interventions for reducing horizontal relative displacements between vault supports.

• Steel and Composite Structures
• /
• 제45권3호
• /
• pp.409-423
• /
• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Steel and Composite Structures
• /
• 제50권5호
• /
• pp.563-581
• /
• 2024

This paper presents a novel finite element model for the free vibration analysis of variable-thickness functionally graded porous (FGP) microplates resting on Pasternak's medium in the hygro-thermal environment. The governing equations are established according to refined higher-order shear deformation plate theory (RPT) in construction with the modified couple stress theory. For the first time, three-node triangular elements with twelve degrees of freedom for each node are developed based on Hermitian interpolation functions to describe the in-plane displacements and transverse displacements of microplates. Two laws of variable thickness of FGP microplates, including the linear law and the nonlinear law in the x-direction are investigated. Effects of thermal and moisture changes on microplates are assumed to vary continuously from the bottom surface to the top surface and only cause tension loads in the plane, which does not change the material's mechanical properties. The numerical results of this work are compared with those of published data to verify the accuracy and reliability of the proposed method. In addition, the parameter study is conducted to explore the effects of geometrical and material properties such as the changing law of the thickness, length-scale parameter, and the parameters of the porosity, temperature, and humidity on the free vibration response of variable thickness FGP microplates. These results can be applied to design of microelectromechanical structures in practice.

• Structural Engineering and Mechanics
• /
• 제7권2호
• /
• pp.181-202
• /
• 1999

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren't continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

• Steel and Composite Structures
• /
• 제24권2호
• /
• pp.151-176
• /
• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2006년도 춘계학술대회 논문집
• /
• pp.387-388
• /
• 2006

This article provides a dynamic analysis model for huge marine engine that examined analytically variation effects of frequency response by fitting of transverse stays such as hydraulic type. First, vibration analysis using the three dimensional finite element models for the huge marine engine has performed in order to find out the dynamic characteristics. Second, three dimensional finite elements model for the huge marine engine was modifued so that generate forcing nodes in crosshead part and top bracing nodes in cylinder frame part. Third, a system matrix and output matrix was derived for the general siso(single input single out) state space model. Finally, developed state space model for the three dimensional finite elements model for the huge marine engine without the additional modifying process.