• 제목/요약/키워드: Elastic plate method

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Free vibrations of arbitrary quadrilateral thick plates with internal columns and uniform elastic edge supports by pb-2 Ritz method

  • Wu, L.H.
    • Structural Engineering and Mechanics
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    • 제44권3호
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    • pp.267-288
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    • 2012
  • Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

Large amplitude forced vibration of functionally graded nano-composite plate with piezoelectric layers resting on nonlinear elastic foundation

  • Yazdi, Ali A.
    • Structural Engineering and Mechanics
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    • 제68권2호
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    • pp.203-213
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    • 2018
  • This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.

Hydroelastic Response of VLFS with Submerged-Plate Using Modified Hydrodynamic Coefficients

  • Lee, Sang-Min
    • 한국항해항만학회지
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    • 제31권7호
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    • pp.569-578
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    • 2007
  • The primary objective of this study is to present a modified method of hydroelastic analysis and application of it to the VLFS with submerged plate. The modal analysis method is applied to the VLFS with the submerged plate using the modified hydrodynamic coefficients. Namely, the wave exciting forces are modified by the transmission wave coefficients, while the interaction factor is used for the modification of radiation forces. To validate the proposed method, comparisons between the numerical calculations and experimental data have been carried out for the deflections of VLFS, and it shows good agreement between the calculation and experiment. The results presented in this study demonstrate that the elastic response of the VLFS is strongly affected by the hydrodynamic interaction induced by the submerged plate. As a result, we can confirm that the submerged plate is useful for reducing the hydroelastic deflection of VLFS, and the proposed method is valuable for predicting the elastic response of VLFS with attached the submerged plate.

직교 이방성 관통 다공 후판의 탄성 해석 (Elastic Analysis of Orthotropic Thick Plates with Perforated Many Holes)

  • 김우식;권택진
    • 한국공간구조학회논문집
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    • 제2권1호
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    • pp.59-65
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    • 2002
  • The structures with many perforated openings are widely used as a load-carrying element in the fields of civil engineering works, top slab of prestressed concrete reactor vessel, petrochemical industries and the like. Perforated concrete plates are usually thick. Therefore, the effect of transverse shear deformation is not negligible. This paper describes a new analytical method of perforated plates combining both the finite element method for effective elastic constants and the usual method in solving orthotropic plate with transverse shear deformation.

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탄성반력의 영향에 따른 직교 이방성 복합판의 고유 진동 해석 (Vibration Analysis of Orthortopic Composite Plate According to Elastic Reaction Effect)

  • 정영화;심도식;김경진;이세진
    • 산업기술연구
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    • 제17권
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    • pp.199-204
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    • 1997
  • In this paper, the result of application of vibration method to the orthotropic plates with free edges supported on elastic foundation and with a pair of opposite edges under axial forces is presented. Such plates represent the concrete highway slab and hybrid composite pavement of bridges. The reinforced concrete slab can be assumed as a special orthotropic plate, as a close approximation. The highway slab is supported on elastic foundation, with free boundaries. Sometimes, the pair of edges perpendicular to the traffic direction may be subject to the axial forces. The plate is subject to the concentrated load/loads, in the form of traffic loads, or the test equipments. Finite difference method is used to obtain the deflection influence surfaces needed for vibration analysis. The influence of the modulus of the foundation, the aspect ratio of the plate, and the magnitudes of the axial forces and the concentrated attached mass on the plate, under the natural frequency is thoroughly studied.

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면내 선형분포하중을 받는 고정지지된 직교이방성판의 좌굴 (Buckling of Fixedly Supported Orthotropic Plate under In-plane Linearly Distributed Forces)

  • 정재호;채수하;남정훈;윤순종
    • 한국복합재료학회:학술대회논문집
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    • 한국복합재료학회 2000년도 춘계학술발표대회 논문집
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    • pp.5-8
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    • 2000
  • This paper presents the results of an elastic buckling analysis of orthotropic plate under in-plane linearly distributed forces. The analytical solution for the orthotropic plate whose boundaries were assumed to be simply supported was derived in the previous work. In this study the loaded edges of plate are assumed to be simply supported and other two edges are assumed to be fixed. For the buckling analysis Rayleigh-Ritz method is employed. Graphical form of results for finding the elastic buckling strength of orthotropic plate under in-plane linearly distributed forces is presented.

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The effect of voltage and nanoparticles on the vibration of sandwich nanocomposite smart plates

  • Farokhian, Ahmad
    • Steel and Composite Structures
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    • 제34권5호
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    • pp.733-742
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    • 2020
  • Vibration analysis in nanocomposite plate with smart layer is studied in this article. The plate is reinforced by carbon nanotubes where the Mori-Tanaka law is utilized for obtaining the effective characteristic of structure assuming agglomeration effects. The nanocomposite plate is located in elastic medium which is simulated by spring element. The motion equations are derived based on first order shear deformation theory and Hamilton's principle. Utilizing Navier method, the frequency of the structure is calculated and the effects of applied voltage, volume percent and agglomeration of Carbon nanotubes, elastic medium and geometrical parameters of structure are shown on the frequency of system. Results indicate that with applying negative voltage, the frequency of structure is increased. In addition, the agglomeration of carbon nanotubes reduces the frequency of the nanocomposite plate.

Dynamic analysis of rigid roadway pavement under moving traffic loads with variable velocity

  • Alisjahbana, S.W.;Wangsadinata, W.
    • Interaction and multiscale mechanics
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    • 제5권2호
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    • pp.105-114
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    • 2012
  • The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM

  • Abdulrazzaq, Mohammed Abdulraoof;Muhammad, Ahmed K.;Kadhim, Zeyad D.;Faleh, Nadhim M.
    • Coupled systems mechanics
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    • 제9권3호
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    • pp.201-217
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    • 2020
  • This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers.The governing equations achieved by Hamilton's principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise,scale factors and viscous damping.

Thermomechanical postbuckling of imperfect moderately thick plates on two-parameter elastic foundations

  • Shen, Hui-Shen
    • Structural Engineering and Mechanics
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    • 제4권2호
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    • pp.149-162
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    • 1996
  • A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.