Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid

Uğurlu, Bahadır; Kutlu, Akif; Ergin, Ahmet; Omurtag, Mehmet H.

doi:10.1016/j.jsv.2008.03.022

Cited by 47 publications

(18 citation statements)

References 23 publications

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“…Applying the method of separation of variables based on the boundary conditions of Eqs. (11)(12)(13)(14)(15)(16)(17)(18)(19), general solution of Eq. (10) is given as…”

Section: Formulation Of the Fluid Oscillationsmentioning

confidence: 99%

“…Numerous studies have been performed to investigate free and forced vibrations of thin isotropic plates in partial contact with a fluid. Some of the most complete reviews on the subject are presented by Khorshidi [1], Amabili [2,3], Pellicano and Amabili [4], Jeong and Kim [5], Jeong et al [6,7], Kwak [8], Zhou and Cheung [9], Chang and Liu [10], Ergin and Ugurlu [11], Zhou and Liu [12], Ugurlu et al [13] and Kerboua et al [14].…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Khorshidi

Bakhsheshy

2015

Acta Mech

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This study investigates the vibration analysis of a functionally graded (FG) rectangular plate partially in contact with a bounded fluid. The material properties are assumed to vary continuously through the thickness direction according to a simple power-law distribution in terms of volume fraction of material constituents. Wet dynamic transverse displacements of the plate are approximated by a set of admissible trial functions, which are required to satisfy the clamped and simply supported geometric boundary conditions. The fluid velocity potential satisfying fluid boundary conditions is derived, and wet dynamic modal functions of the plate are expanded in terms of finite Fourier series for compatibility requirement along the contacting surface between the plate and the fluid. Natural frequencies of the plate coupled with sloshing fluid modes are calculated using the Rayleigh-Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is validated with available data in the literature. In the numerical results, the effects of boundary conditions, aspect ratios, thickness ratios, gradient index, material properties of the FG plate, depth of the fluid and dimensions of the tank on the wet natural frequencies are investigated.

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“…Applying the method of separation of variables based on the boundary conditions of Eqs. (11)(12)(13)(14)(15)(16)(17)(18)(19), general solution of Eq. (10) is given as…”

Section: Formulation Of the Fluid Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Khorshidi

Bakhsheshy

2015

Acta Mech

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“…According to this technique, the M th term approximate solution of (2), (8) is sought in the form (9) where ( ) i Q t are coordinates in modal space and ( ) i P x are the normal modes of vibration written as (10) No difficulty arises at all to show that for a beam with simply supported end conditions, taking into account equation (10), equation (9) can be written as (11) Substituting equation (11) into the governing equation (8), one obtains (12 ) which after some simplifications and rearrangements yields (13) To determine the expression for ( ) i Q t , the expression on the LHS of equation (13) is required to be orthogonal to the function . Thus, multiplying equation (13) by and integrating with respect to x from x=0 to x=L, leads to (14) where , , (16) and considering only the i th particle of the system, equation (14) can then be written as (17) where , and (18) To obtain the solution of the equation (17), it is subjected to a Laplace transform defined as (19) where s is the Laplace parameter.…”

Section: Solution Proceduresmentioning

confidence: 99%

Deflection profile analysis of beams on two-parameter elastic subgrade

Omolofe

2013

Lat. Am. j. solids struct.

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A procedure involving spectral Galerkin and integral transformation methods has been developed and applied to treat the problem of the dynamic deflections of beam structure resting on biparametric elastic subgrade and subjected to travelling loads. The case of the response to moving constant loads of this slender member is first investigated and a closed form solution in series form describing the motion of the beam while under the actions of the travelling load is obtained. The response under a variable magnitude moving load with constant velocity is finally treated and the effects of prestressed, foundation stiffness, shear modulus and damping coefficients are investigated. Results in plotted curves indicate that these structural parameters produce significant effects on the dynamic stability of the load-beam system. Conditions under which the beam-load system may experience resonance phenomenon are also established some of these findings are quite useful in practical applications.

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“…When these important engineering structures are resting on an elastic foundation, the structure-foundation interaction effects play significant roles in their response behaviour and alter the dynamic states of B. Omolofe a T.O. Adeloye the structures from those vibrating in the absence of foundation [Ugurlu et al (2008)]. Hence, the dynamic behaviour of structures on elastic foundation is of great importance in structural, aerospace, civil, mechanical and marine engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Behavioral Study of Finite Beam Resting on Elastic Foundation and Subjected to Travelling Distributed Masses

Omolofe

Adeloye

2017

Lat. Am. j. solids struct.

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The classical problem of the response characteristics of uniform structural member resting on elastic subgrade and subjected to uniform partially distributed load is studied in this work. The closed form solutions of the governing fourth order partial differential equations with variable coefficients are presented using an elegant analytical technique for the moving force and mass models. Various results and analyses are carried out on each of the pertinent boundary conditions and phenomenon of resonance is studied for the dynamical system. It was found that in all illustrative examples considered, for the same natural frequency, the critical speed for moving distributed mass problem is smaller than that of the moving distributed force problem. Hence, resonance is reached earlier in moving mass beam-load interaction problem. Finally, this work has suggested valuable methods of analytical solution for this category of problems for all boundary conditions of practical interest.

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Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid

Cited by 47 publications

References 23 publications

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Deflection profile analysis of beams on two-parameter elastic subgrade

Behavioral Study of Finite Beam Resting on Elastic Foundation and Subjected to Travelling Distributed Masses

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