Free Vibrations of a Rectangular Plate Carrying a Distributed Mass

Kopmaz, Osman; Tellı, Sevda

doi:10.1006/jsvi.2001.3977

Cited by 51 publications

(41 citation statements)

References 7 publications

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“…Few papers study the effects of distributed mass in vacuo. Kopmaz & Telli (2002) presented a mathematical model of a rectangular plate carrying a uniformly distributed mass using Galerkin's method to discretize the partial differential equations of the plate. Wong (2002) proposed a formulation to the eigenvalue problem of plates with distributed mass loading based on the Rayleigh-Ritz energy variational principle.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of submerged rectangular microplates with distributed mass loading

Brett

et al. 2009

Proc. R. Soc. A.

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This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh-Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

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Section: Introductionmentioning

confidence: 99%

Vibration analysis of submerged rectangular microplates with distributed mass loading

Brett

et al. 2009

Proc. R. Soc. A.

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“…natural frequencies, mode shapes and damping ratio of the diplexer) [15]. The free vibrational frequencies of a rectangular plate with a distributed load were examined in [16], and the high frequency vibrations of thin plates were studied in [17].…”

Section: Application Of Different Heat Treatment Tomentioning

confidence: 99%

Application of Different Heat Treatment to Spheroidal Graphite Cast Iron and its Effect for Damping and Mode Shapes

Dahil

Karabulut

2017

T FAMENA

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SummaryIn this study, damping and mode shapes were investigated after boriding and austempering the spheroidal graphite cast iron (SGCI). The samples were boronised and austempered at 900℃ for 2 hours by employing the pack cementation method. The samples were cooled and tempered in a salt bath at 250℃ and 375℃ for 1 hour. Once the boriding and austempering processes were completed, the samples were cooled at room temperature and washed with plenty of water. The modal frequencies, damping ratios and mode shapes of these samples exposed to different heat treatments were acquired by using the experimental modal analysis (MA) method. The same characteristic features were acquired with the finite element method (FEM), and the results were compared. It was found that after the heat treatment the sample austempered at 250 o C had a harder surface and a higher frequency than other samples.

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“…Later, some researchers [13][14][15][16] found that the distribution of the external load has significant influences on the dynamic characteristics of the structural system; therefore, they replaced the concentrated mass model by the distributed mass model. However, because the literature regarding the dynamic behaviour of a flat plate subjected to a moving distributed mass is not found so far, this paper aims at studying this problem.…”

mentioning

confidence: 98%

“…subjected to various moving loads, where the loads are modelled as concentrated forces or concentrated masses. Wong [13] and Kopmaz and Telli [14] have studied the free vibration characteristics of a plate loaded with a distributed mass. Ong and Lu [15] and Romanelli and Laura [16] have performed the forced vibration analysis of plates subjected to stationary distributed loads.…”

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confidence: 99%

Use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load

2006

Numerical Meth Engineering

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SUMMARYThis paper presents the theory regarding a moving distributed mass element, so that the dynamic responses of a rectangular plate subjected to a moving distributed mass, with the effects of inertia force, Coriolis force and centrifugal force considered, can be easily determined. In which, the property matrices of the moving distributed mass element are derived by means of the principle of superposition and the definition of shape functions, and the overall property matrices of the entire vibrating system are determined from the combination of the last element property matrices of the moving distributed mass element and those of the plate itself. Since the property matrices of the moving distributed mass element have something to do with the instantaneous position and the distribution of the moving mass, they are time-dependent and so are the overall property matrices of the entire vibrating system. Based on the last concept, the equations of motion for a rectangular plate subjected to a moving distributed mass are established and solved to yield the dynamic responses of the entire vibrating system. Numerical results reveal that the factors such as the contact area (between the moving distributed mass and the plate), moving-load speed, inertia force, Coriolis force and centrifugal force affect the vibration characteristics of the plate to some degree.

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Free Vibrations of a Rectangular Plate Carrying a Distributed Mass

Cited by 51 publications

References 7 publications

Vibration analysis of submerged rectangular microplates with distributed mass loading

Vibration analysis of submerged rectangular microplates with distributed mass loading

Application of Different Heat Treatment to Spheroidal Graphite Cast Iron and its Effect for Damping and Mode Shapes

Use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load

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