Use of the Analytical-and-Numerical-Combined Method in the Free Vibration Analysis of a Rectangular Plate With Any Number of Point Masses and Translational Springs

Wu, Jong‐Shyong; Luo, S.-S.

doi:10.1006/jsvi.1996.0697

Cited by 55 publications

(33 citation statements)

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“…M is the adsorbate mass and ∂w/∂t| r=r o ,θ=θ o is the corresponding velocity at (r o , θ o ). Here, the effect of an adsorbate is modelled as a concentrated mass [32][33][34]. To write down the above expressions for the potential and kinetic energies, the following five assumptions are used.…”

Section: Model Developmentmentioning

confidence: 99%

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Detecting the mass and position of an adsorbate on a drum resonator

Zhang

Zhao

2014

Proc. R. Soc. A.

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The resonant frequency shifts of a circular membrane caused by an adsorbate are the sensing mechanism for a drum resonator. The adsorbate mass and position are the two major (unknown) parameters determining the resonant frequency shifts. There are infinite combinations of mass and position which can cause the same shift of one resonant frequency. Finding the mass and position of an adsorbate from the experimentally measured resonant frequencies forms an inverse problem. This study presents a straightforward method to determine the adsorbate mass and position by using the changes of two resonant frequencies. Because detecting the position of an adsorbate can be extremely difficult, especially when the adsorbate is as small as an atom or a molecule, this new inverse problem-solving method should be of some help to the mass resonator sensor application of detecting a single adsorbate. How to apply this method to the case of multiple adsorbates is also discussed.

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Section: Model Developmentmentioning

confidence: 99%

“…In a forward problem, the adsorbate mass and position are given to calculate the resonant frequency [30][31][32][33][34]. However, in the real application of a mass resonator, resonant frequencies are the measured quantities; the adsorbate mass and position are the unknowns to be determined [35].…”

Section: Introductionmentioning

confidence: 99%

Detecting the mass and position of an adsorbate on a drum resonator

Zhang

Zhao

2014

Proc. R. Soc. A.

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“…[10] the response of a modified system was given in terms of the eigenfunctions of the unmodified system, thus, simplifying the analysis. Wu and Luo [11] used this principle for the vibration analysis of a rectangular plate with attached point masses and springs.…”

Section: Introductionmentioning

confidence: 99%

“…[10,11] is extended so as to include the effect of added stiffeners, instead of springs, at arbitrary locations and orientations on the plate. This is then combined with the optimisation approach presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Optimisation of the structural modes of automotive-type panels using line stiffeners and point masses to achieve weak acoustic radiation

et al. 2015

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“…The effect of different locations of the concentrated mass on the fundamental frequency of the plate is presented in detail. Wu and Luo [13] determined the natural frequencies and the corresponding mode shapes of a uniform rectangular flat plate carrying any number of point masses and translational springs by means of the analytical and numerical combined method (ANCM). Avalos et al [14] studied transverse vibrations of simply supported rectangular plates with rectangular cutouts carrying an elastically mounted concentrated mass.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

Mali

Singru

2013

Advances in Acoustics and Vibration

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This paper is concerned with a vibration analysis of perforated rectangular plates with rectangular perforation pattern of circular holes. The study is particularly useful in the understanding of the vibration of sound absorbing screens, head plates, end covers, or supports for tube bundles typically including tube sheets and support plates used in the mechanical devices. An energy method is developed to obtain analytical frequencies of the perforated plates with clamped edge, support conditions. Perforated plate is considered as plate with uniformly distributed mass. Holes are considered as concentrated negative masses. The analytical procedure using the Galerkin method is adopted. The deflected surface of the plate is approximated by the cosine series which satisfies the boundary conditions. Finite element method (FEM) results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well for holes of small size.

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Use of the Analytical-and-Numerical-Combined Method in the Free Vibration Analysis of a Rectangular Plate With Any Number of Point Masses and Translational Springs

Cited by 55 publications

References 0 publications

Detecting the mass and position of an adsorbate on a drum resonator

Detecting the mass and position of an adsorbate on a drum resonator

Optimisation of the structural modes of automotive-type panels using line stiffeners and point masses to achieve weak acoustic radiation

Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

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