Transverse Vibrations of Simply Supported Rectangular Plates With Rectangular Cutouts Carrying an Elastically Mounted Concentrated Mass

Avalos, D.R.; Larrondo, H.A.; Laura, P.A.A.; Rossi, R.E.

doi:10.1006/jsvi.1996.0811

Cited by 11 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present paper extends considerably previous works on the subject (Laura et al, 1977;Ercoli et al, 1992;Á valos et al, 1993;Á valos et al, 1997;Larrondo et al, 1998;Á valos et al, 1999) where, in general, simply supported edges were considered. The use of beam functions allows for a very complete combination of classical boundary conditions.…”

Section: Introductionmentioning

confidence: 89%

Natural frequencies of thin, rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

Bambill¹,

Felix²,

Rossit³

2006

International Journal of Solids and Structures

View full text Add to dashboard Cite

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh-Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or ''patch'', carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.

show abstract

Section: Introductionmentioning

confidence: 89%

Natural frequencies of thin, rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

Bambill¹,

Felix²,

Rossit³

2006

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…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. Ostachowicz et al [15] presented new results for the identification of the location of a concentrated mass on isotropic plates by means of a genetic algorithm search technique based on changes in natural frequencies.…”

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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The rigidity of the flexible plate with cutouts is depended mostly upon the number of cutouts [1,2]. Avalos et al [1] have investigated the transverse vibration of rectangular plate with a rectangular cutout. Based on the work, they [2] have also investigated the transverse vibration of the rectangular plate with two cutouts.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling and Simulation of Transverse Free Vibration Analysis of a Rectangular Plate with Cutouts Using Energy Principles

Shi

Xiao

Jin

et al. 2018

Shock and Vibration

View full text Add to dashboard Cite

A modeling method is proposed for the vibration characteristics of rectangular plates with cutouts having variable size. Different from the existing modeling method by considering the cutout as an extremely thin part of the plate, the energy principles in conjunction with Rayleigh-Ritz solution technique are employed for the modeling of the structure. Under this theoretical framework, the effect of the cutout is taken into account by subtracting the energies of the cutout domains from the total energies of the whole plate with arbitrary boundary conditions. The displacement of the rectangular plate with nonuniform physic parameters is expressed as the combination of a two-dimensional trigonometric cosine series and supplementary terms introduced to ensure the uniform convergence of the solution over the entire solution domain including the cutouts boundary. The effectiveness and reliability of the eigenmodes of the rectangular plate with cutouts are checked against the results obtained by the finite element method (FEM). The cutout number, position, and size are varied to illustrate the effect of the cutouts on the vibration characteristics of the rectangular plate with cutouts.

show abstract

Transverse Vibrations of Simply Supported Rectangular Plates With Rectangular Cutouts Carrying an Elastically Mounted Concentrated Mass

Cited by 11 publications

References 0 publications

Natural frequencies of thin, rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

Natural frequencies of thin, rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

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

Modeling and Simulation of Transverse Free Vibration Analysis of a Rectangular Plate with Cutouts Using Energy Principles

Contact Info

Product

Resources

About