Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method. Liew, K., Kitipornchai, S., Leung, A., & Lim, C. International Journal of Mechanical Sciences, 45(5):941–959, May, 2003. ![Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to deÿne the transverse de ection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions.
@article{liew_analysis_2003,
title = {Analysis of the free vibration of rectangular plates with central cut-outs using the discrete {Ritz} method},
volume = {45},
issn = {00207403},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0020740303001097},
doi = {10.1016/S0020-7403(03)00109-7},
abstract = {We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to deÿne the transverse de ection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions.},
language = {en},
number = {5},
urldate = {2020-02-03},
journal = {International Journal of Mechanical Sciences},
author = {Liew, K.M. and Kitipornchai, S. and Leung, A.Y.T. and Lim, C.W.},
month = may,
year = {2003},
pages = {941--959},
}
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