Affiliations: State University of Campinas, Computational Mechanics
Department, Rua Mendeleiev, 200, Cidade Universitária,Caixa Postal 6122,
13083-970 Campinas, SP, Brazil
Abstract: Modeling beam reinforced thin plates at mid and high frequencies
through the most commonly used methods such as finite and boundary element
methods frequently leads to unsatisfactory results, since the accuracy of these
methods depends on the relation between the dimensions of the elements in which
the structure was discretized and the wavelength. Due to this characteristic,
the modeling using these techniques will require that the size of the elements
becomes smaller as the frequency increases, while its number needs to be
increased. For structures that are usual in some areas, like the aerospace
industry, this will be possible only with an unreasonable computational effort,
which is responsible for restricting the use of these methods practically to
low-frequency applications. Semi-analytical methods such as the spectral
element method do not need mesh refinement at higher frequencies, but they were
very limited in the geometries and boundary conditions that can be treated.
This paper presents a spectral element for rectangular thin plates reinforced
symmetrically along the sides with Euler beams, which can be used to model
plates with arbitrary boundary conditions. The method was verified by comparing
its results with those obtained from a Finite Element model.
Keywords: Spectral element method, reinforced plates, vibration, mid-frequencies
