Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

Abstract

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

A generic type of frequency-domain spectral element model for the dynamics of a laminated composite plate

“…By following the approach introduced in the previous studies of the authors [18][19][20]22], the free wave solutions that satisfy the weak form given by Eq. (12) can be obtained approximately by using the boundary splitting method [21] and the SSEM in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are used [16].…”

“…where N u (x,y;x), N v (x,y;x), and N w (x,y;x) are one-by-12(N x + N y ) dynamic shape function matrices defined by Table 1 Comparison of natural frequencies (Hz) of the S-S-S-S uniform square composite plate with lay-up [0/90] S (Example 1) obtained by exact theory [24], ANSYS [22], and the present SEM. Note: n n = total number of active nodes used in the analysis.…”

“…However, as the four corner nodes of the spectral element models are inactive (fixed), their applications were limited to very specific types of plates. Recently, Park and Lee [22] developed a spectral element model for isotropic rectangular plates by modifying the boundary splitting method used in their previous study [19], in order to make the inactive four corner nodes active. Their spectral element model can be assembled in two plate directions without any limitation.…”

“…Comparison of natural frequencies (Hz) of the C-F-F-F square composite plate with centered square hole (Example 4) obtained by ANSYS[22] and the present SEM for 3 types of lay-ups.…”

Spectral Methods for Modelling of Wave Propagation in Structures in Terms of Damage Detection—A Review

“…In summary, an efficient and accurate FDSFEM model is developed to conduct free vibration analysis of stepped thickness rectangular plates with various boundary conditions. By the use of the boundary splitting method, a new frequency domain spectral element model for the analysis of finite rectangular plate elements with arbitrary boundary conditions has been developed by [126]. The high solution accuracy and computational efficiency of the proposed new spectral element model are validated by comparison with exact theory, the standard FEM, and the ANSYS (Release 11.0 Documentation for ANSYS, ANSYS, Inc., Canonsburg, PA, USA, 2006).…”