scholarly journals Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Ilwook Park ◽  
Usik Lee ◽  
Donghyun Park
Keyword(s):  
Frequency Domain ◽  
Computational Efficiency ◽  
Element Model ◽  
Spectral Element ◽  
Thin Plates ◽  
Plate Element ◽  
Kantorovich Method ◽  
Arbitrary Boundary ◽  
Finite Plate ◽  
Element Method

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

scholarly journals On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

2008 ◽  
Vol 15 (3-4) ◽  
pp. 425-434 ◽  
Author(s):  
N.B.F. Campos ◽  
J.R.F. Arruda
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Low Frequency ◽  
Element Model ◽  
Spectral Element ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Thin Plates ◽  
Arbitrary Boundary ◽  
Element Method

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.

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

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Ilwook Park ◽  
Taehyun Kim ◽  
Usik Lee
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Element Model ◽  
Spectral Element ◽  
Plate Element ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Plate Elements ◽  
Rectangular Plate Element

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.

scholarly journals Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jungho Park ◽  
Ilwook Park ◽  
Usik Lee
Keyword(s):  
Transverse Vibration ◽  
Splitting Method ◽  
Element Model ◽  
Spectral Element ◽  
Arbitrary Boundary ◽  
Modeling And Analysis ◽  
One Dimensional ◽  
Proposed Model ◽  
Standard Finite Element Method ◽  
Element Method

Although the spectral element method (SEM) has been well recognized as an exact continuum element method, its application has been limited mostly to one-dimensional (1D) structures, or plates that can be transformed into 1D-like problems by assuming the displacements in one direction of the plate in terms of known functions. We propose a spectral element model for the transverse vibration of a finite membrane subjected to arbitrary boundary conditions. The proposed model is developed by using the boundary splitting method and the waveguide FEM-based spectral super element method in combination. The performance of the proposed spectral element model is numerically validated by comparison with exact solutions and solutions using the standard finite element method (FEM).

scholarly journals Effects of Delamination on Guided Waves in a Symmetric Laminated Composite Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Seungwan Kim ◽  
Usik Lee
Keyword(s):  
Frequency Domain ◽  
Composite Beam ◽  
Guided Waves ◽  
Structural Integrity ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Element Model ◽  
Spectral Element ◽  
Composite Beams ◽  
Variation Method

For successful structural health monitoring and structural integrity evaluation of a laminated composite structure, it is important to study the effects of delamination on the propagations of the guided waves in a delaminated composite beam by using an accurate and computationally efficient method. Thus, we developed a “frequency-domain” spectral element model for the symmetric composite beams. First-order-shear-deformation-theory (FSDT) based Timoshenko beam theory and Mindlin-Herrmann rod theory are adopted for the flexural (bending) waves and axial (extensional) waves, respectively. A spectral element model is derived from the governing equations of motion by using the variation method in the frequency domain. After validating the accuracy of the proposed spectral element model, the model is used to investigate the effects of delamination on the propagation of guided waves in examples of composite beams.

scholarly journals Vibrational analysis of Levy-type plates by using SEM

2018 ◽  
Vol 1 (1) ◽  
pp. 18 ◽  
Author(s):  
Shota Kiryu ◽  
Buntara Sthenly Gan
Keyword(s):  
Natural Frequencies ◽  
Vibrational Analysis ◽  
Element Model ◽  
Spectral Element ◽  
Thin Plates ◽  
Rigid Pavement ◽  
Structural Dynamic ◽  
Element Discretization ◽  
Stiffness Matrices ◽  
Vibrational Characteristics

The use of the frequency-dependent spectral method in structural dynamic related problems is known to provide very accurate solutions while reducing the number of degree-of-freedom to resolve the computational and cost drawbacks. This paper investigated the vibrational characteristics of a rigid pavement road which is modeled by an isotropic Levy-type rectangular thin plates. The Spectral Element Method (SEM) in the frequency domain is developed to formulate the free vibration problems of the plate. Transcendental stiffness matrices are well established in vibration, derived from the exact analytical solutions of the differential equations of a plate element. The present spectral element model has four line-type degree-of-freedoms (DOF) on each edge of the Levy-type rectangular plate. Natural frequencies are found using the Wittrick-Williams algorithm. Numerical examples are given to show the effectiveness, efficiency, and accuracy of the SEM by using one element, unlike the FEM, the SEM gives exact solutions of the natural frequencies of plates without element discretization procedures.

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