Modeling wave propagation in moderately thick rectangular plates using the spectral element method

Shirmohammadi, Fatemeh; Bahrami, Saeed; Saadatpour, M.M.; Esmaeily, Asad

doi:10.1016/j.apm.2014.11.044

Cited by 20 publications

(8 citation statements)

References 16 publications

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“…The mesh size of the FEM when 50 × 50 elements are used (see the 4th column of Table 1) is the same as the inner mesh size of the SEM when a single element is used (see the last column of Table 1). Table 1 shows that the natural frequencies by the FEM are accurate only up to the mode (1, 2), whereas the natural frequencies by the SEM are accurate up to the higher mode (10,10). This clearly verifies the high accuracy of the present SEM when compared with the FEM.…”

Section: Numerical Results and Discussionsupporting

confidence: 62%

“…Despite the outstanding features of the SEM, it is mostly used in one-dimensional (1D) structures [3,4]. The SEM application to two-dimensional (2D) structures such as plates has been limited to very specific geometries and boundary conditions, for example, Levy-type plates [6][7][8][9][10] and infinite or semi-infinite plates [11][12][13][14][15]. Some researchers [16,17] have introduced the spectral super element method (SSEM) for rectangular plates with prespecified boundary conditions on two parallel edges in one direction (say, the -direction).…”

Section: Introductionmentioning

confidence: 99%

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

Park

Kim

Lee

2016

Mathematical Problems in Engineering

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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.

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Section: Numerical Results and Discussionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

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

Park

Kim

Lee

2016

Mathematical Problems in Engineering

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“…The spectral element method (SEM) is a highly precise and efficient frequency-domain solution method where the spectral element equation is formulated in the frequencydomain and solved by using the spectral analysis method [9][10][11]. The procedure of the SEM is similar to that of the conventional finite element method.…”

Section: Introductionmentioning

confidence: 99%

Study on Transmission Characteristics of Vertical Rail Vibrations in Ballast Track

Sheng

Zhao

Wang

et al. 2017

Mathematical Problems in Engineering

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A plane half-track model and a periodic track-substructure model are established. The spectral element method and spectral transfer matrix method are developed and applied to investigate the track decay rate (TDR) and transmission rate (TR) of the vertical rail vibrations, which can reflect the transmission characteristics in the longitudinal and downward directions, respectively. Furthermore, the effects of different track parameters on TDR and TR are investigated. The results show that the antiresonance frequency of the rail and the out-of-phase resonance frequency of the rail and sleeper form the boundary frequencies of the highattenuation zone for longwise vibration transmission, where the vibration absorption of the sleeper is significant. The downward transmissibility of vertical rail vibrations is greatest around the antiresonance frequency of the rail. Vertical rail vibrations are primarily transmitted in the downward direction at low frequencies, while they are mainly transmitted along the rail at high frequencies. Stiffer rail pads can make more vibrations transmitted downwards to the sleeper above the antiresonance frequency of the rail, while the changes of other track parameters have different effects on the transmission characteristics. Additionally, a field measurement is performed for verification, and the simulations are well consistent with measurements.

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“…For the vibration analysis of 1D and 2D moving load problems, numerous analysis methods have been proposed in the literature. ese include the modal analysis method (mode superposition method or eigenfunction expansion method) [1][2][3][4], integral transform method (ITM) [5][6][7], Galerkin method [8,9], differential quadrature method [10,11], finite difference method [12,13], finite element method (FEM) [14][15][16][17][18], dynamic stiffness method [19,20], and frequency-domain spectral element method (SEM) [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

“…Despite the outstanding features of the SEM, it has been applied to very few moving load problems, for instance, in [21][22][23][24] for 1D structures and in [25] for 2D structures. For 1D structures, Azizi et al [21] seem to be the first to have applied the SEM to continuous beams and bridges under a moving point force.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency‐Domain Spectral Element Method

Kim

Lee

2018

Shock and Vibration

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A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.

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Modeling wave propagation in moderately thick rectangular plates using the spectral element method

Cited by 20 publications

References 16 publications

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

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

Study on Transmission Characteristics of Vertical Rail Vibrations in Ballast Track

Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency‐Domain Spectral Element Method

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