A spectral super element for modelling of plate vibration. Part 1: general theory

Birgersson, F.; Finnveden, Svante; Nilsson, Carl-Magnus

doi:10.1016/j.jsv.2004.11.012

Cited by 51 publications

(49 citation statements)

References 16 publications

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“…[16] Equations for and refer to reference 8. in detail. Hence, if an input force vector F is given, the nodal displacement W can be found using a dynamic stiffness matrix D of the structure by The size of the combined dynamic stiffness will be determined by the largest dofs in the model.…”

Section: Wfe Equationsmentioning

confidence: 99%

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

Ryue¹

2014

The Journal Of The Acoustical Society Of Korea

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Wave reflection and transmission characteristics in waveguides are an important issue in many engineering applications. A combined spectral element and finite element (SE/FE) method is used to investigate the effects of local non-uniformities but limited at relatively low frequencies because the SE is formulated by using a beam theory. For higher frequency applications, a method named a combined spectral super element and finite element (SSE/FE) method was presented recently, replacing spectral elements with spectral super elements. This SSE/FE approach requires a long computing time due to the coupling of SSE and FE matrices. If a local non-uniformity has a uniform cross-section along its short length, the FE part could be further replaced by SSE, which improves performance of the combined SSE/FE method in terms of the modeling effort and computing time. In this paper SSEs are combined to investigate the characteristics of waves propagating along waveguides possessing geometric non-uniformities. Two models are regarded: a rail with a local defect and a periodically ribbed plate. In the case of the rail example, firstly, the results predicted by a combined SSE/FE method are compared with those from the combined SSEs in order to justify that the combined SSEs work properly. Then the SSEs are applied to a ribbed plate which has periodically repeated non-uniformities along its length. For the ribbed plate, the propagation characteristics are investigated in terms of the propagation constant.

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Section: Wfe Equationsmentioning

confidence: 99%

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

Ryue¹

2014

The Journal Of The Acoustical Society Of Korea

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“…8 The damping loss factor has been obtained using the SAFE method and taking into consideration the complex stiffness matrix. 9 To model ultrasonic wave propagation in different waveguides, the SAFE method is used. 10 The titanium repair patches bonded to the aircraft aluminum skin have been inspected using ultrasonic guided waves, wave structures were plotted using a theoretical method and selected the mode shape with maximum in-plane displacement for inspection, although the effect of material damping did not take into consideration.…”

Section: Introductionmentioning

confidence: 99%

Generation of Low-Attenuation Lamb Wave Modes in Three-Layer Adhesive Joints

Birgani¹,

Sodagar²,

Shishesaz³

2017

IJAV

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In this paper, the attenuation of lamb waves in three-layer adhesive joints, including two elastic plates bonded together by a viscoelastic adhesive layer, is investigated using the global matrix method and then a suitable incidence angle is calculated to generate a low-attenuation lamb wave using an angle beam transducer. The theoretical boundary value problem in adhesive joints with a perfect bond and traction-free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with lowest attenuation. A characteristic equation is derived by applying continuity and boundary conditions in adhesive joints using the global matrix method. Phase velocity and attenuation dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. Also, the transducer incidence angle is calculated in terms of frequency to generate lamb wave modes with low attenuation level using the theoretical method.

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“…From the aforementioned literature, we find that the SEM applications to 2D structures have been limited to plates with very specific geometries and boundary conditions. Birgersson et al [16] and Mitra and Gopalakrishnan [17] presented spectral element models for rectangular plates by using a spectral super element method (SSEM). However their spectral element models can be assembled only in one plate direction (e.g., the x-direction).…”

Section: Introductionmentioning

confidence: 99%

“…However their spectral element models can be assembled only in one plate direction (e.g., the x-direction). Park and his colleagues [18][19][20] developed spectral element models for membranes and isotropic and orthotropic composite plates by using a combination of the boundary splitting method [21] and SSEM [16]. Their spectral element models can be assembled in two plate directions (i.e., the x-and y-directions).…”

Section: Introductionmentioning

confidence: 99%

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

Park

Lee

2017

Composite Structures

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A spectral super element for modelling of plate vibration. Part 1: general theory

Cited by 51 publications

References 16 publications

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

Generation of Low-Attenuation Lamb Wave Modes in Three-Layer Adhesive Joints

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

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