Modelling wave propagation in two-dimensional structures using finite element analysis

Mace, B.R.; Manconi, Elisabetta

doi:10.1016/j.jsv.2008.04.039

Cited by 322 publications

(191 citation statements)

References 30 publications

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“…where T denotes the transpose and q n is the vector of nodal dofs of all the elements nodes which lie on the nth corner of the element [24]. Following the same logic, the vector of nodal force is given by…”

Section: Description Of the Wfemmentioning

confidence: 99%

“…where * stands for the conjugate transpose, T for the temperature, φ for the angle that is examined, V j is the displacement vector associated with the jth propagating wave and is obtained from the wave mode q 1j [24] and the components of the wavenumber k xj and k yj give:…”

Section: Loss Factormentioning

confidence: 99%

“…This way the calculation of the wavenumbers and eigenvectors is achieved with considerably lower cost of time than the previous ones. WFEM has been used in one dimension [22,23] and in two dimensions analyses [24] producing quite satisfying results. Using FE for the structure's modelling has given researchers the ability to broaden the potentials of the method, calculating loss factor [25] with the help of existing theories [26].…”

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confidence: 99%

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Acoustic transmission properties of pressurised and pre-stressed composite structures

Ampatzidis

Chronopoulos

2016

Composite Structures

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This work was focused on the examination of the effect of the pre-stress, namely tension and pressure, on the wave propagation and acoustic behaviour of composite laminates. The dispersion characteristics of two dimensional layered and sandwich structures were predicted using Wave Finite Element Method (WFEM). The structures were examined in non-stressed and pre-stressed scenarios. After extracting the mass and stiffness matrix of a small periodic segment of the structure using commercially available Finite Elements software, a polynomial eigenvalue problem was formed, the solutions of which consisted of the propagation constants of the waves of the structure. This way the wavenumbers and eigenvectors of the out of plane structural displacements were extracted. These wave propagation magnitudes were then used to calculate important Statistical Energy Analysis (SEA) quantities, such as modal density and radiation efficiency. The effect of pre-stress on these quantities, along with its effect on loss factor of the structure were examined.

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Section: Description Of the Wfemmentioning

confidence: 99%

Section: Loss Factormentioning

confidence: 99%

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confidence: 99%

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Acoustic transmission properties of pressurised and pre-stressed composite structures

Ampatzidis

Chronopoulos

2016

Composite Structures

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“…In this case, SAFE can be used to model the inner layers of the waveguide, and the SAFE model is then coupled to other boundary models of the infinite surrounding layer, such as the perfectly matched layer (PML) method [21][22][23], the boundary element method (BEM) [24], the infinite element method [25], or the absorbing layer method [26]. In addition to SAFE, other numerical techniques are available for calculating the eigenmodes of guided waves, such as the BEM [27,28], the wave finite element method (WFE) [29][30][31][32] and the scaled boundary finite element method (SBFEM) [33][34][35][36]. BEM represents exactly the radiation boundary condition and reduces the dimensions of the numerical problem by one.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study on the Excitation of Guided Waves in Rectangular Plates Using Multiple Point Sources

Duan

Niu

Gan

et al. 2017

Metals

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Ultrasonic guided waves are widely used to inspect and monitor the structural integrity of plates and plate-like structures, such as ship hulls and large storage-tank floors. Recently, ultrasonic guided waves have also been used to remove ice and fouling from ship hulls, wind-turbine blades and aeroplane wings. In these applications, the strength of the sound source must be high for scanning a large area, or to break the bond between ice, fouling and plate substrate. More than one transducer may be used to achieve maximum sound power output. However, multiple sources can interact with each other, and form a sound field in the structure with local constructive and destructive regions. Destructive regions are weak regions and shall be avoided. When multiple transducers are used it is important that they are arranged in a particular way so that the desired wave modes can be excited to cover the whole structure. The objective of this paper is to provide a theoretical basis for generating particular wave mode patterns in finite-width rectangular plates whose length is assumed to be infinitely long with respect to its width and thickness. The wave modes have displacements in both width and thickness directions, and are thus different from the classical Lamb-type wave modes. A two-dimensional semi-analytical finite element (SAFE) method was used to study dispersion characteristics and mode shapes in the plate up to ultrasonic frequencies. The modal analysis provided information on the generation of modes suitable for a particular application. The number of point sources and direction of loading for the excitation of a few representative modes was investigated. Based on the SAFE analysis, a standard finite element modelling package, Abaqus, was used to excite the designed modes in a three-dimensional plate. The generated wave patterns in Abaqus were then compared with mode shapes predicted in the SAFE model. Good agreement was observed between the intended modes calculated in SAFE and the actual, excited modes in Abaqus.

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“…The novelty of the method consists in the development of a frequency dependent procedure for defining the SEA subsystems. A promising approach is the wave and finite element (WFE) method to modelling the dynamics of structures which are piecewise homogeneous or periodic in one or two dimensions or which are axisymmetric [9].…”

Section: Introductionmentioning

confidence: 99%

A stochastic BEM formulation for vibro-acoustic analysis of structures in the mid-to-high frequency range

Pratellesi

Pierini

Baldanzini

et al. 2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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Predicting the acoustic behaviour of a complex structure in the mid-frequency range is a challenging task due to the complexity of the structure and the involved physical phenomena. Since, in the high-and even mid-frequency range, the variability of the product may have a significant effect on its NVH behaviour, it is important to include this sensitiveness in numerical models. In other respects a detailed description of the structures is necessary for structure borne contributions.The approach proposed in this paper provides a robust method for the vibroacoustic analysis of 3D acoustic domains coupled with structural components in the mid-frequency range.The method is based on a probabilistic approach which introduces uncertainties in the Boundary Element formulation: random geometrical parameters are introduced into the integral representations in order to model the increasing sensitivity of the harmonic vibrational responses to any parameter perturbation when the frequency increases.The stochastic formulation is solved in terms of the expectations of the square boundary kinematic unknowns and is valid in the entire frequency domain.The effectiveness of the formulation is demonstrated in this paper with a numerical application to a 3D model of an acoustic cavity coupled with a vibrating structure and with an internal source.

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Modelling wave propagation in two-dimensional structures using finite element analysis

Cited by 322 publications

References 30 publications

Acoustic transmission properties of pressurised and pre-stressed composite structures

Acoustic transmission properties of pressurised and pre-stressed composite structures

A Numerical Study on the Excitation of Guided Waves in Rectangular Plates Using Multiple Point Sources

A stochastic BEM formulation for vibro-acoustic analysis of structures in the mid-to-high frequency range

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