### Citations

304 | Matrix Polynomials
- Gohberg, Lancaster, et al.
- 1982
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Citation Context ...et of eigenvalues of Q(λ). The set contains 2n distinct eigenvalues, that may be real or complex (Tisseur and Meerberg, 2001). However, there only exists a set of n linearly independent eigenvectors (=-=Gohberg et al., 1982-=-). If the coefficient matrices are real, the spectrum Λ(Q) is symmetric with respect to the real axis of the complex plane. Therefore, eigenvalues are either real or come in complex conjugate pairs (λ... |

260 | The quadratic eigenvalue problem
- Tisseur, Meerbergen
- 2001
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Citation Context ... 1D SAFE is easily derived, as a special case of the 2D SAFE. 4.1.1 Quadratic Eigenvalue Problems Quadratic Eigenvalue Problems (QEP) occurs extensively within dynamic analysis of mechanical systems (=-=Tisseur and Meerberg, 2001-=-). Let’s consider the linear second order PDE, Mq̈ + Cq̇ +Kq = f, (4.1) where M , C, K are n×n (complex) matrices. The solution may be expressed as an eigensolution of the corresponding QEP, where the... |

85 | On waves in an elastic plate - Lamb - 1917 |

56 |
Handbook on nondestructive testing of concrete."
- Malhotra, Carino, et al.
- 1991
(Show Context)
Citation Context ...(A-scan), that may be combined to create an image of the inspected body (Baggens, 2015). For concrete structures such measurements are typically performed in the frequency range of 20 kHz to 500 kHz (=-=Malhotra and Carino, 2004-=-). A guided wave inspec7 tion system, typically, operate at lower frequencies (i.e. longer wavelength). Hence, the wavelength is such that the wave interacts with the boundaries of the wave guide to c... |

11 | Ultrasonics: Fundamentals and Applications, - Kuttruff - 1991 |

9 |
Finite Element Model for Waves Guided along Solid Systems of Arbitrary Section Coupled to Infinite Solid Media.
- Castaings, Lowe
- 2008
(Show Context)
Citation Context ...tes (Ahmad et al., 2013). It has also been shown to be suitable for modelling damped medium (Bartoli et al., 2006), anisotropic medium (Predoi et al., 2007) and leaky medium (Hayashi and Inoue, 2014; =-=Castaings and Lowe, 2008-=-) In general, the approach when solving the dispersive relation using SAFE is to make a Finite Element (FE) discretisation of the cross-section domain (2D SAFE) or line domain (1D SAFE). In the wave-p... |

9 | Guided wave propagation in three-layer pavement structures - Ryden, MJS |

6 | Fundamentals of Biomechanics. - Ozkaya, Nordin - 1991 |

4 | Surface Wave Testing of Pavements - Rydén |

3 |
Systematic errors in Impact-Echo thickness estimation due to near field effects
- Baggens, Ryden
- 2015
(Show Context)
Citation Context ...+ ν)(1− 2ν) is a function in the square root of Young’s modulus E. The P-wave velocity is of particular interest because of its use in estimating plate thickness using modes with zero group velocity (=-=Baggens and Ryden, 2015-=-). When the group velocity is zero the wave group propagation velocity is zero but the phase velocity remains non-zero. Thus, it exists localized resonance. In the frequency range of interest, 100 Hz ... |

3 |
Waves in Anisotropic Viscoelastic Plate. Study of Wavefronts and Attenuation
- Neau, Lamb
- 2003
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Citation Context ...perimentally defined at a characteristic frequency. Therefore, as long as the working frequencies doesn’t differ greatly from the characteristic frequency, the difference between the models is small (=-=Neau, 2003-=-). A proportionally damped system is a system where the damping is given as a linear combination of the mass and stiffness distribution, C ∝ c1M + c2K, where C is the damping matrix, M is the mass mat... |

3 | Wave propagation and damping in linear viscoelastic laminates - Shorter |

2 |
Semi-analytical finite element method for modeling of lamb wave propagation
- Ahmad, Vivar-Perez, et al.
- 2013
(Show Context)
Citation Context ...m of missing roots. SAFE has since been successfully used to model a wide variety of structures, such as: rails (Hayashi et al., 2003), periodic structures (Predoi et al., 2007) and composite plates (=-=Ahmad et al., 2013-=-). The new capabilities afforded by the development of SAFE, and its potential application to civil engineering problems, serve as motivation to this master thesis. 1.3 Aim and objective The aim of th... |

2 | Surface waves in inversely dispersive media. Near surface geophysics - Rydén, Park - 2004 |

1 |
Non-Destructive evaluation of plate-like concrete structures: elatic properties and thickness. Licentiate thesis
- Baggens
- 2015
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Citation Context ...on 1.1 Field of research Non-Destructive Testing (NDT) is a “general term which refers to the task of evaluating some sort of property without introducing any permanent damage on the studied object” (=-=Baggens, 2015-=-). Within the field of non-destructive testing there exists a wide variety of methods, spanning different fields of physics: from electromagnetism, through resistivity to acoustics. In this thesis we’... |

1 | User’s Guide and Documentation version 4.3a. COMSOL AB. URL www.comsol.com - COMSOL - 2006 |

1 |
Calculation of leaky Lamb waves with a semianalytical finite element method. Ultrasonics 54 (6), 1460–1469. URL <GotoISI>://WOS:000338610100006
- Hayashi, Inoue
- 2014
(Show Context)
Citation Context ..., 2007) and composite plates (Ahmad et al., 2013). It has also been shown to be suitable for modelling damped medium (Bartoli et al., 2006), anisotropic medium (Predoi et al., 2007) and leaky medium (=-=Hayashi and Inoue, 2014-=-; Castaings and Lowe, 2008) In general, the approach when solving the dispersive relation using SAFE is to make a Finite Element (FE) discretisation of the cross-section domain (2D SAFE) or line domai... |

1 |
Numerical and analytical calculation of modal excitability for elastic wave generation in lossy waveguides
- Treyssede, Laguerre
- 2013
(Show Context)
Citation Context ...the excited field. Hence, it may be determined which mode that will be dominant for a given excitation. Thereby, the NDT inspection system setup may be optimized in terms of sensor type and location (=-=Treyssede and Laguerre, 2013-=-). Let’s consider a lossless wave guide (i.e. an undamped wave guide). Let the lossless excitability for a given mode m be, e (m) ij = iω 4 ∫ Ω 〈P 〉t dΩ U (m) i U (m) j ∗ , where U (m) i = {U (m)1 , U... |