Lamb wave frequency–wavenumber analysis and decomposition
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...In a related effort, frequency-wavenumber analysis was used to discriminate between bulk and surface wave modes scattered from a surface-breaking crack [12, 13]....
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"Lamb wave frequency–wavenumber anal..." refers background in this paper
...Once the frequency– wavenumber (f–k) relations are known, group velocity dispersion curves of different modes can also be calculated (Rose, 1999)....
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...…modes Ai (i = 0, 1, .) in terms of the surface particle motion with regard to the mid-plane, which are described in Rayleigh–Lamb equations (Rose, 1999) Symmetricmodes : tan (qh) tan (ph) = 4k 2qp (k2 q2)2 ð1Þ Antisymmetricmodes : tan (qh) tan (ph) = (k 2 q2)2 4k2qp ð2Þ where p2 = v2 c2L…...
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...The fundamentals of Lamb waves can be found in many textbooks, such as Graff (1975), Rose (1999), and Viktorov (1967)....
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...From the Rayleigh–Lamb equations, the relationship between frequency f and wavenumber k can be solved numerically (Rose, 1999)....
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...which are described in Rayleigh–Lamb equations (Rose, 1999)...
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1,933 citations
"Lamb wave frequency–wavenumber anal..." refers background in this paper
...straightforwardly extended to multidimensional signals such as the time–space wavefield data, which is in terms of the time variable t and the space vector x (Johnson and Dudgeon, 1993)....
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...Accordingly, the multidimensional FT in equation (3) reduces to 2D FT, which can be expressed as (Johnson and Dudgeon, 1993) U ( f , kx)=F2D u(t, x)½ = ð‘ ‘ ð‘ ‘ u(t, x)e j(2pft kxx)dtdx ð6Þ The inverse 2D FT becomes u(t, x)=F 12D U ( f , kx)½ = 1 2p ð‘ ‘ ð‘ ‘ U ( f , kx)e j(2pft kxx)dfdkx ð7Þ F2D…...
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...The concept of Fourier analysis is straightforwardly extended to multidimensional signals such as the time–space wavefield data, which is in terms of the time variable t and the space vector x (Johnson and Dudgeon, 1993)....
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...Accordingly, the multidimensional FT in equation (3) becomes three-dimensional (3D) FT, which can be expressed as (Johnson and Dudgeon, 1993)...
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...Accordingly, the multidimensional FT in equation (3) becomes three-dimensional (3D) FT, which can be expressed as (Johnson and Dudgeon, 1993) U ( f , kx, ky)=F3D u(t, x, y)½ = ð‘ ‘ ð‘ ‘ ð‘ ‘ u(t, x, y)e j(2pft kxx kyy)dtdxdy ð8Þ The inverse 3D FT becomes u(t, x, y)=F 13D U ( f , kx, ky) = 1 (2p)2…...
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1,877 citations
"Lamb wave frequency–wavenumber anal..." refers background in this paper
...The fundamentals of Lamb waves can be found in many textbooks, such as Graff (1975), Rose (1999), and Viktorov (1967)....
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1,413 citations
"Lamb wave frequency–wavenumber anal..." refers background in this paper
...Lamb waves are a subset of guided waves that propagate between two parallel surfaces such as in shell and plate structures (Lamb, 1917)....
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...Lamb wave propagation study setup Lamb wave dispersion curves Lamb waves are a subset of guided waves that propagate between two parallel surfaces such as in shell and plate structures (Lamb, 1917)....
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