Complex wavenumber of Lamb waves in lossy materials

[AnderDM]

Dear all,

I have a question related to acoustic propagation in isotropic lossy media, more specifically generation of Lamb waves at fluid-solid interfaces. There goes the question:

I am trying to obtain the Lamb wave velocity and attenuation dispersion curves of viscoelastic materials, aplying the transfer matrix method. Lamb waves are generated from an homogeneous non attenuating longitudinal wave propagating in a fluid incident with a certain angle in the isotropic viscoelastic plate.

I am using the plate transfer matrix for isotropic materials (B. Hosten, 1991) , which equaling the top and bottom stresses (to zero) and the displacements (not zero) derives Lamb waves dispersion equation.

The dispersion equation is dependant on frequency and excitation angle. It is clearly stated that for those frequency-angle values where a solution exists, the real wavenumber of the lamb wave is derived from:

Real(K_Lamb) = K_Fluid*sin(angle);

However, I must be missing something cause I do not know how to relate the frequency-angle to the complex wavenumber of the lamb wave.

Any help on the matter would be highly appreciated.

Thanks in advance.

 

[AndyW]

Thank you for your question regarding the generation of Lamb waves in isotropic lossy media. As a scientist with expertise in acoustics, I would be happy to provide some guidance on this topic.

Firstly, it is important to understand that Lamb waves are a type of guided wave that propagate in solid materials, such as plates, and are typically generated by a localized source. In your case, you are interested in studying the generation of Lamb waves at fluid-solid interfaces in viscoelastic materials.

The transfer matrix method is a commonly used technique for analyzing the propagation of guided waves in layered media, such as the fluid-solid interface in your case. This method involves breaking down the layered structure into individual transfer matrices, which can then be combined to obtain the overall transfer matrix for the entire structure. This transfer matrix can then be used to calculate the dispersion curves for the guided waves, including the Lamb wave velocity and attenuation.

In terms of obtaining the complex wavenumber of the Lamb wave, it is important to consider the frequency-angle dependence of the dispersion equation. As you have mentioned, the real wavenumber of the Lamb wave can be derived from the frequency and excitation angle using the equation Real(KLamb) = KFluid*sin(angle). However, the complex wavenumber can be calculated by solving the dispersion equation for the imaginary part of K.

In summary, the frequency-angle dependence of the dispersion equation is essential in obtaining both the real and complex wavenumbers of the Lamb wave. I hope this helps to clarify your understanding of the topic. If you require further assistance, please do not hesitate to reach out.