Dear researchers,
I have some basic questions. I tried to calculate the complex wave number (the real wave number and attenuation constant) of a sandwich plate. In this problem, the two outer layers and the damping layer are all viscoelastic. The composite plate is a thin one. I utilized Abdulhadi’s model. (See reference (2) on the attached file.) The governing equation of this model includes sixth degree differentiation term in space. So there must be three kinds of waves.
Last year, we derived explicit expression of the complex wave number of a longitudinal wave in a viscoelastic rod and a flexural wave in a viscoelastic beam (plate). (See references (4) and (5).) We derived an iterative procedure to calculate the complex wave number of a sandwich plate. This procedure is a combination of our formula and Abdulhadi's model.
On the other hand, I tried to solve the wave number equation analytically. This trial was influenced by the recent work of Piana(1) et al. The first complex wave number agreed with our iterative procedure. But the second and third waves have funny behaviors. For example, the real wave number of the second wave shows finite value even at the zero frequency. We call here the first wave “apparent wave”, and the second and third wave “latent waves”.
(Questions) (1) Does the funny behavior of the latent waves come from bad mathematical treatments? Or is there any physical reason? (2) Can the latent waves really be observed? For further details, please see the attached file. The references are at the end of this file.
I am looking forward to hearing from you.
Sincerely, Ryuzo Horiguchi (Kao Corporation)
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