Hi everyone,
I am attempting to replicate the results of a published paper to determine the mass-effective density in order to elucidate the bandgap formation mechanism. The paper is titled "Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators" and can be found at the following link: Article Flexural vibration bandgaps of the multiple local resonance ...
.However, I seem to have encountered an issue at some step in my process. I remodeled the composite wedge mass elastic metamaterial plate (WMEMP) proposed in the study and used the same material properties, ensuring they were assigned correctly. I utilized the Frequency Domain tab in the Solid Mechanics module in COMSOL 5.6. I set up the periodic condition for two pairs of faces in the x- and z-directions, corresponding to the first irreducible Brillouin zone (Γ-X-M-Γ). According to the paper, I assigned a prescribed displacement with a magnitude of 2mm along the y-direction on the faces set up in periodic conditions. The calculated equation for mass-effective density presented in the paper (Equation 4) is illustrated in the following figure.
The parameters used in the equation include:
- Fy(r) acquired from the simulated result at four faces with the assigned displacement. I used the function: "solid.RFtotaly" and applied it as an integral over the four faces with periodic conditions.
- V is the volume of the unit cell (V = 0.000042875 m^3).
- A is the harmonic displacement magnitude (A = 0.002 m).
- The angular frequency w=2*pi*f (with f being the swept frequency from 1-500 Hz).
The obtained mass-effective density is presented in Figure 4 as follows. Using the specified equation to calculate, I found that while the second bandgap matches the results, two distinct lower-frequency bandgaps are observed in my results, differing from the one presented in the paper.
Could anyone help identify which part I may have misunderstood or incorrectly set up? Thank you very much for your assistance!
Sincerely,
Binh
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