Numerical simulation data for the dynamic properties of rainbow metamaterials

Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles “Rainbow metamaterials for broadband multi-frequency vibration attenuation: numerical analysis and experimental validation” (Meng et al., 2019 [1]) and “Optimal design of rainbow elastic metamaterials” (Meng et al., 2019 [2]). In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0–500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials.


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Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles "Rainbow metamaterials for broadband multifrequency vibration attenuation: numerical analysis and experimental validation" (Meng et al., 2019 [1]) and "Optimal design of rainbow elastic metamaterials" (Meng et al., 2019 [2]). In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0e500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials.

Data
This article gives the numerical simulation data of dynamic properties of rainbow metamaterials (i.e. resonating elastic metamaterials composed of a P-shaped beams and parallel plate insertions as backbone structures along with the spatially varying cantilever-mass resonators as shown in Fig. 1). The rainbow metamaterial can exhibit single or multifrequency bandgaps depending on whether the two sets of resonators attached to different side walls are symmetric [1,2]. The receptance functions and mode shapes of the rainbow metamaterial are numerically calculated by Finite Element (FE) models set up in Ansys Mechanical APDL. The receptance function values of the rainbow metamaterial are obtained as shown in Fig. 3.
Typical mode shapes of the rainbow metamaterials with corresponding natural frequencies equal to the critical peak and dip frequencies marked in the receptance function curve of Fig. 3 are plotted in Fig. 4(a)-(h) respectively.
Raw simulation data for the receptance functions and mode shapes are shared respectively as supplemental files "FRFcal.db" and "Modeshape cal.db".

Experimental design, materials, and methods
In the FE model, the modelling assumptions are as follows: the P-shaped beam and parallel plate insertions are modelled by Shell181 element, the cantilever beams Beam188 element, and the Specifications Table   Subject Mechanical Engineering Specific subject area Finite element simulation of metamaterials Type of data

Value of the Data
The data allows the prediction of frequency response functions and modal shapes of the rainbow metamaterials with Finite Element simulation method in Ansys Mechanical APDL The numerical simulation data could not only act as an alternative method of modelling the rainbow metamaterial, the modal shapes can reveal the underlying vibration attenuation mechanism that cannot be given out by the presented analytical model [1,2], which would aid readers to fully understand the rainbow metamaterials. The numerical simulation data can be easily reproduced by researchers in the areas of metamaterials or Finite Element modelling, hence serve as a workbench for the analysis and design of rainbow metamaterials.
spatially varying mass21 element. All the boundaries of the rainbow metamaterial beam are unconstrained.
For the receptance function simulation, a load force F ¼ 1 N in Z-direction is exerted on one end of the beam as shown in Fig. 2. Harmonic analysis is subsequently conducted with the 'full' method, which solves the simultaneous equation of motion directly. Receptance functions of the metamaterial beam within the frequency range 0e500 Hz are consequently obtained with ratios of predicted displacements at the other end of the beam and the exciting force. With regard to mode shape simulation,     Tables 1 and 2.
The obtained mode shapes could explain the critical points in receptance function curve, which also reveals the vibration mechanism of the rainbow metamaterial. As can be seen from Fig. 4(a), (e), (f) and (h), vibration of the rainbow metamaterial at frequenciesf 2 , f 3 , f 4 and f 7 is subjected to mode shapes with dramatically deformed resonators and undeformed backbone structure, namely, the vibration of backbone structure is suppressed at these frequencies, dips therefore appear in the receptance curve as shown in Fig. 3. By contrast, obvious deflection of the backbone structure as well as the resonators could be seen from the mode shapes with natural frequencies f 1 , f 5 , f 6 and f 8 , which means the backbone structure vibrates dramatically as the resonators at these frequencies, peaks thus can be seen from Fig. 3 at corresponding frequencies.