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Acoustic radiation response of functionally graded sandwich plates cored by butterfly-shaped honeycombs with negative Poisson’s ratio

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Abstract

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative Poisson’s ratios have unique mechanical deformation characteristics, superior strength to density ratio and high stiffness, both of which can be used to build lightweight sandwich constructions. The purpose of this study is to investigate the vibration acoustic response of porous functionally graded honeycomb sandwich plates with a negative Poisson’s ratio (NPR). Under simply supported boundary conditions, the dynamic equation of the sandwich plate is derived based on the Hamilton principle, and the eigenvalue of the modal function matrix is coupled with the Navier method to obtain the natural frequency. The theoretical calculation results are compared with the finite element software COMSOL simulation results, so as to verify the validity and correctness of the theoretical model proposed in this paper. The far-field radiation sound pressure level of sandwich plate under point force loading is derived by Rayleigh integral theory. The correctness of the proposed model is verified by comparing the radiation sound pressure level calculated by the theoretical model with the results obtained by the finite element software simulation. The effects of porous functionally graded materials (FGM) and cellular structure parameters on the acoustic radiation characteristics of sandwich plates are discussed in detail. The results show that: The relative error between the theoretical results and the literature results is 5.43 %. Under the same conditions, the amplitude of the radiation sound pressure level (SPL) decreases by about 29.48 % in the low frequency stage, 28.9 % in the medium frequency stage and 11.08 % in the high frequency stage under the point excitation when the cellular side length is 6 mm compared with 8 mm in the low frequency stage. The movement trend and amplitude of the sandwich plate’s emitted SPL are significantly impacted by changes in the characteristics of the cellular structure.

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Abbreviations

P :

Elasticity modulus

E :

Young’s modulus

Lx :

Length of plate

Ly :

Width of plate

h :

Thickness of plate

h c :

Sandwich layer height

p :

Gradient index

λ 0 :

Porosity

SPL :

Sound pressure level

a 1, β 1 :

Cellular inclination angle

t :

Cellular thickness

L 1, L 3 :

Cellular side length

c :

Ceramic

m :

Metal

FGM :

Functionally graded material

TDET :

Three-dimensional elasticity theory

FG-CNTRC :

Functionally graded carbon nanotube reinforced composite

TSDT :

Third-order shear deformation theory

FRP :

Fibred reinforced plastic

NPR :

Negative Poisson’s ratio

EBT :

Euler beam theory

SEM :

Spectral element technique

CSPT :

Conventional sandwich plate theory

FSDT :

First-order shear deformation theory

HSDT :

Higher-order shear deformation theory

CPT :

Classical plate theory

RTSDT :

Reddy third-order shear deformation theory

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Acknowledgments

This work is supported by Research Program supported by the National Natural Science Foundation of China (Grant No. 52205105) and the Yunnan Fundamental Research Projects (Project No. 202101AU070160 and 202201AT070145).

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Authors and Affiliations

  1. Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, 650500, China

    E. Rao & Tao Fu

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  1. E. Rao
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  2. Tao Fu
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Corresponding author

Correspondence to Tao Fu.

Additional information

E. Rao is M.D. candidate in the Faculty of Mechanical and Electrical Engineering at Kunming University of Science and Technology. Her research interests are the acoustic response of sandwich structures and metamaterial structures.

Tao Fu received his Ph.D. in 2019 from School of Mechatronics Engineering, Harbin Institute of Technology. He is master supervisor of Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology. His research work is focused on vibration and noise control of novel sandwich structure.

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Rao, E., Fu, T. Acoustic radiation response of functionally graded sandwich plates cored by butterfly-shaped honeycombs with negative Poisson’s ratio. J Mech Sci Technol 38, 2321–2333 (2024). https://doi.org/10.1007/s12206-024-0413-5

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  • DOI: https://doi.org/10.1007/s12206-024-0413-5

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