Vibrations Analysis of star-shaped auxetic plate using the Differential Quadrature Method

Auxetic metamaterials, known for their unique property of a negative Poisson's ratio, have garnered significant attention in vibration analysis due to their exceptional mechanical properties. The presence of a negative Poisson's ratio enhances their energy absorption and deformation capacity. In vibration analysis, auxetic structures exhibit remarkable frequency-tuning capabilities, enabling the adjustment of resonance properties for specific applications. Finite Element Analysis (FEA) and experimental studies show that auxetic unit cells contribute to improved isolation and reduction of vibrations across a wide frequency range. Furthermore, integrating auxetic materials into hybrid systems offers a pathway for enhancing multifunctional properties, such as combining stiffness and damping. This paper aims to examine the governing equations of an auxetic material with a four-star structure, analyze its bending vibrations, and present frequency results using the Differential Quadrature Method (DQM) and numerical simulations. The DQM is highly capable of handling diverse boundary conditions and demonstrates considerable accuracy compared to simulations. Its high computational speed makes it an ideal solution method for engineering applications.

کلیدواژه ها:

Auxetic metamaterials ، Vibration analysis ، Differential Quadrature Method ، star-shaped auxetic