Vibration and Acoustic Response of Metamaterial Micro-FG Beams Considering Surface Effects and Couple Stress Theory Under Various Beam Theories

In this paper, vibration and acoustic response of the metamaterial functionally graded (FG) microbeams are studied, which takes into account the surface effects based on the Gurtin-Murdoch theory of stress. The surface effects were explained using the Gurtin-Murdoch theory. The carbon nanotubes (CNTs) are used for the reinforcement of the microbeam, and the Mori-Tanaka model is applied to consider the impact of the nanoparticles and their agglomeration. The frequency and bandgap of the microstructure are obtained by using an analytical method. This paper will address and analyze the influence of the geometric parameters, the FG index, percentage of nanoparticles, and agglomeration, as well as the small-scale parameter, on the vibration of the microbeam. The FG metamaterial microbeam has a frequency that grows strongly with microbeam thickness and small-scale effects, with an increase in frequency up to 82% owing to the increased bending stiffness and 5.48T owing to size-dependent hardening. Effective stiffness varies with changes in frequency of reinforcement of nanoparticles by nanoparticles, frequency of reinforcement of agglomeration, and the gradient index of FGM, all of which reduce the frequency. The microbeam has a bandgap range of 1.0 x 10 ⁷ Hz to 2.63 x 10 ⁷ Hz, and it has been found to control the acoustic waves with local resonance.