This paper investigates the attenuation behavior of flexural waves in functionally graded and disordered piezoelectric metamaterials. These structures are expediently designed by tuning the shunted piezoelectric electrical circuit. The transfer matrix method is employed to calculate the dispersive relationship of one-dimensional graded piezoelectric meta beams. It is found that the attenuation zone of the graded arrangement becomes wider compared with the result of the corresponding periodic structures. Moreover, the attenuation zone becomes wider by increasing the capacitance ratio’s absolute value in a specific region. We demonstrate that the graded system generating the rainbow effect can slow down the flexural wave propagation in the host structure and increase the interaction time between elastic waves and local electrical circuits through the time-domain analysis. Besides, we study further the two-dimensional graded and disordered piezoelectric meta plates. Numerical results show that the bandwidth of the latter on average is broader than that of the former. Moreover, the disordered system can keep the continuity of the dominant attenuation zone and further increase the attenuation bandwidth within the larger capacitance ratio. These graded and disorder configuration concepts may pave a new way for elastic wave manipulation to realize broadband vibration suppressions and frequency selective spatial separations.

The vibrational characteristics of multilayer magnetic nanocomposite beams reinforced by graphene nanoplatelets (GPLs) are analytically investigated in this paper. The effects of an elastic foundation are also studied. The material properties of piece-wise GPL-reinforced nanocomposites (GPLRCs) are assumed to be graded in the thickness direction of the beams and can be estimated by using the modified Halpin–Tsai model and rules of mixtures. The two-dimensional elasticity theory is adopted to derive the governing equation combined with the state space method, and the analytical frequency equations for simply supported beams are obtained. In addition, the effects of a magnetic field are involved via Maxwell’s equation, and the corresponding Lorentz forces are considered in this work. Numerical examples are carried out to examine the effects of magnetic fields in various directions, the GPL distribution pattern, the scale parameter and weight function of GPLs, as well as an elastic foundation, on the vibration behaviors of functionally graded (FG)-GPLRC beams.

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

Based on the first-order shear deformation theory (FSDT) and Kelvin–Voigt viscoelastic model, one derives a wave equation of longitudinal guide waves in viscoelastic orthotropic cylindrical shells, which analytically solves the wave equation and explains the intrinsic meaning of the wave propagation. In the numerical examples, the velocity curves of the first few modes for the elastic cylindrical shell are first calculated, and the results of the available literature are compared to verify the derivation and programming. Furthermore, the phase velocity curves and attenuation coefficient curves of the guide waves for a functionally graded (FG) shell are calculated, and the effects of viscoelastic parameters, material gradient patterns, material volume fractions, and size ratios on the phase velocity curves and attenuation curves are studied. This study can be widely used to analytically model the wave propagating in inhomogeneous viscoelastic composite structures and present a theoretical basis for the excellent service performance of composite structures and ultrasonic devices.