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A hybrid planar micro-lattice made of functionally graded materials is proposed where the active and passive constituents are constructed by functionally graded beams with and without partially distributed piezoelectric attachments respectively. The analytical model for predicting complex band structure is presented via the spectral element method in combination with the modified couple stress theory and power law, whose accuracy is validated by the finite element method. By adjusting size dependence, feedback control gain, material gradient and arrangement of piezo-patches, controllable wave propagation and attenuation is achieved, which further advances the implementation of optimizations to obtain ultra-wide low frequency stop bands. [ABSTRACT FROM AUTHOR]

This paper investigates the complex band diagram of flexural waves in the phononic plate with semi-infinite heavy fluid loading. The system under examination is a square plate lattice with two-dimensional periodicity immersed in a fluid domain with infinite height. The numerical models based on the wave field transformation and the Galerkin method combined with the finite element discretization technique are developed to investigate the real and imaginary parts of the dispersion relation of flexural waves propagating through the phononic plate incorporating the fluid-loading effects. A perfect agreement is found between the location and width of stop bands from the real band diagram and the attenuation diagram, which supports the validity of the numerical models. Moreover, the complex band diagram is verified by the transverse vibration transmittance of the finite phononic plate. The results demonstrate that the external fluid loading is able to adjust the location, bandwidth, and decaying level as well as affect the degree of attenuation anisotropy of the complete and directional band gaps. [ABSTRACT FROM AUTHOR]

In order to acquire multiple and wider stop bands in periodic sandwich lattice, this work applies the inertial amplification mechanisms to the composite sandwich beam with pyramidal truss cores and presents a theoretical study on the wave propagation characteristics of the proposed sandwich lattice. An analytical model based on the plane wave expansion method and the Galerkin method is developed to investigate the dispersion relation of transverse waves propagating through the sandwich beam, whose validity is verified by the numerical simulations of spatial decaying performance predicted by the finite element method. Numerical results of complex band structures show that the proposed sandwich beam can obtain multiple stop bands and possess much wider bandwidth. Employing the developed model, the effects of varying attached substructure, the layout of truss members and the material damping on the attenuation performance are discussed to show the flexibility and to obtain thorough understanding of the system. [ABSTRACT FROM AUTHOR]