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To gain a complete view on the unique spatial attenuation phenomenon arising from the periodicity and the material viscoelasticity of the two-dimensional phononic crystals with finite out-of-plane extension, this paper presents a theoretical study of the viscoelastic phononic crystal slabs to investigate the wave transmission characteristics in terms of the dispersion relations for the propagating, evanescent, and complex modes. A numerical approach based on the theory of three-dimensional elasticity is proposed to eliminate the restrictions of plane analysis and to obtain the complex band diagrams using the wave expansion functions combined with the finite discretization technique. This formulation allows one to perform the simulations associated with the nonlinear frequency-dependent viscoelastic property which is accurately described by a generalized Maxwell model in this work. Numerical results are presented to show the validity of the established model and to reveal the dissipation mechanisms inside and outside the band gaps as well as to investigate the effects induced by the material viscoelasticity on the attenuation diagrams. Furthermore, the influences of the out-of-plane extension, the geometrical size and the shape of the etcfhed holes are detailed discussed to obtain thorough understandings of such a finite solid viscoelastic periodic lattice which is indispensable to practical applications. [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]