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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]

Phononic crystals of the smaller scale show a promising future in the field of vibration and sound reduction owing to their capability of accurate manipulation of elastic waves arising from size-dependent band gaps. However, manipulating band gaps is still a major challenge for existing design approaches. In order to obtain the microcomposites with desired band gaps, a data drive approach is proposed in this study. A tandem neural network is trained to establish the mapping relation between the flexural wave band gaps and the microphononic beams. The dynamic characteristics of wave motion are described using the modified coupled stress theory, and the transfer matrix method is employed to obtain the band gaps within the size effects. The results show that the proposed network enables feasible generated micro phononic beams and works better than the neural network that outputs design parameters without the help of the forward path. Moreover, even size effects are diminished with increasing unit cell length, the trained model can still generate phononic beams with anticipated band gaps. The present work can definitely pave the way to pursue new breakthroughs in micro phononic crystals and metamaterials research. [ABSTRACT FROM AUTHOR]

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]

Low-frequency transverse wave propagation plays a significant role in the out-of-plane vibration control. To efficiently attenuate the propagation of transverse waves at low-frequency range, this letter proposed a new type phononic beam by attaching inertial amplification mechanisms on it. The wave propagation of the beam with enhanced effective inertia is analyzed using the transfer matrix method. It is demonstrated that the low-frequency gap within inertial amplification effects can possess much wider bandwidth than using the local resonance method, thus is more suitable for designing applications to suppress transverse wave propagation. [ABSTRACT FROM AUTHOR]

With the purpose of obtaining complete stop bands which allow one isolate both longitudinal and transverse vibrations in functionally graded beams, this paper adopts the inertial amplification mechanisms via attaching them on the base beam whose material properties are described by the power-law function to study the nature of propagation and attenuation characteristics. The dynamic model of the inertial amplification mechanism is developed to capture inertial forces when the coupled axial-bending deformation is present in the base structure. By employing the principle of the virtual work and the Bloch theory, a discrete formulation is presented to exploit the complex band diagram. Numerical analyses show that multiple stop bands whose attenuation performances are comparable to that of resonance gaps can be obtained, demonstrating the efficiency on suppressing wave propagation over a wide frequency band, which is helpful to expand the range of engineering applications with functionally graded materials for vibration and sound reduction. Furthermore, the effects of the geometrical characteristics of attached substructure, power-law index and material damping are investigated. [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]