Abstract. In this work, we discuss and numerically validate a strategy to attain reversible macroscopic changes in the wave propagation characteristics of cellular metamaterials with soft microstructures. The proposed cellular architecture is characterized by unit cells featuring auxiliary populations of symmetricallydistributed smart cantilevers stemming from the nodal locations. Through an external stimulus (the application of an electric field), we induce extreme, localized, reversible curling deformation of the cantilevers-a shape modification which does not affect the overall shape, stiffness and load bearing capability of the structure. By carefully engineering the spatial pattern of straight (non activated) and curled (activated) cantilevers, we can induce several profound modifications of the phononic characteristics of the structure: generation and/or shifting of total and partial bandgaps, cell symmetry relaxation (which implies reconfigurable wave beaming), and chirality switching. While in this work we discuss the specific case of composite cantilevers with a PDMS core and active layers of electrostrictive terpolymer P(VDF-TrFE-CTFE), the strategy can be extended to other smart materials (such as dielectric elastomers or shape-memory polymers).

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In this paper, free vibration analysis of functionally graded thick, annular plates with linear and nonlinear thickness variation along the radial direction is investigated by using the polynomial-Ritz method. The material properties of the functionally graded plates are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The solution procedure is based on the linear, small strain, three-dimensional elasticity theory. Potential (strain) and kinetic energies of the plates are formulated, and the polynomial-Ritz method is used to solve the eigenvalue problem. In this analysis method, a set of orthogonal polynomial series for three displacement components in a cylindrical polar coordinate are used to extract an eigenvalue equation yielding natural frequencies. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant digits is demonstrated. Numerical results are presented and compared with the available literature. The vibration frequencies are given in several examples for various boundary conditions for the first time.

This study presents large deformations of slender elastic and viscoelastic beams with multiple piezoelectric patches attached on their top and bottom surfaces. The slender beams can undergo large in-plane 2-D deformations due to electric fields applied through the piezoelectric patches and mechanical actuations. A nonlinear electro-mechanical constitutive equation is considered for the piezoelectric patches, while linear elastic and viscoelastic constitutive equations are used for the beams. Reissner's finite-deformation beam theory is adopted in formulating the large 2-D deformation, and modified in order to incorporate the deformation due to the electric field input. For an elastic beam, closed form solutions are obtained for the deformations of the beam under electric field actuation, while a nonlinear shooting method is used to analyze the deformation of the beam under both electrical-and mechanical stimuli. For viscoelastic beams, time-dependent deformations of the beams under electric field actuations through the piezoelectric patches are solved numerically. By applying electric fields with different amplitude at different locations of patches, desired deformed shapes in active flexible beams can be achieved, which is useful for analyses and designs of active foldable systems. This study also highlights the effect of viscoelastic materials on the shape changes in foldable electro-active beams.

This paper presents numerical analyses of elastic and viscoelastic smart flexible and foldable composite structures under electric field actuation. The studied composites comprise of multiple distributed piezoelectric patches bonded to the surfaces of inactive thin planar structures (substrates). Upon applications of electric field input, the planar structures can undergo three-dimensional large rotational deformations while their strains and stretches remain relatively small. A nonlinear time-dependent electro-mechanical coupling relation for the piezoelectric patches is considered to simulate more precisely response of piezoelectric materials when subjected to large magnitude of electric field. Co-rotational Lagrangian finite element approach is used for solving the governing equations of the deformations of flexible and foldable electroactive composite structures. Various three-dimensional shape changes of originally planar structures are achieved with different arrangements of integrated patches and subjected to different magnitude of electric fields. The effect of viscoelastic substrates and time-dependent electro-mechanical coupling of piezoelectric materials on the deformed shapes is also studied. This analysis can help designers in simulating desired deformed shapes and determining external stimuli to be prescribed prior to fabricating smart and flexible composites.