We report on broadband-to-narrowband elastic wave filtering resulting from time-periodic modulation of the stiffness of a one-dimensional elastic waveguide. Time modulation produces flat dispersion bands at frequencies that are multiple integers of half the modulation frequency. These flat bands lead to the selective reflection of a broadband incident wave at the interface between a non-modulated medium, and one with time-modulated stiffness properties. This results from the vanishing group velocity at the flat band frequencies, which prevents their propagation into the modulated domain. Thus, the considered modulated waveguide is understood as a single port system, in which a broadband incident wave (input) results in a narrowband reflected wave (output) at a frequency defined by modulation. The appearance of the flat bands for a time-modulated waveguide is here illustrated analytically and through numerical simulations. The filtering characteristics of a non-modulate/modulated interface are observed experimentally by implementing a square-wave modulation scheme that employs an array of piezoelectric patches bonded to an elastic waveguide subject to transverse motion. The patches are shunted through a negative electrical capaticance that, when connected, implements a stiffness reduction for the resulting electromechanical waveguide. Switching the capacitance on and off effectively modulates the stiffness of the waveguide, and illustrates the filtering characteristics associated with time-modulation of the equivalent elastic properties. We envision that a similar approach could be extended to investigate other properties of time-modulated elastic metamaterials, such as non-reciprocity and one-way filtering of elastic waves.Time-dependent material properties have been the object of considerable attention over the years. Parametric effects in time-modulated media have long been used for amplification of electromagnetic waves 1,2 and surface acoustic waves 3,4 . Non-reciprocal elements based on both up and down converter amplifiers have been introduced in the early 1960s 5 . The interest in time-modulated media, motivated by their application for parametric amplification in electromagnetic waveguides and for signal processing applications, has led to numerous studies of both periodic 6-11 and non-periodic modulation schemes 12 . Recently, time-modulation of relevant physical properties, imposed in a traveling-wave form, has been explored to achieve non-reciprocal behavior not only in optics, but also in acoustics and mechanics [13][14][15] . For example, magnetless, efficient and compact radiofrequency communication systems are designed with spatiotemporally modulated gratings to be shielded from

In this work we experimentally achieve 1 kHz-wide directional band-gaps for elastic waves spanning a frequency range from approximately 8 to 11 kHz. One-way propagation is induced by way of a periodic waveguide consisting in an aluminum beam partially covered by a tightly packed array of piezoelectric patches. The latter are connected to shunt circuits and switches which allow for a periodic modulation in time of the cell properties. A traveling stiffness profile is obtained by opportunely phasing the temporal modulation of each active element, mimicking the propagation of a plane wave along the material, therefore establishing unidirectional wave propagation at bandgap frequencies.Nonreciprocal devices have been pursued in various research domains and physical platforms, including quantum [1], electromagnetic [2,3], acoustic [4][5][6] and elastic [7-9] media. These devices support wave propagation from a point (A) to one other (B), but not vice-versa, opening up new possibilities for the control of energy flow with unprecedented performance in communication systems [10], unidirectional insulators [11] and converters [12,13], among others. Important contributions in the context of one-way phonon transport have been formulated by Fleury et. al. [14,15], demonstrating directional wave manipulation in acoustic cyrculator devices. Also, elastic and acoustic directional waveguides have been conceived and physically realized, in analogy with the Quantum Hall effect (QHE), achieving backscattering immune and one-way topological edge states [16][17][18][19][20]. Other approaches to nonreciprocity leverage nonlinear phenomena [21,22], metastability [23], bifurcation and chaos [24] which are particularly attractive solutions due to the presence of solely passive elements. However, the exploitation of nonlinear dynamics usually requires high wave amplitudes, thus making the physical realization impractical for compact devices. An effective platform to break reciprocity is offered by space-time modulated systems [25,26]. Notable recent examples have employed programmable magnetic lattice elements [27] and magnetic springs [28]. In this work we experimentally investigate nonreciprocity in a phononic beam, where spatial and temporal modulations are induced upon electric control of equivalent elastic properties. Namely, the spatial modulation is induced by bonding a pattern of piezoelectric elements on a passive substrate, which effectively alter the Young-s modulus of the waveguid through negative capacitance shunts [29], which are manipulated in time through a switching logic. This enables the formation of a traveling stiffness profile, which produces an asymmetric dispersion relation, which is a hallmark of nonreciprocity.As shown in [29], the proposed configuration an effective mean to test non-reciprocity of spatio-temporally modulated media, and may also be adopted as a flexible platform to explore other phenomena associated with temporal and spatio-temporal modulation, among which parametric amplification [29], conversi...

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In this paper a resonant control technique, called negative derivative feedback (NDF), for structural vibration control is presented. Resonant control is a class of control logics, based on the modal approach, which calculates the control action through a dynamic compensator in order to achieve a damping increase on a certain number of system modes. The NDF compensator is designed to work as a band-pass filter, cutting off the control action far from the natural frequencies associated with the controlled modes and reducing the so-called spillover effect. In the paper the proposed control logic is compared both theoretically and experimentally with the most common state-of-the-art resonant control techniques.

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.

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