Granular Media-Based Tunable Passive Vibration Suppressor

and vibration suppression device is composed of statically compressed chains of spherical particles. The device superimposes a combination of dissipative damping and dispersive effects. The dissipative damping resulting from the elastic wave attenuation properties of the bulk material selected for the granular media is independent of particle geometry and periodicity, and can be accordingly designed based on the dissipative (or viscoelastic) properties of the material. For instance, a viscoelastic polymer might be selected where broadband damping is desired. In contrast, the dispersive effects result from the periodic arrangement and geometry of particles composing a linear granular chain. A uniform (monatomic) chain of statically compressed spherical particles will have a low-pass filter effect, with a cutoff frequency tunable as a function of particle mass, elastic modulus, Poisson fs ratio, radius, and static compression. Elastic waves with frequency content above this cutoff frequency will exhibit an exponential decay in amplitude as a function of propagation distance. System design targeting a specific application is conducted using a combination of theoretical, computational, and experimental techniques to appropriately select the particle radii, material (and thus elastic modulus and Poisson fs ratio), and static compression to satisfy estimated requirements derived for shock and/or vibration protection needs under particular operational conditions. The selection of a chain of polymer spheres with an elastic modulus .3 provided the appropriate dispersive filtering effect for that exercise; however, different operational scenarios may require the use of other polymers, metals, ceramics, or a combination thereof, configured as an array of spherical particles. The device is a linear array of spherical particles compressed in a container with a mechanism for attachment to the shock and/or vibration source, and a mechanism for attachment to the article requiring isolation (Figure 1). This configuration is referred to as a single-axis vibration suppressor. This invention also includes further designs for the integration of the single-axis vibration suppressor into a six-degree-of-freedom hexapod "Stewart"mounting configuration (Figure 2). By integrating each singleaxis vibration suppressor into a hexapod formation, a payload will be protected in all six degrees of freedom from shock and/or vibration. Additionally, to further enable the application of this device to multiple operational scenarios, particularly in the case of high loads, the vibration suppressor devices can be used in parallel in any array configuration

Nonlinear Waves in Disordered Diatomic Granular Chains

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.Comment: 10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results

Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies

Nanoelectromechanical systems (NEMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling, mechanically induced transparency, Rabi oscillation, two-mode squeezing and phonon lasing. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps, energy transport, non-linear dynamics and localization, and topological properties, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10–30 MHz). The design of our systems is inspired by NEMS-based phonon waveguides and includes the voltage-induced frequency tuning of the individual resonators. Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter. The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials’ compliance and mechanical non-linearities

An Experimental Investigation of Acoustic Band Gaps and Localization in Granular Elastic Chains

We assembled a chain composed of a periodic arrangement of aluminum and steel spheres encased in a 4-rod polycarbonate holder with tunable static precompression applied by means of a lever actuated system. To excite periodic oscillations we perturbed the chain with a piezo-stack actuator driven by both continuous and finite bursts of a sinusoidally varying periodic signal. The amplitude of the periodic signal ranged from linear to strongly nonlinear regimes. We report the tunability of the frequency range for the band gap edges as a function of the material parameters, chain geometry and stress conditioning. We analyze the data by means of force-time plot and Fast Fourier Transforms (FFT). We observe a dramatic reduction of the transmitted wave amplitude for harmonic excitations with fundamental frequencies within the gap. The application of both continuous and short bursts of perturbation allows for observation of different dynamic phenomena at selected frequency ranges (in particular close to the lower optical branch edge). By varying the amplitude of the dynamic excitation (and therefore the level of the nonlinearity present in the system) we seek localized discrete breathing modes and surface instabilities. The comparison between continuum theory, discrete numerical modeling and experiments show a qualitative agreement and provide fundamental understanding for future investigation and numerous engineering applications. The challenges and considerations involved with the construction of an experimental system capable of capturing and leveraging on the described phenomena will be detailed

Analytical and Experimental Analysis of Bandgaps in Nonlinear one Dimensional Periodic Structures

Wave propagation characteristics of nonlinear one-dimensional periodic structures are investigated analytically, numerically and experimentally. A novel perturbation analysis is first applied to predict the band gap location and extent in terms of linear and nonlinear system parameters. Approximate closed-form expressions capture the effect of nonlinearities on dispersion and depict amplitude dependent cut-off frequencies. The predictions from the perturbation analysis are verified through numerical simulations of harmonic wave motion. Results indicate the possibility of input amplitude as a tuning parameter through which cut-off frequencies can be adjusted to achieve filtering properties over selected frequency ranges. A periodic diatomic chain of stainless steel spheres alternating with aluminium spheres is experimentally investigated. The dynamic behavior of the chain is governed by Hertzian interaction of spheres and by a compressive pre-load which can be adjusted to obtain linear, weakly nonlinear and highly nonlinear behavior. For a weakly nonlinear case, preliminary results in experiments show the tendency for a shift in the band gap edges by varying input amplitude. The paper is a work in progress, for which the experimental results for a weakly nonlinear system are interpreted by the perturbation analysis developed for a specific case of linear and nonlinear power law interaction of exponent 3/2