skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Modeling and simulations of a nonlinear granular metamaterial: application to geometric phase-based mass sensing
Abstract Dynamical simulations of an externally harmonically driven model granular metamaterial composed of four linearly and nonlinearly coupled granules show that the nonlinear normal mode can be expressed in a linear normal mode orthonormal basis with time dependent complex coefficients. These coefficients form the components of a state vector that spans a 2 2 dimensional Hilbert space parametrically with time. Local π jumps in the phase of these components occurring periodically are indicative of topological features in the manifold spanned by the geometric phase of the vibrational state of the metamaterial. We demonstrate that these topological features can be exploited to realize high sensitivity mass sensor. The effect of dissipation on sensitivity is also reported. Nonlinear granular metamaterials with very low dissipation could serve as mass sensors with considerable sensitivity to small mass changes via large changes in geometric phase.  more » « less
Award ID(s):
1640860
PAR ID:
10354800
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Modelling and Simulation in Materials Science and Engineering
Volume:
30
Issue:
7
ISSN:
0965-0393
Page Range / eLocation ID:
074002
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of Computational and Nonlinear Dynamics)
    Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps. 
    more » « less
  2. ; ; ; ; ; (, The Astrophysical Journal)
    Abstract We study tidal dissipation in hot Jupiter host stars due to the nonlinear damping of tidally driveng-modes, extending the calculations of Essick & Weinberg to a wide variety of stellar host types. This process causes the planet’s orbit to decay and has potentially important consequences for the evolution and fate of hot Jupiters. Previous studies either only accounted for linear dissipation processes or assumed that the resonantly excited primary mode becomes strongly nonlinear and breaks as it approaches the stellar center. However, the great majority of hot Jupiter systems are in the weakly nonlinear regime in which the primary mode does not break but instead excites a sea of secondary modes via three-mode interactions. We simulate these nonlinear interactions and calculate the net mode dissipation for stars that range in mass from 0.5M⊙≤M⋆≤ 2.0M⊙and in age from the early main sequence to the subgiant phase. We find that the nonlinearly excited secondary modes can enhance the tidal dissipation by orders of magnitude compared to linear dissipation processes. For the stars withM⋆≲ 1.0M⊙of nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periodsPorb≲ 1 day. ForM⋆≳ 1.2M⊙, the orbital decay time only becomes short on the subgiant branch, where it can be ≲10 Myr forPorb≲ 2 days and result in significant transit time shifts. We discuss these results in the context of known hot Jupiter systems and examine the prospects for detecting their orbital decay with transit timing measurements. 
    more » « less
  3. ; (, ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems)
    null (Ed.)
    Recently, an electromechanical metamaterial with integrated resonant circuit elements was developed that enables on-demand tailoring of the operating frequency and interface routes for topological wave transmission. However, limitations to the operating frequency region still exist, and a full exploration of the adaptive characteristics of the topological electromechanical metamaterial has yet to be undertaken. To advance the state of the art, this study investigates the ability to enhance the range of operating frequencies for topological wave transmission in a piezoelectric metamaterial by the reconfiguration of lattice symmetries and connection of negative capacitance circuitry. In addition, the capability to modify the interface mode localization is analyzed. The plane wave expansion method is utilized to define a working frequency region for protected topological wave transmission by evaluating a local topological charge. Numerical simulations verify the existence of topologically protected interface modes and illuminate how the localization and shape of these modes can be altered via external circuit parameters. Results show that the reconfiguration of the lattice structure and connection to negative capacitance circuity enhances the operating frequency bandwidth and interface mode localization control, greatly expanding the adaptive metamaterial capabilities. 
    more » « less
  4. ; ; ; (, Ultrasonics)
    Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count – index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are investigated. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures. 
    more » « less
  5. ; ; (, Journal of Structural Dynamics)
    This paper describes a hybrid approach for modeling nonlinear vibrations and determining essential (normal form) coefficients that govern a reduced-order model of a structure. Incorporating both computational and analytical tools, this blended method is demonstrated by considering a micro-electro-mechanical vibrating gyroscopic rate sensor that is actuated by segmented DC electrodes. Two characterization methods are expatiated, where one is more favorable in computational tools and the other can be used in experiments. Using the reduced model, it is shown that tuning the nonuniform DC bias results in favorable changes in Duffing and mode-coupling nonlinearities which can improve the gyroscope angular rate sensitivity by two orders of magnitude. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email