NDLI: Higher-Order Multiple Scales Analysis of Weakly Nonlinear Lattices With Implications for Directional Stability

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Volume 8: 30th Conference on Mechanical Vibration and Noise

Higher-Order Multiple Scales Analysis of Weakly Nonlinear Lattices With Implications for Directional Stability

Selective Wave Filtering in Time-Modulated Elastic Metamaterials

The Dynamics of Large Systems of Globally Coupled, Mistuned Electromechanical Resonators

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Higher-Order Multiple Scales Analysis of Weakly Nonlinear Lattices With Implications for Directional Stability

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Matthew, D. Fronk Michael, J. Leamy
Copyright Year	2018
Abstract	Recent focus has been given to nonlinear periodic structures for their ability to filter, guide, and block elastic and acoustic waves as a function of their amplitude. In particular, two-dimensional (2-D) nonlinear structures possess amplitude-dependent directional bandgaps. However, little attention has been given to the stability of plane waves along different directions in these structures. This study analyzes a 2-D monoatomic shear lattice composed of discrete masses, linear springs, quadratic and cubic nonlinear springs, and linear viscous dampers. A local stability analysis informed by perturbation results retained through the second order suggests that different directions become unstable at different amplitudes in an otherwise symmetrical lattice. Simulations of the lattice’s equation of motion subjected to both line and point forcing are consistent with the local stability results: waves with large amplitudes have spectral growth that differs appreciably at different angles. The results of this analysis could have implications for encryption strategies and damage detection.
Sponsorship	Design Engineering Division Computers and Information in Engineering Division
File Format	PDF
ISBN	9780791851852
DOI	10.1115/DETC2018-85929
Volume Number	Volume 8: 30th Conference on Mechanical Vibration and Noise
Conference Proceedings	ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Language	English
Publisher Date	2018-08-26
Publisher Place	Quebec City, Quebec, Canada
Access Restriction	Subscribed
Subject Keyword	Stability Dampers Acoustics Encryption Equations of motion Waves Energy gap Filters Simulation Symmetry (physics) Engineering simulation Damage Shear (mechanics) Springs Periodic structures
Content Type	Text
Resource Type	Article

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