NDLI: Classification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression

Content Provider	Springer Nature Link
Author	Detroux, Thibaut Starosvetsky, Yuli Kerschen, Gaetan Vakakis, Alexander F.
Copyright Year	2014
Abstract	In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i.e., under condition of 1:1 resonance); this type of Hamiltonian periodic orbits have been labeled as nonlinear normal modes. To this end we formulate an auxiliary system which consists of a two-dimensional, vibro-impact lattice composed of non-uniform “effective particles” oscillating in an anti-phase fashion. The analysis is based on the idea of balancing linear momentum in both horizontal and vertical directions for separate, groups of particles, whereby each such a group is represented by the single effective particle of the auxiliary system. It is important to emphasize that the auxiliary model can be defined for general finite, squarely packed granular crystals composed of n rows and m columns. The auxiliary model is successful in predicting the total number of such periodic orbits, as well as the amplitude ratios for different periodic regimes including strongly localized ones. In fact this methodology enables one to systematically study the generation of mode localization in these strongly nonlinear, highly degenerate dynamical systems. Good correspondence between the results of the theoretical model and direct numerical simulations is observed. The results presented herein can be further extended to study the intrinsic dynamics of the more complex granular materials, such as heterogeneous two-dimensional and three-dimensional granular crystals and multi-layered structures.
Starting Page	673
Ending Page	696
Page Count	24
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	76
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-01-23
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Periodic orbits Rotatory waves Squarely packed granular crystal Effective particles Hertzian interaction Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Nonlinear normal modes and band zones in granular chains with no pre-compression

Bifurcation of periodic orbits in discontinuous systems

Periodic orbits for the generalized Yang–Mills Hamiltonian system in dimension 6

Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

Revealing the evolution, the stability, and the escapes of families of resonant periodic orbits in Hamiltonian systems

Generating an adaptive multiresolution image analysis with compact cupolets

On the dynamics of the rigid body with a fixed point: periodic orbits and integrability

Structure of saddle-node and cusp bifurcations of periodic orbits near a non-transversal T-point

Stable periodic orbits in a pair of chaotic oscillators coupled by an extremely weak diffusive connection

Classification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression

Similar Documents

Nonlinear normal modes and band zones in granular chains with no pre-compression

Bifurcation of periodic orbits in discontinuous systems

Periodic orbits for the generalized Yang–Mills Hamiltonian system in dimension 6

Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

Revealing the evolution, the stability, and the escapes of families of resonant periodic orbits in Hamiltonian systems

Generating an adaptive multiresolution image analysis with compact cupolets

On the dynamics of the rigid body with a fixed point: periodic orbits and integrability

Structure of saddle-node and cusp bifurcations of periodic orbits near a non-transversal T-point

Stable periodic orbits in a pair of chaotic oscillators coupled by an extremely weak diffusive connection

Classification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression