Parametric excitation of rotational soft modes of the buckled discrete elastic ring
Abstract
In the present study, we explore the existence and characteristics of a rotating vibrational mode in a discrete buckled ring that manifests under transverse harmonic forcing. The study is conducted through mathematical analysis complemented by numerical simulations. The ring is composed of uniformly distributed concentrated masses connected by linear and torsional springs and supported by an elastic foundation. The buckled state of interest results from homogeneous in-plane compression and is characterized by vibrational modes that have a rotating nature because of the rotational symmetry of the system. The resulting vibrational mode, called a rotational soft mode, is characterized by large amplitude rotations of the ring deformation while keeping its angular momentum zero. It is shown that rotational soft modes can be activated via transverse harmonic forcing through parametric resonance, which is possible only when nonlinearities are introduced to the foundation. In the absence of nonlinear behavior, transverse vibrations of the ring cannot lead to excitation of the rotational mode. Analysis of a constrained kinematics model shows that linear stiffness of the foundation leads to decoupling of the rotational mode from transverse vibrations. When the foundation is considered piecewise linear, with different stiffness values in compression and in extension, it is shown that three different behaviors are possible for the dynamic response of the forced ring: i) no rotation, ii) a limit cycle within a limited finite rotation angle range, iii) induced rotation between subsequent equilibrium angles. The present study contributes to the understanding of the activation and control of soft modes in buckled structures and may lead to actuation applications in soft robotics, as well as advanced manipulation strategies of molecular systems in the context of nanomechanics.
Versions
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BibTeX
@misc{koutsogiannakis2026parametric,
title = {{Parametric excitation of rotational soft modes of the buckled discrete elastic ring}},
author = {Panagiotis Koutsogiannakis and Massimo Ruzzene},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36320},
eprint = {2609.36320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36320},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parametric excitation of rotational soft modes of the buckled discrete elastic ring
AU - Panagiotis Koutsogiannakis
AU - Massimo Ruzzene
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36320
UR - https://arxiv.org/abs/2609.36320
AB - In the present study, we explore the existence and characteristics of a rotating vibrational mode in a discrete buckled ring that manifests under transverse harmonic forcing. The study is conducted through mathematical analysis complemented by numerical simulations. The ring is composed of uniformly distributed concentrated masses connected by linear and torsional springs and supported by an elastic foundation. The buckled state of interest results from homogeneous in-plane compression and is characterized by vibrational modes that have a rotating nature because of the rotational symmetry of the system. The resulting vibrational mode, called a rotational soft mode, is characterized by large amplitude rotations of the ring deformation while keeping its angular momentum zero. It is shown that rotational soft modes can be activated via transverse harmonic forcing through parametric resonance, which is possible only when nonlinearities are introduced to the foundation. In the absence of nonlinear behavior, transverse vibrations of the ring cannot lead to excitation of the rotational mode. Analysis of a constrained kinematics model shows that linear stiffness of the foundation leads to decoupling of the rotational mode from transverse vibrations. When the foundation is considered piecewise linear, with different stiffness values in compression and in extension, it is shown that three different behaviors are possible for the dynamic response of the forced ring: i) no rotation, ii) a limit cycle within a limited finite rotation angle range, iii) induced rotation between subsequent equilibrium angles. The present study contributes to the understanding of the activation and control of soft modes in buckled structures and may lead to actuation applications in soft robotics, as well as advanced manipulation strategies of molecular systems in the context of nanomechanics.
ER -