Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences· 2026Q1
Predicting subharmonic and superharmonic backbone curves in nonlinear mechanical systems
- 0citations
- Q1SCImago
- 2026year
Short summary
A new mathematical connection reveals that a single primary or secondary backbone curve can predict all other backbone curves in a family for nonlinear mechanical systems under weak periodic forcing and damping.
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Key points
- Primary backbone curves are mathematically connected to all subharmonic and superharmonic backbone curves.
- A single primary or secondary backbone curve member can predict all others in its family.
- This prediction relies on a simple linear scaling relationship.
- The method applies to nonlinear mechanical systems under weak periodic forcing and damping.
- It enables quick theoretical prediction of forced response peaks from higher-order resonances.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We show that conservative (or primary) backbone curves, defined as amplitude–frequency curves of conservative nonlinear normal modes, have a tight mathematical connection with all subharmonic and superharmonic (or secondary) backbone curves, defined as curves connecting peaks of forced response at higher-order resonances. Specifically, under weak periodic forcing and damping, a single primary or secondary member of a backbone curve family determines all other members of that family via a simple linear scaling relationship that we illustrate in examples. This observation provides a quick theoretical prediction for forced response peaks arising from higher-order external resonances without the need for numerical simulations or experiments.
The authors' abstract, as published at the source. Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 2026 · DOI ↗
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Field: Civil and Structural Engineering
Civil and Structural EngineeringEngineering