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Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

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Abstract

High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quantities such as resonance frequencies, wave speeds, buckling loads, and equilibrium states. There are two ways to do this: by using parametric HFE (with or without nonlinearity) or by using external HFE along with strong nonlinearity. The first way, parametric stiffening, has been examined for many different systems, and analytical predictions exist that have been repeatedly confirmed against numerical simulation and laboratory experiments. The current work presents results using the other way, external stiffening: Combining the method of direct separation of motions with results of a modified multiple-scale approach, valid also for strong or even essential nonlinearity, quantitative measures of the stiffening effect are predicted for a generic 1-DOF system and tested with generally good agreement against numerical simulation and laboratory experiments.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported in part by the Danish Council for Independent Research Technology and Production Sciences, Grant No. 274–05-0498.

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Authors and Affiliations

  1. Department of Civil and Mechanical Engineering, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark

    Jon Juel Thomsen & Kristian Ladefoged Ebbehøj

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  1. Jon Juel Thomsen
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  2. Kristian Ladefoged Ebbehøj
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Contributions

JJT performed the theoretical analysis; both authors planned and designed the laboratory experiments, with KLE actually performing and data processing and analysis of these. JJT drafted the manuscript, with substantial input from KLE on the experimental parts. Both authors revised the manuscript critically for important intellectual content, read and approved the submitted manuscript, and agreed to be accountable for all aspects of the work.

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Correspondence to Jon Juel Thomsen.

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Thomsen, J.J., Ebbehøj, K.L. Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment. Nonlinear Dyn 111, 6985–7003 (2023). https://doi.org/10.1007/s11071-023-08255-7

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