A ‘multiple modes’ − ‘multiple parameters’ sensing methodology: Part I – Theoretical modelling

This paper, the first of two companion papers, reports a sensing methodology for synchronous and successive detection of ‘multiple parameters’, via ‘multiple modes’ internal resonance in coupled oscillators.

Detection of ‘multiple parameters’ such as mass, force and damping, characterizing different kinds of perturbations such as weak forces, weak physical fields, trace pollutants or toxic, explosive substances and biological viruses, is crucial for nanotechnology, quantum computer, chemical production, public health and safety etc. with high engineering value.

However, quantitative detection of ‘multiple parameters’ is challenged by too many modes (i.e. more than three ones), intermittent detection, inevitable decoupling, as well as conditional parameter ratio in reported art works.

A ‘multiple modes’ − ‘multiple parameters’ sensing methodology, driven by ‘multiple modes’ internal resonance and supported by two theoretical models, is therefore proposed to address the above challenges with coupled oscillators.

The first theoretical model is established for ‘multiple modes’ internal resonance with 1:3 frequency ratios, while the second one is comprised of two nonlinear sensing theories with and without decoupling respectively, established for synchronous and successive detection of ‘multiple parameters’.

The proposed sensing methodology is physically universal and applicable to parameters, such as mass, force or damping, if convertible to or equivalent to any changes in vibrational coefficients of the oscillator.

The above theoretical models are generalized to different types of vibrational modes, such as flexural, shearing and torsional ones owing to their common characteristic in the higher order mode shapes.

While an experimental validation of the proposed sensing methodology will be discussed in part II.