Newton’s Third Law is not a Dogma but a Computational Hypothesis

Abstract

Experimental modal analysis is an important stage in the development of a flying vehicle structure. In the experiment, the eigenfrequency of the structure is identified by a corresponding resonance peak of its amplitude-frequency response characteristic. Different sensors in the vibration machine provide different amplitude-frequency response characteristics. The resonance peaks obtained through different sensors for one and the same eigenfrequency of the structure are located with a frequency shift of approximately 1 Hz. This frequency-shift effect is an obstacle for the experimental modal analysis of structures with closely located oscillation modes. This paper explains the frequency-shift effect using the particle approach. A particle is a point mass, and a structure is a system of particles connected by springs, with each particle associated with its own structural model. Each particle has a “right” for its own resonance and “lives” in its own parallel reality. Each particle is associated with an acceleration sensor. The number of simultaneously considered models is equal to the number of sensors. The obtained modal-analysis results are related only to the corresponding particle. Newton’s third law of the particle interaction is not used in full when assessing the particles’ interaction. The action and reaction forces are still applied to different particles along the same line in the opposite directions, but these forces are different. Modal-analysis simulation is limited to the 2-DOF and the 3-DOF oscillation models.