Effect of Receptors on The Resonant and Transient Harmonic Vibrations of Coronavirus

By Tomasz Wierzbicki , Wei Li, Yuming Liu, Juner Zhu

18 February 2021

Geometry of the SARS-CoV-2

Wave scattering

Scattering of the rigid shell

Scattering into a deformable elastic shell

Effect of spikes on the scattering

Fourier/Legendre expansion of the spatial pressure distribution

Reynolds number cavitation and viscosity

Resonant vibrations of the smooth shell

Stiffness and strain localization in the single spike

The natural period of vibration of a single spike

Finite element simulation

 

ABSTRACT

The paper is concerned with the vibration characteristics of the Coronavirus family. There are some 25–100 receptors, commonly called spikes protruding from the envelope shell of the virus. Spikes, resembling the shape of a hot air balloon, may have a total mass similar to the mass of the lipid bi-layer shell. The lipid proteins of the virus are treated as homogeneous elastic material and the problem is formulated as the interaction of thin elastic shell with discrete masses, modeled as short conical cross-sectional beams. The system is subjected to ultrasonic excitation. Using the methods of structural acoustics, it is shown that the scattered pressure is very small and the
pressure on the viral shell is simply the incident pressure. The modal analysis is performed for a bare shell, a single spike, and the spike-decorated shell. The predicted vibration frequencies and modes are shown to compare well with the newly derived closed-form solutions for a single spike and existing analytical solutions for thin shells. The fully nonlinear dynamic simulation of the transient response revealed the true character of the complex interaction between the local vibration of spikes and the global vibration of the multi-degree-of-freedom system. It was shown that harmonic vibration at or below the lowest resonant modes can excite large amplitude vibration of spikes. The associated maximum principal strain in a spike can reach large values in a fraction of a millisecond. Implications for possible tearing off spikes from the shell are discussed. Another important result is that after a finite number of cycles, the shell buckles and collapses, developing internal contacts and folds with large curvatures and strains exceeding 10%. For the geometry and elastic properties of the SARS-CoV-2 virus, these effects are present in the range of frequencies close to the ones used for medical ultrasound diagnostics

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