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 local vibration of spikes and 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.

这篇论文关注的是冠状病毒家族的振动特征。有大约 25-100 个受体，通常称为从病毒包膜壳突出的刺突。类似于热气球形状的尖峰，其总质量可能与脂质双层壳的质量相似。病毒的脂质蛋白被视为均质弹性材料，问题被表述为薄弹性壳与离散质量的相互作用，建模为短锥形横截面梁。该系统受到超声波激励。利用结构声学的方法，表明散射压力非常小，病毒外壳上的压力只是入射压力。对裸壳、单个尖峰和带尖峰装饰的外壳执行模态分析。预测的振动频率和模式显示与新推导的单个尖峰的封闭形式解决方案和薄壳的现有分析解决方案相比较。瞬态响应的完全非线性动态仿真揭示了尖峰局部振动与多自由度系统全局振动之间复杂相互作用的真实特征。结果表明，处于或低于最低共振模式的谐波振动可以激发尖峰的大幅振动。尖峰中相关的最大主应变可以在几分之一毫秒内达到很大的值。讨论了可能从壳上撕下尖刺的影响。另一个重要的结果是，在有限次数的循环之后，外壳会弯曲并坍塌，发展具有大曲率和应变超过 10% 的内部接触和折叠。对于 SARS-CoV-2 病毒的几何形状和弹性特性，这些影响存在于接近用于医学超声诊断的频率范围内。