Free vibration of biopolymer spherical shells of high structural heterogeneity

A refined elastic shell model is used to study the effect of high structural heterogeneity on natural frequencies and vibration modes of biopolymer spherical shells. With this model, the structural heterogeneity of a biopolymer spherical shell is characterized by an effective bending thickness (which can be quite different from the average thickness) and the transverse shear modulus (which can be much lower than the in-plane shear modulus). Our results show that actual natural frequencies of axisymmetric spheroidal modes of a biopolymer spherical shell can be much lower than those predicted by the classical homogeneous shell model based on the average thickness, although natural frequencies of axisymmetric torsional modes are close to those predicted by the classical model. For example, with physically realistic parameters for virus capsid STMV, the natural frequencies of spheroidal modes predicted by the present model are about 30-50% lower than those predicted by the classical model, in better agreement with known simulation results. In addition, in the low frequency range of several viral capsids, the number of independent non-axisymmetric vibration modes predicted by the present model is considerably larger than that predicted by the classical homogeneous shell model, in qualitative agreement with known atomistic simulations. These results suggest that the refined shell model could offer a relatively simple model to simulate mechanical behavior of biopolymer spherical shells of high structural heterogeneity.