The steady-state response of a Maxwell viscoelastic cylinder to sinusoidal oscillation of its boundary

Abstract

The steady-state response of a Maxwell viscoelastic cylinder to periodic sinusoidal oscillation of its boundary was studied as a simplified model of the brain responding to low-amplitude angular vibration of an idealized skull. The objectives were to identify conditions in which peak strain occurred on the interior of the cylinder, and to identify ways to scale strains from differently sized cylinders. This latter objective is motivated by the work of Holbourn to inform scaling of intracranial strains experienced under similar acceleration of skulls of different animals. The mechanical response was dictated by two dimensionless parameters that incorporate material properties and external loading frequency. The location and magnitude of maximum strain were examined with respect to these governing parameters in steady state. A frequency-dependent mapping of brain constitutive data to idealized Maxwell models was applied to predict the location and magnitude of peak strains inside a cylinder with mechanical properties representing the adult human brain. Results suggest that peak strains occur on the interior of such a cylinder for skull oscillation within a specific frequency band.