Trimming of imperfect hemispherical shell including point mass distributions

Abstract Generally, a hemispherical shell is well-known simple structure for application in engineering fields such as Hemispherical Resonator Gyroscope (HRG), Energy Harvester (EH), etc. In this regard, numerous researchers have investigated the perfect shell model to analyze vibration characteristics due to the conciseness to manufacture the structure. However, a slight imperfection on the structure may result in significant inaccuracy of a signal in the practical point of view. Actually, frequency difference due to the irregularity of structure induces error on the resonator, and thus the reduction of imperfections can be a crucial feature during the operation of devices. As a method for controlling motion as well as characteristic in the vibration, the eliminating frequency split, in other words “trimming”, is introduced in this study. To obtain the eigenfrequency and to model the point masses, Rayleigh's energy method is applied to get the analytical solution. In order to show the accuracy of present study, data are compared with COMSOL Multiphysics®. Finally, the trimming mass is analytically predicted by the function of initially attached masses and angular positions.