Space inflatable technology is a promising solution to placing large metrology systems in space. Lighter weight, higher packaging efficiency, and easier maintenance are among a few of their advantages over mechanically deployed structures. On the other hand, their large volume after deployment makes them susceptible to disturbances in space. Therefore, vibration control is one major issue for this technology. The present work is an extension of the previous work of the author on continuum modeling of these structures for their vibrations analysis. Kinetic and strain energy expressions of the fundamental lattice elements of a structure are expanded in terms of the nodal displacement components. Certain assumptions are made to reduce the order of strain components in a three-dimensional structure in order to find the equivalent continuum model. Additionally, this work includes the effects of strain rates on the kinetics of these structures. The frequency results for various structures are compared to those of a previous model which neglects such effects. It is shown that the frequency changes are noticeable when the strain rate components are included in the kinetic energy derivations.