This article deals with structural vibration attenuation and control using periodic materials for isolation of structures. An innovative approach to achieve wider low-frequency attenuation zones using a combination of different one-dimensional periodic units has been explored to provide close to a vibration-free environment for civil engineering structures subjected to seismic and other excitations. The wave attenuation regions for the base isolation system made of periodic materials have been derived from the theory of phononic materials and investigated using parametric studies and finite element modelling. The concept of combined periodicity is implemented on bridges to achieve wider attenuation zone and higher response reduction. A novel concept of using a hollow-shell periodic isolation system on bridges has been presented to minimize the effect of seismic waves on these structures. A substantial reduction in the seismic response of a bridge model has been observed over the entire frequency domain with the introduction of the proposed isolation systems. The proposed hollow-shell periodic isolation system reduces the seismic response of structures with efficient material utilization as compared to the typical solid-periodic isolation systems. The proposed isolation systems thus open up new directions for research and potential implementation of periodic materials for seismic response reduction and earthquake-resistant design of structures.