An armor system with a composite laminate having at least four alternating layers (two bi-layers) of a first material and a second material, the first material having a lower acoustic impedance than the second material. The first material is a viscoelastic polymer with a glass transition temperature less than the expected operational temperature range, and the second material can be a hard material such as steel, aluminum, or ceramic. The laminate can include many alternating layers of elastomer and hard material, and can be adhered or affixed to a thicker armor substrate. Additional protective elements such as corrugated metal-ceramic panels and armored glass cylinders can be added to improve resistance to armor piercing rounds, explosively formed penetrators, or other threats.