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. The second material layer can be a layer of hollow or solid spheres. Additional protective elements such as front surface hemispheres or conical projections, and corrugated panels can be added to improve resistance to armor piercing rounds, explosively formed penetrators, or other threats.