Design of materials with special dynamic properties using negative stiffness components

This work presents design concepts to synthesize composite materials with special dynamic properties, namely, materials that soften at high frequencies. A typical rubber-like material hardens with frequency and a material which reverses this behavior will find application in product design for vibration absorption such as automobile engine mounts. Such dynamic properties are achieved through the use of a two-phase material that has inclusions of a viscoelastic material of negative elastic modulus in a typical matrix phase that has a positive elastic modulus. Possible realizations of the negative stiffness inclusion phase are presented. One way to realize the negative stiffness phase is by using a lattice containing bistable structures. A numerical homogenization technique is used to compute the average viscoelastic properties of such composites. A methodology is presented for the automatic design of such special materials using topology optimization techniques. The method and the vibration-isolation properties of a composite material designed with it are demonstrated through examples.