Vibration control and probabilistic failure delays in auxetic viscoelastic beams and panels through engineered designer viscoelastic materials

Dynamic responses of auxetic linear viscoelastic beams and plates are investigated under time dependent loadings. In auxetic elastic materials the presence of negative Poisson's ratios (PRs) leads to high shear modulus values, which in turn facilitate smaller torsional and shear deformations. However, it has been shown that viscoelastic PRs are time dependent due to the strong influence of stresses and their time histories on PR time functionalities [1 - 5]. Nor are viscoelastic PRs limited to the linear elastic range of -1 to 0.5 [6]. Consequently, they cannot be considered primary material properties. Elastic PR values form the initial conditions of corresponding viscoelastic ones regardless what subsequent time paths the latter may pursue. However, while such initial PRs may serve as a limited initial response guide, their subsequent time behavior is no indicator of viscoelastic material behavior. Instead one needs to deal directly with relaxation shear moduli to identify damping possibilities in order to control motion through the inherent dissipation properties of viscoelastic material. Creep buckling instabilities and probabilities of material failures are analyzed to determine survival times. Optimum designer materials, particularly viscoelastic functionally graded ones with high shear relaxation values, are studied to minimize bending and shear stresses while concurrently lowering displacements and failure probabilities and extending survival times. Representative results from several simulation studies indicate that through the use of optimal designer properties, failure probabilities can be decreased while structural lifetimes can be increased. Most relevant technical areas: Analytical methods, dynamics of modern materials, or system identification and inverse problems.