Evaluation of Negative Stiffness Elements for Enhanced Material Damping Capacity

Abstract

Constrained negative stiffness elements in volume concentrations (1% to 2%) embedded within viscoelastic materials have been shown to provide greater energy absorption than conventional materials [Lakes et al., Nature (London) 410, 565–567 (2001)]. This class of composite materials, called meta-materials, could be utilized in a variety of applications including noise reduction, anechoic coatings and transducer backings. The mechanism underlying the meta-material's behavior relies on the ability of the negative stiffness element to locally deform the viscoelastic material, dissipating energy in the process. The work presented here focuses specifically on the design of the negative stiffness elements, which take the form of buckled beams. By constraining the beam in an unstable, S-shaped configuration, the strain energy density of the beam will be at a maximum and the beam will accordingly display negative stiffness. To date, physical realization of these structures has been limited due to geometries that are difficult to construct and refine with conventional manufacturing materials and methods. By utilizing the geometric freedoms allowed by the Selective Laser Sintering (SLS) machines, these structures can be built and tuned for specific dynamic properties. The objective of this research was to investigate the dynamic behavior of SLS-constructed meso-scale negative stiffness elements with the future intention of miniaturizing the elements to create highly absorptive meta-materials. This objective was accomplished first through the development and analysis of a mathematical model of the buckled beam system. A characterization of the Nylon 11 material was performed to obtain the material properties for the parts that were created using SLS. Applying the mathematical model and material properties, a tuned meso-scale negative stiffness structure was fabricated. Transmissibility tests of the meso-scale structure revealed that the constrained negative stiffness system was able to achieve overall higher damping and vibration isolation than an unconstrained system. Quasistatic behavior of the system indicated that these elements would be ideal for implementation within meta-materials. Based on the results of the meso-scale system, a method to test a representative volume element for a negative stiffness meta-material was developed for future completion.