Structural assemblies incorporating negative stiffness elements have been shown to provide both tunable damping properties and simultaneous high stiffness and damping over prescribed displacement regions. In this paper we explore the design space for negative stiffness based assemblies using analytical modeling combined with finite element analysis. A simplified spring model demonstrates the effects of element stiffness, geometry, and preloads on the damping and stiffness performance. Simplified analytical models were validated for realistic structural implementations through finite element analysis. A series of complementary experiments was conducted to compare with modeling and determine the effects of each element on the system response. The measured damping performance follows the theoretical predictions obtained by analytical modeling. We applied these concepts to a novel sandwich core structure that exhibited combined stiffness and damping properties 8 times greater than existing foam core technologies.
A theoretical model is developed for the magnetoelectric (M-E) voltage coefficient α for a magnetostrictive-piezoelectric layered composite (MPLC). Three field orientations; including longitudinal, transverse, and in-plane, with two in plane geometries, 2D and 1D, are presented and studied with respect to the volume fraction of piezoelectric phase and the material properties of magnetostrictive phase. Results show that the phase volume fraction to achieve maximum M-E coupling effect is determined by the compliance of magnetostrictive phase. Higher compliance values shift α' peaks to lower piezoelectric volume fraction and weaken α' values. This study also investigates the influence of the piezomagnetic coefficient q<sub>33</sub> and the ratio q<sub>33</sub>/q<sub>31</sub>. For constant ratio of q<sub>33</sub>/q<sub>31</sub>, larger q<sub>33</sub> values increase the M-E coupling effect. On the contrary, changing the ratio of q<sub>33</sub>/q<sub>31</sub> changes the relative α' values for each of the six cases. This demonstrates that the ratio q<sub>33</sub>/q<sub>31</sub> strongly influences the selection of MPLC configurations to produce the largest α'.
The fiber alignment shifts of fiber-solder-ferrule (FSF) joints in butterfly laser module packaging under temperature cycle testing are studied experimentally and numerically. Using a novel image capture camera system as a monitor probe and the Sn-based solders as bonding materials, we have achieved the minimum fiber eccentric offsets of 8 and 20mm in FSF joints with the PbSn and AuSn solders, respectively. The measured results showed that the fiber alignment shifts of FSF joints with the hard AuSn solder exhibited shifts two times less than that with the soft PbSn solder. The experimental measurements of fiber alignment shifts were in good agreement with the numerical calculations of the finite-element method (FEM) analysis. The major fiber shift formation mechanisms of FSF joints in temperature cycling may come from the localized plastic solder yielding introduced by the local thermal stress variation, the redistribution of the residual stresses, and the stress relaxation of the creep deformation within the solder.