Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (He) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite bearns, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data. Nomenclature x = Acceleration i = Velocity X = Displacement F = Force OJ = Frequency 11 = ith Design Variable c = Viscous damping c; = Coefficient of ith Design Variable t; = Critical damping ratio 0] = Stressin thejibelement,ConstraintParameterforOptimization A.; = ithEigenvalue A = Amplitude of Motion W = Average dissipated power t = Time k = Stiffness E/s, Els = Elastic modulus, superscript stands for face sheet and subscript for direction GIJFS,G23FS=Shear modulus, superscript stands for face sheet and subscript for direction [M],[C],[K]= Mass,DampingandStiffnessmatricesof the structure a , f3 = Mass & Stiffness related damping ratios