Experimental and Analytical Estimation of Damping in Beams and Plates with Damping Treatments
University of Kansas
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The research presented in this dissertation is devoted to the problem of damping estimation in engineering structures, especially beams and plates with passive damping treatments. In structural design and/or optimization, knowledge about damping is essential. However, due to the complexity of the dynamic interaction of system components, the determination of damping, by either analysis or experiments, has never been straightforward. In this research, currently-used methods are reviewed and gaps are identified first. Then both analytical and experimental studies on the damping estimation are conducted and possibilities of improvement are explored. Various passive damping treatments using ViscoElastic Materials (VEMs) are designed, manufactured and then added to aluminum and composite beams and plates. Experiments on these damped structures are conducted. Currently used experimental methods, namely, the free-decay method, the modal curve-fitting method and the Power Input Method (PIM), are used to process the experimental data and investigate the damping characteristics. Especially, 1) experimental procedures of the power input method are carefully identified and investigated; 2) the power input method is applied to non-uniformly damped structures; 3) the power input method is applied in an extended frequency range (from 0 to 5000 Hz) to meet emerging needs of the transportation industries. A new analytical power input method is proposed for evaluating the loss factor of builtup structures, based on the finite element model with assigned properties of the constituents. Finite Element (FE) models of beams and plates with various damping configurations are developed so a frequency response solution suffices to provide mobility and energy results needed by the new analytical power input method. The analytical power input method is evaluated by comparison with the commonly used Modal Strain Energy (MSE) method. Instead of making an approximate correction of the constant material properties, this analytical power input method directly takes into account the frequency-dependent material properties of the viscoelastic material using the MSC/NASTRAN direct frequency response solution. Features of each method are compared and summarized. Especially, 1) the complex frequency-dependency of viscoelastic materials used in constrained layer damping is modeled using MSC Patran/NASTRAN; 2) a new procedure of estimating loss factors is presented, using the concept of the power input method. Particle damping is also investigated. A fluid analogy is proposed and applied to composite beams and metallic plates. Results show that the fluid analogy can effectively estimate peak damping frequencies and peak damping levels. Both experimental and analytical loss factor results for various engineering structures are presented and discussed.
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