Stress Wave Scattering in Solids for Mitigating Impulsive Loadings
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Stress waves scatter upon encountering discontinuities on their propagating path. Discontinuity is a general term that can be attributed to any change in the material, geometry, and boundary condition of the structures. When a propagating wave approaches a discontinuity, new reflected and transmitted waves will be generated within the structure and the amplitude of the incident wave may be either attenuated or amplified. Considering this phenomenon, the discontinuities within finite structures can be arranged in specific configurations to develop efficient architectures for attenuating the effects of impulsive loadings. This dissertation investigates the effect of discontinuities on the wave propagation characteristics of structures and proposes new architectures for attenuating the stress waves. The effects of different types of material and geometric discontinuities are thoroughly explored, and their attenuation capacity is investigated using explicit formulas. Based on these concepts, an optimal design problem is defined for finding the most effective structural configurations which can attenuate the effects of impulsive loadings. Due to the highly nonlinear nature of the optimization problem combined with lack of gradient information about the objective function with respect to design variables, a genetic algorithm (GA) optimization procedure is used for the optimal design of the newly defined attenuating systems. Four types of stress wave attenuators are proposed in this dissertation. These attenuators include: (i) layered collinear rod structures, (ii) layered diamond-shape beam structures, (iii) non-collinear beam structures, and (iv) porous plates. The layered stress wave attenuators have constant geometry while their material set-up is optimized during the design procedure. However, the non-collinear beam structures and porous plates are made of a single material, and the design procedure seeks to find the best geometry of these systems for mitigating the effects of impulsive loadings. In addition to the proposed stress wave attenuators, the problem of stress wave attenuation in bi-layered plates with a jagged interface profile is also studied in this dissertation. Similar to the approach used in non-collinear systems and porous plates, the material properties of the bi-layered plates remains unchanged during the design procedure; however, the profile of the interface between the two materials changes for the objective of stress wave attenuation. The results of this dissertation show that with the aid of the developed optimization procedure, very efficient and practical stress wave attenuators can be deployed for protecting structural systems against impulsive loadings with consideration to broad frequency ranges.