Wave tailoring granular materials: effect of randomness and plane wave propagation

Granular Materials;wave propagation;solitary wave;randomness;vibrations

Manjunath, Mohith

关键词: Granular Materials;    wave propagation;    solitary wave;    randomness;    vibrations;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/72754/Mohith_Manjunath.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis addresses some of the fundamental issues/aspects as well as practical significance of impact response in granular media. In the first part of the study, we investigate numerically the effect of randomness in material and geometric properties on wave propagation behavior in 1D and 2D granular media. Results obtained for both 1D chains and 2D media show the kinetic energy amplitude decays with distance, with the rate of decay found to depend on the level of randomness and the distance from point of impact. The kinetic energy amplitude initially decays exponentially before transitioning to a universal power-law regime that is valid for all levels of randomness. The power-law regime is fundamentally due to the presence of secondary waves whose amplitude is higher than that of the primary wave after the point of transition. Another key result quantifies the rate of decay of force amplitude in a 2D square packing system along various directions of propagation. Several contour maps are obtained that demonstrate the directions along which we can obtain minimum or maximum decay, which are practically relevant for material design.In the second part of the study, we focus on plane wave propagation in higher dimensional structures. In the case of 2D and 3D monodisperse granular media, we demonstrate an equivalence with 1D chains and consequently derive the relation between wavefront speed and force amplitude in higher dimensional systems. Subsequent normalization results in a universal wavefront speed-force amplitude relation that is valid across the different ordered 2D and 3D systems such as hexagonal, body-centered cubic and face-centered cubic packings. We also investigate the effect of angular impact on granular media and discuss mechanism through which the shearing component of the loading is propagated in the system. In the case of 2D dimer systems, we consider a square packing system with interstitial intruders. Following the procedure that we developed for monodisperse granular media, we obtain an equivalent nonlocal dimer chain that gives the same response with relevant scaling of material properties. In this study, we demonstrate the existence of a new family of plane solitary waves over a wide range of material and geometric properties. We also indicate a discrete set of solutions for which there is locally maximum decay, thereby showing promise for wave mitigation as well.In the last part of our study, we conduct a preliminary study to investigate the vibration response of beams made of a granular chain embedded in a linear elastic matrix. A nonlinear, dynamic finite element model is developed, in which the granular chain is converted to a series of 1D nonlinear bar elements whose contribution is added to linear quadrilateral elements. We study the bending response by applying a harmonic loading on a composite beam fixed on both ends and show a fundamental difference between the dynamic response of a linear elastic beam and the embedded granular system at resonance. Unlike a linear elastic beam, we find the deflection of an embedded granular system to be finite at resonance. Furthermore, in the presence of precompression, the frequency at which the composite beam deflection is maximum can be controlled based on the level of precompression, acting as an active control feature in material design.