Hello ME Community,
This proposal plans to develop a series of analytical methods to analyze wave propagation behaviors in discrete nonlinear lattices, and research objectives are twofold: system response and stability analyses. Due to the absence of damping and external excitation in general, the solution for wave propagation is in a hyperplane with two dimensions. Hence, a modified IHB method combined with the least squares method is used to improve the robustness of the IHB method. The direction interpolation method (DIM) is developed to achieve smooth tracking at turning points. A method based on Hill's method is used to identify the stability and bifurcation of solutions for wave propagation in discrete strongly nonlinear structures, and to achieve tracking of bifurcations combined with the DIM. The outcomes are expected to establish predictive tools for nonlinear lattice dynamics and guide the design of adaptive metamaterials.
You are invited to join the PhD Proposal Defense of Bingxu Zhang on Thursday, October 9, beginning at 10am, in the ME Conference Room (ENGR210-I).
Advisor: Weidong Zhu
Title: Wave Propagation in Discrete Nonlinear Lattices
Abstract:
This research focuses on theoretical analysis of wave propagation in strongly nonlinear discrete lattices. Discrete periodic lattices as a kind of matematerials have attracted a lot of attention due to their unique properties such as propagation and attenuation zones, tunable band gaps, nonreciprocal wave propagation, and so on. When the nonlinearity of the lattices is weak, the perturbation methods can capture some basic properties of wave propagation. However, the perturbation methods will be invalid and the incremental harmonic balance (IHB) method can be used to analyze wave propagation when the increase of the amplitude or system properties lead to nonlinear enhancement. But the IHB method may sometimes be invalid due to convergence issues.
Title: Wave Propagation in Discrete Nonlinear Lattices
Abstract:
This research focuses on theoretical analysis of wave propagation in strongly nonlinear discrete lattices. Discrete periodic lattices as a kind of matematerials have attracted a lot of attention due to their unique properties such as propagation and attenuation zones, tunable band gaps, nonreciprocal wave propagation, and so on. When the nonlinearity of the lattices is weak, the perturbation methods can capture some basic properties of wave propagation. However, the perturbation methods will be invalid and the incremental harmonic balance (IHB) method can be used to analyze wave propagation when the increase of the amplitude or system properties lead to nonlinear enhancement. But the IHB method may sometimes be invalid due to convergence issues.
This proposal plans to develop a series of analytical methods to analyze wave propagation behaviors in discrete nonlinear lattices, and research objectives are twofold: system response and stability analyses. Due to the absence of damping and external excitation in general, the solution for wave propagation is in a hyperplane with two dimensions. Hence, a modified IHB method combined with the least squares method is used to improve the robustness of the IHB method. The direction interpolation method (DIM) is developed to achieve smooth tracking at turning points. A method based on Hill's method is used to identify the stability and bifurcation of solutions for wave propagation in discrete strongly nonlinear structures, and to achieve tracking of bifurcations combined with the DIM. The outcomes are expected to establish predictive tools for nonlinear lattice dynamics and guide the design of adaptive metamaterials.