Nonlinear dynamic stiffness and substructures
Professor Leung, Andrew Yee Tak (Principal investigator)
RGC General Research Fund (GRF)
HKU Project Code
General Research Fund (GRF)
To reduce the number of unknowns in a nonlinear engineering system while capturing the interesting physical significance. In order to do so, we need to begin with Lagrangian formulation, to put the equations in incremental Hamiltonian form, to initiate the singular points by Melnikov functions, to treat the nonconservative parameters by continuation, to deal with symmetry by group theory, to reduce the number of unknowns by the Lyapunov-Smith reduction method, to classify the type of solutions by bifurcation theory (and matrix perturbation), to solve the incremental equations by matrix polynomials, to unfold the boundaries separating different kinds of solutions by vanishing the determinant of the tangential stiffness over the parametric space, and to verify by experiments.