Almost all modern devices vibrate when working or being excited, and during this process, two things bring challenges to engineers: first, devices lose a substantial amount of energy to unwanted vibrations and noise because they transfer the desired energy to heat through damping and friction; Second, energy distribution during vibration is hard to control in some situations, which makes the devices exposed to wear and failure. Targeted Energy Transfer (TET) is one of the most prolific topics in the area of vibration mitigation and isolation, which involves the irreversible transfer of energy from a primary linear structure to a series of local, nonlinear attachments called nonlinear energy sinks (NESs). This work investigates the area which were not covered by TET theory, as well as expand the discussion of TET to various nonlinearity, different modes interactions and multi-dimensional energy dissipations to explore the essential mechanism behind nonlinear energy dissipation and expand the application of TET. The first portion discusses energy transfers in a 2 degree-of-freedom (DOF) structure with equivalent masses, by studying the nonlinear normal modes (NNMs) of the system, the interactions between NNMs that was governing the energy transfer in the structure was revealed. Then by applying different excitations to the structure, the energy transfer that is inversed to the TET theory was investigated and then validated. Next, a nonlinearity named quasi-zero stiffness (QZS) was investigated, by introducing the softening and hardening characteristics of the QZS spring, energy transfer from low to high frequencies was achieved, which compensate the limitations of typical cubic or stiffening nonlinearity and expand the capability of TET and efficient energy mitigation. Then, energy dissipation in a 2D structure using impacts and sliding was investigated. By introducing constrained motion in a superellipse model, the motion of and interactions between the impactor and ellipses were predicted and evaluated. This 2D energy absorber provides a paradigm for energy isolation of complex system
