A two-degree-of-freedom nonlinear mechanical system describing a damped linear oscillator weakly coupled to a lightweight grounded bistable nonlinear energy sink is proposed to investigate the targeted energy transfer (TET) under asymmetric local nonlinear potentials. The bifurcations of equilibria are discussed to reflect the bistable and asymmetric characteristics of the system. Through projections of isoenergetic manifolds, the topological features of the Hamiltonian dynamics under $1:1$ internal resonance have been investigated, which induces conditions for energy localization and exchange. In the general case, the topological features of the Hamiltonian dynamics related to the nonlinear normal modes (NNMs) are classified by the Poincar$\acute{\text{e}}$ map, the relations between the NNMs and the Hamiltonian dynamics have been interpreted through the frequency energy plots. The results show that introducing the asymmetric characteristics may enhance the TET and realize the complete TET.

提出了一种描述阻尼线性振荡器弱耦​​合到轻量级接地双稳态非线性能量阱的二自由度非线性机械系统，以研究不对称局部非线性势下的目标能量传递（TET）。讨论了平衡的分岔，以反映系统的双稳态和不对称特性。通过等能流形的投影，哈密顿动力学的拓扑特征 $1：1$已经研究了内部共振，其诱导了能量定位和交换的条件。在一般情况下，与非线性正常模式 (NNM) 相关的哈密顿动力学的拓扑特征由 Poincar 分类$\acute{\text{e}}$图中，NNM 和哈密顿动力学之间的关系已经通过频率能量图进行了解释。结果表明，引入不对称特性可以增强TET并实现完整的TET。