Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefits of IR in micro/nanosystems.

在过去十年中，利用微/纳米系统中的非线性特性已成为人们日益关注的主题。其中，通过内部谐振（IR）进行的有力的模间耦合引起了广泛关注，因为它可以提出在微/纳米机械谐振器内引导能量的新策略。然而，在实际应用中利用红外的一个挑战是在非线性微/纳米谐振器的振动模式之间施加所需的频率可通约性。在这里，我们通过实验和分析研究了夹钳梁谐振器中的 1:2 和 2:1 IR，以深入了解 IR 的详细机制。结果表明，非对称结构（例如非棱柱梁）中第二和第三弯曲模式之间的模间耦合提供了轻松实现强IR的最佳条件，并将高能量转移到内部谐振模式。在这种情况下，这些弯曲模式之间源自拉伸效应的二次耦合是优于其他类型几何非线性的主要非线性机制。本文提出的设计策略可以通过对谐振器几何参数的简单修改来集成到典型的微/纳米机电系统（M/NEMS）中，因此，我们期望这项研究能够激发进一步的研究并促进范式转换应用探索红外在微/纳米系统中的各种好处。