Research on Internal Resonance Mechanisms in Micromechanical Resonators and Their Application in Frequency Stabilization Background Introduction Micromechanical resonators play a crucial role in modern timekeeping and sensing devices due to their high frequency, high quality factor, and high sensitivity. However, the extremely low damping character...

Stochastic Response Spectrum Study of Nonlinear Systems: Introduction and Analysis Methods of Fractional Derivative Elements Academic Background In the fields of engineering and physics, nonlinear dynamic systems are widely used to model complex phenomena. However, predicting the response of these systems under stochastic excitation becomes highly ...

Academic Background In the fields of engineering and materials science, precise control of robotic manipulator displacement and force is crucial for studying the mechanical properties of materials, especially when dealing with objects exhibiting nonlinear viscoelastic deformation. For instance, in textiles, aerospace, medical, and energy production...

Background Introduction Complex systems are ubiquitous in nature, appearing in various forms such as neural networks, social networks, and power grids. Understanding the dynamical transitions within these systems is often achieved through mathematical models, particularly coupled nonlinear oscillators, which exhibit a wide variety of collective beh...

Academic Background With the increasing demand for high-speed and lightweight design in the aviation industry, more and more aviation transmission shaft systems have adopted supercritical design. Supercritical design means that the drive shaft must cross its first critical speed, but when crossing the critical speed, the shaft system will produce s...