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...
Academic Background In nonlinear dynamical systems, frequency switching has garnered significant attention in recent years due to its ubiquitous presence in the real world and its distinctive fast-slow dynamics. Frequency switching can induce divergence behaviors at certain switching thresholds, destabilizing bursting solutions in slowly excited ve...
Background Introduction In aerospace engineering, thin laminated composite structures (such as wings) are prone to vibration under high-speed airflow, which may lead to instability phenomena such as flutter or divergence, affecting the safety and performance of aircraft. Particularly, when delamination (i.e., adhesive failure between layers) exists...
Parameter Identification of a Nonlinear Vertical Axis Rotating Machine: An Innovative Approach Based on Reduced Order Modeling and Data Assimilation Academic Background In modern engineering, the modeling of nonlinear dynamic systems is a crucial research area. However, such systems often involve parameters that are difficult to measure or estimate...
Academic Background Introduction The motion of a pendulum is one of the fundamental problems in classical mechanics, while the vibration of a pendulum on a flexible and stretchable string involves more complex nonlinear dynamic phenomena. Such problems have broad significance in practical applications, such as in engineering structures, biomechanic...
Background In modern scientific and industrial research, the dynamic behavior of non-Newtonian fluids has garnered significant attention due to their unique rheological properties and wide-ranging applications. Unlike Newtonian fluids, non-Newtonian fluids such as polymers, slurries, and biological fluids exhibit complex nonlinear relationships bet...