A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

Honeycomb is a splendid kind of structure for aerospace engineering with the advantages of light weight, good shock absorption, and good structural stability. This article aims to provide methods to isolate Pyroshocks based on a honeycomb structure and guarantee the safety of such equipment against a high-frequency shock response. According to stress wave theory, an equation for stress wave transmittance of the honeycomb structure is derived considering the effect of cell wall length and thickness, where desirable honeycomb parameters are obtained. The complexity of the transfer path of the honeycomb structure is exploited to build the spacecraft–rocket interface, which could increase the impedance of the stress wave dramatically. Both finite element analysis and experiments are carried out to validate the shock isolation strategies. The influence of parameters, such as cell wall length and the thickness of the stainless-steel honeycomb, on the isolation performance is analyzed. It is revealed that the honeycomb structure has a significant effect on Pyroshock isolation performance when the wall length of the honeycomb cell is 8 mm and the thickness of the cell is 0.1 mm.

In this work, the practical prescribed performance tracking issue for a class of fractional-order nonlinear multiple-input multiple-output (MIMO) systems with asymmetric full-state constraints and unmeasurable system states is investigated. A neural network (NN) nonlinear state observer is developed to estimate the unmeasurable states. Furthermore, the barrier Lyapunov functions with the settling time regulator are employed to deal with the asymmetric full-state constraint from the fractional-order MIMO system. On this ground, the prescribed performance adaptive tracking control approach is designed, assuring that all system states do not exceed the prescribed boundaries, and the tracking errors converge to the predetermined compact sets within a predefined time. Finally, two simulation examples are presented to show the effectiveness and practicability of the proposed control scheme.

In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.

An analytical dynamic model is presented for a spacecraft with multiple large flexible structures. Based on the partial differential equations (PDEs) of the motion of the solar panel and deployable arm, the governing equations of the main-body and deployable antenna and the boundary conditions at each end point are used to obtain the frequency and mode shapes of the system. Then, the ordinary differential equations (ODEs) of the system can be obtained from the orthogonality relations and mode shape. The influence of the deployable antenna on the frequencies and mode shapes of the spacecraft is investigated. The frequency veering and mode interchanged phenomenon are observed with the variation of the diameter of the deployable antenna. Using the ODEs, the dynamic responses of the spacecraft are calculated to study the influence of the control torque on the attitude and position of the antenna in the attitude maneuver.

Blisk, as a critical component of aero−engines, is prone to fatigue cracks that can severely impair its dynamic performance and operational safety. This paper develops a finite element model of a blisk with breathing cracks to investigate the effects of crack distribution (adjacent blades vs. separated blades) and blade twist angle on natural frequencies, frequency−veering and mode localization, and response localization under varying operating conditions. Resonance vibration tests are conducted on blisk and cracked blisk specimens using the frequency dwell method to obtain natural frequencies and vibration responses, thereby experimentally validating the numerical model. The results indicate that cracks reduce the global stiffness, leading to a decrease in natural frequencies and modal localization phenomena. Furthermore, in the frequency−domain responses, nonlinear components such as sub−harmonics, ultra−sub−harmonics, and super−harmonics are observed in addition to the harmonics of the excitation frequency. Moreover, the cracked blisk with a 45° blade twist angle exhibits typical nonlinear vibration behaviors and the most pronounced response localization. This study provides a basis for crack monitoring and resonance fatigue warning.