The high-frequency pulse flow, equivalent to the natural frequency of rocks, is generated by a self-excited oscillating cavity to achieve resonance rock-breaking. The flow field and oscillating mechanism of the self-excited oscillating cavity were simulated using the large eddy simulation method of Computational Fluid Dynamics (CFD). A field-scale testing apparatus was developed to investigate the impulse characteristics and verify the simulation results. The results show that the fluid at the outlet at the tool is deflected due to the pulse oscillation of the fluid. The size and shape of low-pressure vortices constantly change, leading to periodic changes in fluid impedance within the oscillating cavity. The impulse frequency reaches its highest point when the length-diameter ratio is 0.67. As the length-diameter ratio increases, the tool pressure loss also increases. Regarding the cavity thickness, the impulse frequency of the oscillating cavity initially decreases, then increases, and finally decreases again. Moreover, both the impulse frequency and pressure loss increase with an increase in displacement. The numerical simulation findings align with the experimental results, thus confirming the validity of the theoretical model. This research provides theoretical guidance for the practical application of resonance rock-breaking technology.

Microresonators have a variety of scientific and industrial applications. The measurement methods based on the natural frequency shift of a resonator have been studied for a wide range of applications, including the detection of the microscopic mass and measurements of viscosity and stiffness. A higher natural frequency of the resonator realizes an increase in the sensitivity and a higher-frequency response of the sensors. In the present study, by utilizing the resonance of a higher mode, we propose a method to produce the self-excited oscillation with a higher natural frequency without downsizing the resonator. We establish the feedback control signal for the self-excited oscillation using the band-pass filter so that the signal consists of only the frequency corresponding to the desired excitation mode. It results that careful position setting of the sensor for constructing a feedback signal, which is needed in the method based on the mode shape, is not necessary. By the theoretical analysis of the equations governing the dynamics of the resonator coupled with the band-pass filter, it is clarified that the self-excited oscillation is produced with the second mode. Furthermore, the validity of the proposed method is experimentally confirmed by an apparatus using a microcantilever.

In this study, a dynamic equation for a micromechanical resonant accelerometer based on electrostatic stiffness is analyzed, and the parameters influencing sensitivity are obtained. The sensitivity can be increased by increasing the detection proof mass and the area facing the detection capacitor plate and by decreasing the stiffness of the fold beams and the initial distance between the plate capacitors. Sensitivity is also related to the detection voltage: the larger the detection voltage, the greater the sensitivity. The dynamic equation of the closed-loop self-excited drive of the accelerometer is established, and the steady-state equilibrium point of the vibration amplitude and the stability condition are obtained using the average period method. Under the constraint conditions of the PI controller, when the loading acceleration changes, the vibration amplitude is related to the reference voltage and the pre-conversion coefficient of the interface circuit and has nothing to do with the quality factor. When the loading voltage is 2 V, the sensitivity is 321 Hz/g. Three Allan variance analysis methods are used to obtain the frequency deviation of 0.04 Hz and the amplitude deviation of 0.06 mVwithin 30 min at room temperature. When the temperature error in the incubator is ±0.01 °C, the frequency deviation decreases to 0.02 Hz, and the resolution is 56ug. The fully overlapping Allan variance analysis method (FOAV) requires a large amount of data and takes a long time to implement but has the most accurate stabilityof the three methods.

Solving the orbital stabilization of a class of underactuated systems near its open-loop unstable equilibrium point is a challenging task but useful in repetitive tasks. This paper addresses the control problem of an inverted cart-pendulum\'s motion driven by a two-relay controller. This controller is tuned to set the desired amplitude and frequency using the locus of the perturbed relay system, which is a frequency-domain method. We solved the periodic motion of the pendulum occurring in its open-loop unstable equilibrium point. The experimental results showed that the proposed two-relay controller forced the pendulum into a periodic motion around the upright position.

In this study, we demonstrate a self-excited oscillation induced in cholesteric liquid crystalline droplets under a temperature gradient. At equilibrium, a winding Maltese cross pattern with a point defect was observed via polarised microscopy in the droplets dispersed in an isotropic solvent. When the temperature gradient was applied, the pattern was deformed owing to the Marangoni convection induced by the gradient. Here, when both the droplet size and temperature gradient were sufficiently large, the periodic movement of the defect together with the pattern deformation was observed, which demonstrated the self-excited oscillation of the director field. To describe this phenomenon, we theoretically analysed the flow and director fields by using Onsager\'s variational principle. This principle enabled the simplified description of the phenomenon; consequently, the time evolution of the director field could be expressed by the phenomenological equations for the two parameters characterising the field. These equations represented the van der Pol equation, which well expressed the mechanism of the self-excited oscillation.

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier-Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid-structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.