A Calculation Method for the Deformation Behavior of Warp-Knitted Fabric

In this paper, a new method to simulate the structure and loop deformation behavior of double-bar reflex-lapping warp-knitted fabrics based on the structural characteristics is proposed. A simplified mass-spring model was built in which loops knitted by filaments were considered as particles with the uniform mass distribution connected by structure springs for overlaps and shear springs for underlaps. Deformation forces and direction on particles were analyzed to describe the displacement and deformation behavior of particles. A loop model with eight control points was established, and the relationship between control points and particles was studied combining the quadratic Bezier curves. The deformation simulation was implemented by a simulator program with C# and JavaScript via web technology on Visual Studio 2015. The stereoscopic sense of filaments was realized by changing the direction and intensity of the light. The results show that the fabric deformation and the loop shape can be accurately achieve using the simplified mass-spring model compared with the real sample.

An improved dynamic modeling approach of aerostatic thrust bearing considering frequency-varying stiffness and damping of air film

The damped mass-spring model is often employed for the dynamic modeling and vibration analysis of aerostatic bearing systems by taking the air film as equivalent springs. However, the stiffness and damping of the air film are frequency-dependent, making the commonly used approach of taking static stiffness or fixed value as the spring coefficient no longer applicable for a bearing subject to a complex external force containing different frequencies. To address this issue, this paper develops the damped mass-spring model for the aerostatic thrust bearing considering the frequency-varying stiffness and damping by means of the linear superposition method. It indicates that the air bearing is still a linear system despite the frequency-dependent character of dynamic coefficients because the bearing vibration satisfies the superposition principle. The improved dynamic modeling approach is able to accurately and efficiently predict the overall dynamic response of the thrust plate when the it is subjected to a multi-frequency vibration. In solving the overall dynamic response, the stiffness and damping associated with the responses of the transient part and steady part correspond to the natural vibration frequency and external disturbance frequencies, respectively. The feasibility and accuracy of the improved modeling approach are partly or completely verified by the direct trajectory calculation method, the CFD dynamic mesh simulation and a modal test. The proposed modeling method provides an effective way for the vibration analysis of air bearings, and in the meantime avoids the possible numerical errors caused by the traditional modeling approach.

Investigation on Damping Characteristics of Hydrostatic Bearing Film by Using Scale Method

The resonant peaks can be suppressed by damping, those effects is dependent on damping ratio of system. In this paper, we propose a scaling method to evaluate the damping ratio of hydrostatic bearings for the data from model test. This method fits specifically for the overdamping of all hydrostatic bearing. This is direct and the easiest method to obtain the damping characteristics of oil film for the lowest band before the first resonant peak. The frequency responses of acceleration per force for a single-degree-of-freedom mass-spring-damper model is used to generate the evaluation scales for the damping ratios of the modal test results of worktable mounting on hydrostatic bearing. The case study for experimental results of the impact response are evaluated for damping ratio of the hydrostatic film by these method. Furthermore, using this scaling method, the influences of three types of compensations on the damping ratio of a hydrostatic bearing are compared. The results reveal that the constant flow has the largest damping ratio, and the capillary restrictor has the smallest one.

Potential Artifacts of Sequential State Estimation Invariants

In sequential estimation methods often used in general climate or oceanic calculations of the state and of forecasts, observations act mathematically and statistically as forcings as is obvious in the innovation form of the equations. For purposes of calculating changes in important functions of state variables such as total mass and energy, or in volumetric current transports, results are sensitive to mis-representation of a large variety of parameters including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Errors are both stochastic and systematic, with the latter, as usual, being the most intractable. Here some of the consequences of such errors are first analyzed in the context of a simplified mass-spring oscillator system exhibiting many of the issues of far more complicated realistic problems. The same methods are then applied to a more geophysical barotropic Rossby wave plus western boundary current system. The overall message is that convincing trend and other time-dependent determinations in "reanalyis" like estimates requires a full understanding of both models and observations.

A 3D Multidirectional Piezoelectric Energy Harvester using Rope-Driven Mechanism for Low Frequency and Ultralow Intensity Vibration Environment

Though numerous piezoelectric vibration energy harvesters (PVEHs) have been designed and investigated to provide power supply for wireless sensors or wearable devices, it remains a challenge for traditional PVEHs to work effectively in an environment of low frequency, low acceleration and multidirectional vibrations. This work presents a PVEH using a low-frequency energy-capturing resonant system formed by a rolling ball in a hemispherical shell and driven by a rope. Due to the symmetry of the sphere, the ball can be excited at multiple directions in 3D space, and the piezoelectric beam can be pulled by the ball through a rope in multiple directions. Thus, the efficient multidirectional energy harvesting under low frequency (< 10 Hz) and ultralow intensity (< 0.1 g) vibrations could be realized. A mass-spring-damper equivalent model was built to understand the operation mechanism of the proposed PVEH. The results show that the proposed PVEH has a potential to collect energy in any direction in 3D space, and could achieve a good angle bandwidth with 360° for φ and 240° for β under the excitation of a = 0.04 g, f = 6.8 Hz with the acceleration defined in the spherical coordinate system. The developed PVEH can generate 6.5 μW under a low-intensity excitation (0.03 g), and the normalized power density can reach 22.63 μW/(cm3g2Hz). Moreover, the minimum start-up acceleration analysis of the proposed PVEH indicates that the PVEH can capture multidirectional energy from vibrations as low as 0.01 g. In addition, both simulation and experimental study on rope redundancy and ball mass show that they can be used to adjust the device performance easily without structure re-fabrication. Overall, this study demonstrates a new mechanism that could effectively harvest low frequency, ultralow intensity and multidirectional vibration

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.