本书从理论解析和数值模拟两方面入手探讨了振动式陀螺（也称谐振式陀螺）相关的动力学理论和基于有限元的数值模拟方法，分为两章分别介绍。主要的创新之处在于：

1. 通过对科氏力和离心力作用下的双自由度谐振系统的研究，揭示了离心力对振动式陀螺有效量程起限制作用的原因，探究了科氏力和离心力作用下系统的正则运动，以及系统动力学方程稳态解参数和正则解参数之间的关系，证明了恒定转速下离心力项对动力学方程正则解形式无影响的结论。
2. 针对复杂结构在旋转条件下难于模拟的问题，提出了参数化建模方法和旋转有限元方法，并设计了一种用于计算旋转结构自然频率和模态的高效算法，该算法被应用于多环结构在高转速下的模态稳定性分析。此外，还提出了多环陀螺虚拟样机技术和基于该技术的陀螺性能参数的优化方法。

=> MEMS陀螺动力学理论和数值模拟技术

希望对您的学习和工作有所帮助！

Micro-electromechanical system (MEMS) vibratory gyroscopes are inertial sensors for measuring angular velocity based on a micro-machined proof-mass that can detect rotating-induced inertial force (i.e., Coriolis force). During the past several decades, great advancement has been achieved in the fields of design and fabrication of MEMS vibratory gyroscopes, however, little investigation on understanding and improving their measurement range could be found in the literature. We find that most of the commercial single-axis force-rebalance MEMS vibratory gyroscopes have a measurement range of the order 10^2 . A question naturally arises: is there any physical reasoning to the limit of the measurement range? To answer this question, we propose a theoretical method to investigate the limit by creating a mathematical model for typical single-axis force-rebalance MEMS vibratory gyroscopes. A deeper analysis gives the answer to the question, for the first time.

The paper can be found here:

=> Paper

I hope this paper is helpful to your research and other academic activities.

While the subject of ballistics has been investigated for several centuries, nowadays, the design of a ballistic component or device is still not an easy task, but usually a process of trial and error, or an iterative process of analysis, testing and tweaking. Concerning the design of a gun with a gas-operated piston system, it is challenging to accurately determine how a gas-operated piston system would affect the interior ballistic performance of the gun (e.g., muzzle velocity) due to gas loss and how large the chamber/gas-room pressure would be for safety purpose. To address this problem, a numerical approach based on the coupled Euler-Lagrange technique and a constitutive model for the combustion gas mixture of solid propellants is presented, where the constitutive model is developed by combining Vieille’s law for combustion and the equation of state for gas mixture. The model is validated by experiments for a double base propellant. The approach is then applied to study the effect of a gas-operated piston system on the interior ballistic performance of typical gun designs with different gas port radiuses. The interior ballistic parameters like the muzzle velocity and the highest barrel pressure are computed. Results show that these designs of gas ports influence the interior ballistic parameters very little. In addition, a larger gas port radius results in a larger gas room pressure, which indicates a faster operation of the gas-operated piston.

The paper can be found here:

=> Paper

I hope this paper is helpful to your research and other academic activities.

The software is prepared for an undergraduate course on numerical methods.

You may make copies for education and research.

The software can be found here:

=> Manual
=> LUsol
=> a
=> b

The lecture notes were prepared for an undergraduate course on the fundamentals and applications of the finite element method in solid mechanics.

You may make copies of these notes for education and research.

The lecture notes can be found here:

=> Lecture_notes

Silicon multi-ring structures connected by spokes are ideal candidate to carry circumferential traveling waves in the design of MEMS vibratory gyroscope. However, these structures are prone to instability at high-speed rotation. This paper presents an efficient approach to determine the critical and flutter speeds of these structures for their various natural modes, and thereby to predict their in-plane instability. Through extensive parametric study, the effects of various design parameters on the instability of these structures are obtained and discussed. The results show that stability of these structures could be enhanced by increasing number of spokes, reducing number of rings, and reducing gaps between rings. Furthermore, it is found that these structures are more stable with circumferential traveling waves with a larger nodal diameter.

Based on a continuum theory that accounts for the underlying molecular physics of polar elastomers (PEs), a typical boundary value problem (BVP) is developed to analyze the electro-mechanical instability (EMI) of PEs with randomly distributed dielectric particles. Through extensive numerical simulations, the effects of various parameters such as particle volume fraction, particle size and enhancement factor related to polar groups on the critical voltage leading to EMI of PEs are investigated. The results are presented in 3D phase diagrams, which may better help researchers to understand EMI of PEs and guide them in synthesis, design, and application of PEs in the fields of chemistry, physics, bio-engineering, etc.

MMASC is a nonlinear finite element package for simulating mechanical behaviors of soft composites subjected to external stimuli in a multi-physics context.

The main features of the package are as following:

1. It supports Tet/Hex meshes.

2. It is coded in modern Fortran and has an interface for UMAT/VUMAT, UEL/VUEL etc.

3. It supports multi-physics nonlinear analysis, either static or dynamic, either implicit or explicit.

4. It supports two-scale analysis with options of 3 different homogenization methods.

   • Affine method
   • Periodic method
   • Mixed method

5. It has a unique math-core and is independent of external libraries.

The current released version is only for electromechanical coupling problems.

The following is an example about coupling electric field and displacement field analysis for rubber-like materials (such as elastomers and gels). The problem is defined as shown in Fig. 1.

Four different analyses procedures (see Fig. 2) are incorporated into this version of MMASC, and each of the procedure defines two analysis steps.

The first step is controlled by mechanical pre-stress and the second step is controlled by electric potential or charge. In order to compare the two-scale procedure and one-scale procedure, this example just assumes that both macroscale domain and microscale unit cell are uniform. The results are shown in Fig. 3. While this example is simple, its extension to cases for heterogeneous materials is natural. Please consult to the user manual of MMASC.

You can find the program(Windows) here:

MMASC

The input files for the example here:

macro.inp
micro.inp

You may download these 3 files in a folder and then open a terminal to run the program.

A simulation result

You are free to redistribute this version of MMASC. And I hope the program is helpful to your research.

The source codes can be found here:

1 => Standard Viscoelasticity -> Arruda-Boyce solid + Newtonian fluid

2 => Standard Viscoelasticity -> Gent solid + Newtonian fluid

3 => Single element benchmarking

A demonstration:

(a) showing experiment setup with hydrogel electrodes (b) showing the modeling in simulation (c) experimental and simulation results for canbon grease electrodes (d) for hydrogel electrodes

I hope these codes can also be used for educational purposes, other than research.