scholarly journals A unified element stiffness matrix model for variable cross-section flexure hinges in compliant mechanisms for micro/nano positioning

2019 ◽  
Vol 25 (11) ◽  
pp. 4257-4268 ◽  
Author(s):  
Yanling Tian ◽  
Mingxuan Yang ◽  
Fujun Wang ◽  
Chongkai Zhou ◽  
Xingyu Zhao ◽  
...  
Keyword(s):  
Cross Section ◽  
Matrix Model ◽  
Stiffness Matrix ◽  
Compliant Mechanisms ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Element Stiffness Matrix ◽  
Flexure Hinges

Combined Compliance Method of the Variable Cross Section Flexure Hinge and its Verification

2015 ◽  
Vol 798 ◽  
pp. 85-91
Author(s):  
Qing Ling Liu ◽  
Xing Xin Wang
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Flexure Hinge ◽  
Variable Cross ◽  
Structure Characteristics ◽  
Compliant Structure ◽  
Flexure Hinges ◽  
Different Types ◽  
Characteristics Analysis ◽  
The Right

Flexure hinge is the most basic compliant structure, the compliance is one of the important performance parameter. The structure characteristics is analysed and the new method used for calculating the compliance is performed in this paper. Based on the structure characteristics analysis of the right circle, corner filleted and elliptical flexure hinge (symmetric and non-symmetric), half flexure hinges are analysed and the compliance formulas are given by selecting the reasonable integral variable. The combined compliance formulas of 12 kinds flexure hinge (simple, hybrid (symmetric,non-symmetric)) are obtained by half different types of flexure hinge being combined. The right circular flexure hinge, right circular elliptical hybrid flexure hinge and non-symmetric elliptical flexure hinge are selected and their compliance are calculated with the formulas in this paper and in literatures, which results indiceted the validity and correctness of the combined compliance method.

Variable Cross-Section Thin-Walled Composite Structure Modeling Based on the Super-Element Method

2016 ◽  
Vol 829 ◽  
pp. 95-99
Author(s):  
J. Xia ◽  
Zhi Jin Wang ◽  
A.S. Kretov
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Variable Cross Section ◽  
Structure Modeling ◽  
Variable Cross ◽  
Section Shape ◽  
Thin Walled ◽  
Calculation Analysis ◽  
Element Method

For slender structures (for example larger aspect ratio wing or fuselage), when they are under loads, the in-plane cross-section shape of these structures remains unchanged. Using this feature, in this paper, a new method called super-element method (SEM) is proposed with the hypothesis of in-plane rigidity. The stiffness matrix of one super-element which has reduced degrees of freedom compared with FEM is derived and they are assembled together to get the stiffness matrix of whole structure. Then through the boundary conditions, the stress and displacement distribution can be calculated out. Calculation analysis of three examples reveals the validity and feasibility of super-element method.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals Theoretical and Experimental Studies on MEMS Variable Cross-Section Cantilever Beam Based Piezoelectric Vibration Energy Harvester

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 772
Author(s):  
Xianming He ◽  
Dongxiao Li ◽  
Hong Zhou ◽  
Xindan Hui ◽  
Xiaojing Mu
Keyword(s):  
Power Density ◽  
Cantilever Beam ◽  
Cross Section ◽  
Energy Harvester ◽  
Variable Cross Section ◽  
Vibration Energy ◽  
Variable Cross ◽  
Vibration Energy Harvester ◽  
Piezoelectric Vibration Energy Harvester ◽  
Piezoelectric Vibration

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.

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