scholarly journals Appendix A Natural Frequency of a Cantilever Beam with Variable Cross Section

2019 ◽  
pp. 333-335
Keyword(s):  
Natural Frequency ◽  
Cantilever Beam ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross

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.

scholarly journals First natural frequency of multi-segment floor joists with variable cross section

2019 ◽  
Vol 28 (4) ◽  
pp. 526-538
Author(s):  
Marek Chalecki ◽  
Jacek Jaworski ◽  
Olga Szlachetka
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Constant Width ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Uniform Load ◽  
Simply Supported ◽  
Made In

The Rayleigh’s method can be used to determine the first natural frequency of beams with variable cross-section. The authors analyse multi-segment simply supported beams, symmetrical with respect to their midpoint, having a constant width and variable height. The beams consist generally of five segments. It has been assumed that the neutral bar axis deflected during vibrations has a shape of a beam deflected by a static uniform load. The calculations were made in Mathematica environment and their results are very close to those obtained with FEM.

Springing Responses Analysis and Segmented Model Test on a 550,000 Dead Weight Tonnage Ore Carrier

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hui Li ◽  
Di Wang ◽  
Chen-Ming Zhou ◽  
Kai-Hong Zhang ◽  
Hui-Long Ren
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Regular Waves ◽  
Dead Weight ◽  
Low Stiffness ◽  
Similarity Law ◽  
Good Agreement

In hydroelastic model tests, segmented ship models are usually used to make sure that the model scale and the full size ship satisfy the similarity law of structural natural frequency and distribution of ship bending stiffness. However, springing barely occurs in those tests because the natural frequency of segmented ship models is too high for the regular waves required to be generated in a tank. In order to investigate the springing effect, three sets of backbone of variable cross section are adopted in the test. One set of backbones satisfies the similarity law of natural frequency, and two extra sets of low stiffness backbones are used so that the springing effect can appear and be measured. Experimental results show that the springing occurs when the wave encounter frequency coincides with the first elastic natural frequency of the ship, or with half or one-third of it. A good agreement has also been obtained between the experimental and the numerical results by a three-dimensional (3D) hydroelasticity method. Based on these results, the contribution of the springing responses to the fatigue damage of the ship is estimated and analyzed.

Design of the PRO/MECHANICA to Variable Cross-Section of Micro-Mechanical Cantilever Based on the Finite Element Method

2012 ◽  
Vol 184-185 ◽  
pp. 146-150
Author(s):  
Chun Li Wei ◽  
Wei Zhang ◽  
Hui Wei
Keyword(s):  
Sensitivity Analysis ◽  
Cantilever Beam ◽  
Cross Section ◽  
Optimization Design ◽  
Variable Cross Section ◽  
Variable Cross ◽  
The Finite Element Method ◽  
Analysis Model ◽  
Modeling Analysis ◽  
Body Design

Abstract: In order to achieve the design of micro-machined micro- mechanical cantilever beam of variable cross-section through the PRO / MECHANICA micro-mechanical variable cross-section cantilever beam to mathematical modeling , analysis model , a standard static analysis , the primary design model , the local sensitivity analysis, global sensitivity analysis and optimization design aspects . By the analysis of research data , this body design is feasible and adaptable stress distribution characteristics of a good , good appearance of the structure .

Numerical Examples of Variable Cross-Section Beam Elements

2012 ◽  
Vol 557-559 ◽  
pp. 822-825
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Xun Lin Diao ◽  
Xiao Dong Jia
Keyword(s):  
Exact Solution ◽  
Cantilever Beam ◽  
Cross Section ◽  
Beam Width ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Numerical Examples ◽  
Beam Elements ◽  
Beam Depth

Based on MATLAB platform, program VCBEP (Variable Cross-section Beam Element based on Positional FEM) is compiled, and the cantilever beam with linear profile and the parabolic simple supported beam are calculated. The variable cross-section beam element is proposed to analyze rectangular beam whose beam depth changes in a linear or quadratic parabolic way and beam width is fixed and the exact solution can be obtained.

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.

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