Out-of-the-Lifting-Plane Stability Analysis of Crane Telescopic Boom with Cable Exerted at the Top

2013 ◽  
Vol 446-447 ◽  
pp. 474-478
Author(s):  
Nian Li Lu ◽  
Liang Du ◽  
Shi Ming Liu ◽  
Yuan Xue
Keyword(s):  
Cross Section ◽  
Carrying Capacity ◽  
Stability Problem ◽  
Recurrence Formula ◽  
Variable Cross Section ◽  
Critical Force ◽  
Variable Cross ◽  
Usual Practice ◽  
Characteristic Equations ◽  
Practical Applications

To enhance the carrying capacity of the crane variable cross-section telescopic boom, the usual practice is using the cable at its top end, it makes the out-of-the-lifting plane stability problem of crane telescopic boom become solving the Euler critical force with follower force. This paper established the deflection differential equations of crane telescopic boom model which under actions of cable, with proper boundary conditions, the recurrence formula of buckling characteristic equations were presented, and some practical applications were given. The influence on buckling critical force of crane boom due to the ratio of the length of cable and crane boom was discussed. Took certain four-sectioned telescopic boom as example, the destabilizing critical force was calculated, the result showed that in comparison with the ANSYS method, the buckling characteristic equations in this paper is completely correct.

Accurate Calculation about Euler Critical Force of Multistep Telescopic Cylinder with Two Different Kinds Support Conditions

2013 ◽  
Vol 345 ◽  
pp. 58-63
Author(s):  
Liang Du ◽  
Peng Lan ◽  
Nian Li Lu
Keyword(s):  
Load Condition ◽  
Order Effect ◽  
Variable Cross Section ◽  
Critical Force ◽  
Variable Cross ◽  
Common Boundary ◽  
Characteristic Equations ◽  
Practical Applications ◽  
Support Conditions ◽  
Deformation Compatibility

Variable cross-section telescopic cylinder is the frenquently-used member being loaded, which the buckling critical force is variable as the boundary and load condition changed. According to two common boundary supprot conditions, this paper established the deflection differential equations of arbitrary multistep telescopic boom by vertical and horizontal bending theory with second-order effect, introduced the boundary condition and deformation compatibility condition, obtained the recurrence expression of buckling characteristic equations, and some practical applications were presented. Took certain four-sectioned telescopic cylinder as example, calculated the buckling critical force by the method and compared the results with ANSYS, the accuracy of the buckling characteristic equations deduced in this paper were verified.

scholarly journals On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam

2019 ◽  
Vol 21 (2) ◽  
pp. 89-96 ◽  
Author(s):  
Foek Tjong Wong ◽  
Junius Gunawan ◽  
Kevin Agusta ◽  
Herryanto Herryanto ◽  
Levin Sergio Tanaya
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Bending Moment ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Minimum Potential Energy ◽  
Concentrated Force ◽  
Practical Applications ◽  
Minimum Potential

A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the beam deflections and rotations at the free end are presented. Examples of application are given for the cases of a relatively slender beam and a deep beam. The present solutions can be useful for practical applications as well as for evaluating the accuracy of a numerical 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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