scholarly journals Моделирование динамического воздействия авиационного двигателя на крыло самолета при отрыве лопатки вентилятора

2021 ◽  
pp. 68-73
Author(s):  
Сергей Владимирович Филипковский ◽  
Валентин Семёнович Чигрин ◽  
Александр Александрович Соболев ◽  
Лариса Алексеевна Филипковская
Keyword(s):  
Elastic Element ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Transient Vibration ◽  
Elastic Suspension ◽  
Engine Operation ◽  
Numerical Studies ◽  
Stiffness Characteristic ◽  
Engine Mount ◽  
Fan Blade

One of the requirements for a projected aircraft is the ability to continue flying and land in the event of a breakdown of one of the engines. One of the calculated cases of engine breakdown is a fan blade breakaway. This phenomenon causes large vibrations of both the engine itself and the aircraft structure.Design model and method for studying engine vibrations with damage in the form of blade breakaway have been developed; numerical studies of unsteady vibrations of an engine suspended on a pylon have been carried out. Herewith, the following load options are considered: engine operation with fan imbalance before shutdown, which is performed by the pilot; sharp braking and jamming of the fan rotor as a result of breakage of the front elastic support of the rotor, which can occur when the blade breaks off; braking the rotor after turning off the engine.The front bearing of the rotor is ball the bearing installed in elastic elements "squirrel wheel". The ball bearing is modeled as a rigid joint. Outside the elastic element, there are two thin-walled shells, which are intermediate load-bearing elements. With an increase in the imbalance of the fan rotor, the gap in the oil damper closes, the damper housing sits on the shells, switching on their rigidity to work. Thus, the stiffness characteristic of the support is bilinear. The stiffness coefficients of the elastic element "squirrel wheel" and the front support shells are determined by the method of numerical simulation. The fan rotor is modeled as a solid body on bearing supports. The stator of the engine is modeled by a rigid body on an elastic suspension. The pylon and the elastic engine mount elements are modeled by beams of variable cross-section operating simultaneously in tension, torsion and bending.A numerical analysis of the transient vibration processes of the D-436-148FM engine on the pylon of the An-178 airplane is carried out. The most dangerous case of damage as the breakdown of the bearing support after the fan blade breakaway is investigated. The results of the calculations are the graphs of the forces in the bearing arrangements and in the hinges of the engine mounting depended on time.

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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