Support Reaction in the Brachistochrone Problem in a Resistant Medium

The key factor determining the strength, reliability, service life and fail-safe operation of the main pipeline is its stress-strain state. The purpose of this article is to develop a mathematical framework and methodology for calculating the stress-strain state of a pipeline section laid in complex geotechnical conditions, taking into account all planned and altitude changes and impacts at various points of operation, as well as during repair and after its completion. The mathematical framework is based on differential equations reflecting the equilibrium state of the pipeline, taking into account the features of the sections (configuration, size, initial stress state, acting forces, temperature conditions, interaction with soil, supports, and pipe layers). The equilibrium equations are drawn up in a curvilinear coordinate system – the same one that is used for in-pipe diagnostics. According to the results of the solution, all stress components are determined at each point both along the length of the pipeline and along the circumference of any section. At the same time, transverse and longitudinal forces, bending moments, shearing forces, pipeline displacements relative to the ground and soil response to displacements are determined. As an example, a solution is given using the developed mathematical framework. During the course of calculation, the places where the lower form of the pipe does not touch the ground and the places where the support reaction becomes higher than a predetermined limit are determined. A comparative analysis was accomplished, and the optimal method for section repair has been selected.

Download Full-text

BIRMABRIGHT B.B.5

Alloy Digest ◽

10.31399/asm.ad.al0085 ◽

1959 ◽

Vol 8 (11) ◽

Keyword(s):

Compressive Strength ◽

Corrosion Resistance ◽

Aluminum Alloy ◽

High Temperature ◽

Physical Properties ◽

Heat Treating ◽

Corrosion Resistant ◽

Temperature Performance ◽

Medium Strength ◽

Resistant Medium

Abstract BIRMABRIGHT B.B.5 is a corrosion resistant, medium-strength magnesium-aluminum alloy in both the cast and wrought conditions. This datasheet provides information on composition, physical properties, hardness, elasticity, tensile properties, and compressive strength as well as fatigue. It also includes information on high temperature performance and corrosion resistance as well as casting, forming, heat treating, machining, and joining. Filing Code: Al-85. Producer or source: Birmabright Ltd.

Download Full-text

A Novel Coaxial Balance Mechanism for Reciprocating Piston Engines

Applied Sciences ◽

10.3390/app11125647 ◽

2021 ◽

Vol 11 (12) ◽

pp. 5647

Author(s):

Nanxiang Guan ◽

Ao Wang ◽

Yongpeng Gu ◽

Zhifeng Xie ◽

Ming Zhou

Keyword(s):

Reaction Force ◽

Vibration Reduction ◽

Second Order ◽

Root Mean Square Velocity ◽

First Order ◽

Support Reaction ◽

Cylinder Piston ◽

Test Points ◽

Balance Mechanism ◽

Inertia Forces

Vibration is an important issue faced by reciprocating piston engines, and is caused by reciprocating inertia forces of the piston set. To reduce the vibration without changing the main structure and size of the original engine, we proposed a novel coaxial balance mechanism design based on a compact unit body. By introducing a second-order balance mass, this mechanism can significantly increase the efficiency of vibration reduction. The proposed mechanism can effectively balance the first-order and second-order inertia forces with the potential of balancing high-order inertia forces. To accurately determine the second-order balance mass, a closed-form method was developed. Simulation results with a single-cylinder piston DK32 engine demonstrate the effectiveness and advantage of the proposed mechanism. At a crankshaft speed of 2350 r/min, compared with the first-order balance device, the average root mean square velocity of the test points on the engine’s cylinder was reduced by 97.31%, and the support reaction force was reduced by 96.54%.

Download Full-text