A Direct Method for Analysis of Branched Torsional Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 1006-1009 ◽  
Author(s):  
N. Shaikh
Keyword(s):  
Natural Frequencies ◽  
Direct Method ◽  
Torsional Vibrations ◽  
Transfer Matrices ◽  
Usual Procedure ◽  
A Direct Method ◽  
Number Of Branches

A general and direct method for the analysis of branched systems is presented, in which transfer matrices are used in Holzer-type solutions. The method is shown here for torsional vibrations, but should be applicable to other branched systems. As presented here, this method is much different than the usual procedure found in the literature. Unlike other methods, no matrix inversions (or equivalent operations) are required to account for branches at a junction. A single determinant giving natural frequencies is arrived at irrespective of the number of branches and junctions. Thus the method is straightforward, compact, and economical for computer solutions.

A Note on the Use of Approximate Solutions for the Bending Vibrations of Simply Supported Cracked Beams

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
L. Rubio ◽  
J. Fernández-Sáez
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Direct Method ◽  
Approximate Solutions ◽  
Cracked Beam ◽  
Bending Vibrations ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
A Direct Method ◽  
Cracked Beams

The main goal of this note is to discuss the applicability of approximate closed-form solutions to evaluate the natural frequencies for bending vibrations of simply supported Euler–Bernoulli cracked beams. From the well-known model, which considers the cracked beam as two beams connected by a rotational spring, different approximate solutions are revisited and compared with those found by a direct method, which has been chosen as reference.

Damage detection of a flywheel shaft

2010 ◽  
Vol 7 ◽  
pp. 211-218 ◽  
Author(s):  
A.G. Khakimov
Keyword(s):  
Damage Detection ◽  
Natural Frequencies ◽  
Torsional Vibrations

Using three natural frequencies of torsional vibrations, it is possible to define the location and size of a transverse notch on the flywheel shaft.

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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