A Vector Approach to Ptolemy's Theorem

2004 ◽  
Vol 77 (5) ◽  
pp. 386
Author(s):  
Erwin Just ◽  
Norman Schaumberger
2004 ◽  
Vol 77 (5) ◽  
pp. 386-388
Author(s):  
Erwin Just ◽  
Norman Schaumberger

Author(s):  
Gabriel Ribeiro ◽  
Marcos Yamasaki ◽  
Helon Vicente Hultmann Ayala ◽  
Leandro Coelho ◽  
Viviana Mariani

2014 ◽  
Vol 984-985 ◽  
pp. 970-976
Author(s):  
Memala W. Abitha ◽  
V. Rajini

The three phase induction motor is a popularly used machine in many of the industries, which is well known for its robustness, reliability, cost effectiveness, efficient and safe operation. The unnoticed manufacturing failure, mistakes during repair work, exceeding life time may be some of the causes of the induction motor failure, which may lead to the unknown shut down time of the industry. The condition monitoring plays important role as it has the influence on the production of materials and profit. In our work, the induction motor is modelled using stationary reference frame and analysed for single phasing stator fault. The techniques used in detecting the single phasing (open circuit) failures are Park’s vector approach and Fast Fourier Transform (FFT). Park’s vector approach is used for detecting the faults occurring at various phases and FFT is used for detecting the faults of the induction motor working under no load and varying loading conditions.


2021 ◽  
Vol 17 (3-4) ◽  
pp. 89-100
Author(s):  
M. Davidson ◽  
A. Patil ◽  
S.A. Rosenfeld ◽  
Z. Zhu

Frequency-based analysis techniques such as response spectrum analysis (RSA) are widely used for designing bridges in seismically active regions. Two well-known analysis procedures that underlie RSA are the solution of the eigenproblem and the approximation of the solution to the eigenproblem (i.e., approximation of eigenvectors and eigenvalues) through use of force-dependent Ritz vectors. While frequency-based methods have achieved widespread adoption in practice, certain simplifications remain common, such as neglecting soil-structure interaction (SSI) due to a fixed-base assumption. In the present study, frequency-based techniques packaged within a research version of a design-oriented computational tool are employed to analyze, assess, and compare results obtained from RSA with use of the eigenanalysis, and separately, Ritz vector approaches. Importantly, for the bridge configurations analyzed, SSI is taken into account. As outcomes, the potential benefits of the Ritz vector approach (as well as modeling strategies) are demonstrated. The study outcomes are intended to aid practicing engineers when the need to account for SSI is recognized as pertinent to a given bridge seismic design application.


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