IMPROVED APPROXIMATIONS VIA RAYLEIGH'S QUOTIENT

✍ Scribed by D.H. Hodges

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 283 KB
• Volume: 199
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0641

✦ Synopsis

Many problems can be solved approximately through the minimization of Rayleigh's quotient, which is equivalent to an ordinary differential equation (ODE) and associated boundary conditions that govern the eigenvalue (say, a free-vibration frequency or buckling load) and the ''mode shape'' associated therewith. In addition to this, there are many other problems for which one-term approximations are both helpful and sufficiently accurate; see, for example, the non-linear examples in reference [1]. To illustrate the methods discussed in this note, however, it is sufficient to consider only that class of problems which can be treated with Rayleigh's quotient. These two methods are Rayleigh's quotient with a free parameter and the method of Stodola and Vianello. Since they are not mutually exclusive, one can sometimes apply both methods simultaneously to obtain outstanding results.