Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are descired. These are finte-difference method, modal methoid, a modified modal method and Nelson's method. The methods are implemented in a general-purpose commercial finite-element program and applied to the following test problems: a cantilever beam and a stiffened cylinder with a cutout. Design variables are a beam tip mass, a beam root height, and specific dimensions of the cylinder model. The methods are compared on the basis of central processor (CP) seconds required to obtain the derivatives, and two of the methords are also evaluated for the rapidity of convergence. Data is persented showing the amount of CP time used to compute the first four eigenvector derivates for each example problem. A scalar measure of the error in the mode shape derivative is defined and numerical results illustrating the rapidity of convergence of the approximate derivative to the exact derivative are presented. Results indcate an advantage in using Nelson's method because this method is exact and requires less CP time, especially when derivates with respect to several design variables are computed.
Comparison of several methods for calculating vibration mode shape derivatives
Vergleich verschiedener Methoden zur Berechnung von Ableitungen von Schwingungsmodenformen
AIAA Journal ; 26 , 12 ; 1506-1511
1988
6 Seiten, 8 Bilder, 1 Tabelle, 14 Quellen
Article (Journal)
English
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