Mass and stiffness modifications to achieve desired natural frequencies

Abstract

SUMMARYA method for determining mass and stiffness modifications to achieve desired natural frequencies is presented. The given data are modal testing results, which consist of a truncated set of natural frequencies and mode shapes. The difficulty arising from the incompleteness of data is overcome by solving an optimization problem rather than seeking an exact solution. The obtained modifications are optimal in a Rayleigh-Ritz sense. The case where the mass and stiffness matrices are interrelated is also considered. Numerical examples demonstrating the various results and the sensitivity of the problem to perturbations are presented.

Calculation of Receptance of a Structure Modified by Mass and Grounded Spring

“…The SM formula given by (2), has been used in a wide variety of applications in the past, such as, in the fields of statistics, networks, structural analysis, asymptotic analysis, optimization and partial differential equations. A more detailed coverage of this approach and various numerical aspects are discussed by Hager [15] and Akgün et al [16].…”

“…The developed methods for both direct and inverse structural modifications are based on the use of modal properties which derived from finite elements (FE) solution or experimental modal analysis (EMA) e.g. [1][2][3] or the use of Frequency Response Functions (FRFs) directly e.g. [4][5][6][7][8][9][10][11][12][13].…”

A method for shifting natural frequencies of a dynamic system to desired values with concentrated mass modifications

“…McMillan and Keane [4] studied shifting resonance from a frequency band applying concentrated masses to a plate. Sivan and Ram [5] developed a method for determining mass and stiffness modifications to achieve desired natural frequencies by using modal analysis. The difficulties arising from truncated data provided by modal analysis were overcome by an optimization procedure.…”

Optimal mass distribution in vibrating systems

“…We find the optimal distribution of mass m k in the discrete model subject to X n k¼1 m k ¼ M, (6) where M is the total mass of the system. It is shown that in chain like systems the problem of n quadratic equations may be solved recursively without the use of eliminants.…”

“…Elhay and Ram [5] generalized the method to include viscous damping. Sivan and Ram have shown in [6] how to obtain required spectrum by structural modification of the masses. Here we find the optimal distribution that optimizes some eigenvalues in the system.…”