An Approximate Normal Mode Method for Damped Lumped Parameter Systems

1967 ◽  
Vol 89 (4) ◽  
pp. 597-604 ◽  
Author(s):  
A. Seireg ◽  
L. Howard
Keyword(s):  
White Noise ◽  
Normal Mode ◽  
Damping Ratio ◽  
Conservative System ◽  
Random Excitation ◽  
Mass System ◽  
Response Data ◽  
Lumped Parameter ◽  
Mode Method ◽  
Normal Mode Method

An approximate normal mode method is introduced which permits any linear non-conservative system to be solved by super position of uncoupled coordinates. Accuracy of the method was found to be good when checked by digital computer for dynamic damper systems subjected to sinusoidal and white noise random excitation. A technique is presented which permits a mathematical model for a damped multimass system to be constructed entirely from experimentally obtained sinusoidal frequency response data. An expression is derived for optimum damping ratio and natural frequency ratio that will minimize the response of a two-mass system to white noise random excitation.

State Space Implementation of the Algorithm of Mode Isolation

2003 ◽  
Vol 125 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Michael V. Drexel ◽  
Jerry H. Ginsberg ◽  
Bassem R. Zaki
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Analytical Framework ◽  
Complex Frequency ◽  
Response Data ◽  
Modal Damping Ratio ◽  
Mode Isolation ◽  
The Time Domain

The Algorithm of Mode Isolation (AMI) extracts modal properties from complex frequency response data. Previous work used classic undamped modes as the analytical framework for the algorithm. The present work extends the algorithm to implement damped modal analysis, in which the eigenvalues and eigenvectors are complex. In order to assess how well this reformulation performs when natural frequencies are close and drive point mobilities are low, a prototypical system consisting of a cantilever beam with attached subsystems is introduced. One of these subsystems is selected to be a tuned vibration absorber for the isolated beam, so the system features a combination of modes whose natural frequencies are close and modes whose drive point mobility is low. The time domain response of this system is evaluated, contaminated with substantial white noise, and then FFT processed in order to obtain synthetic complex frequency response data. The performance of AMI is evaluated by comparing extracted values for natural frequency, modal damping ratio, and complex normal mode vectors to the analytical values. The results reveal that the pair of modes having proximite natural frequencies are accurately identified. Natural frequencies and damping ratios for those modes whose drive mobility is low are identified by processing the ensemble of frequency response functions, but identification of normal mode coefficients for such modes remains problematic.

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