Maintaining Specific Natural Frequency of Damped System despite Mass Modification

In aerospace engineering, structural modifications play an essential role in design of structures. In some cases, it is necessary to guarantee that a specific natural frequency of the structure remains unchanged when additional masses are attached. The methods based on the Sherman-Morrison formula are proposed in this paper, called the optimal selection method and the absolute value method, to maintain the specific natural frequency. The methods are both implemented by installing a spring on the system and can eliminate the effect of the additional mass on the specific frequency. The proposed methods were verified to be effective and accurate through numerical simulations. Results show that the optimal selection method has similar applicability as the existing real value method, and both methods are applicable only in cases of small damping. In addition, the absolute value method has extensive applicability in systems with either small or large damping.

[1]  Per Lidström,et al.  Inverse structural modification using constraints , 2007 .

[2]  Ali Kaveh,et al.  Optimal Structural Analysis , 1997 .

[3]  J. García-Martínez,et al.  A method for performing efficient parametric dynamic analyses in large finite element models undergoing structural modifications , 2017 .

[4]  K. T. Joseph.  Inverse eigenvalue problem in structural design , 1992 .

[5]  Qingguo Fei,et al.  Removing mass loading effects of multi-transducers using Sherman-Morrison-Woodbury formula in modal test , 2019, Aerospace Science and Technology.

[6]  Qingguo Fei,et al.  Utilization of modal stress approach in random-vibration fatigue evaluation , 2017 .

[7]  Donghua Wang,et al.  Eigenstructure assignment in vibrating systems based on receptances , 2015 .

[8]  Yitshak M. Ram,et al.  Mass and stiffness modifications to achieve desired natural frequencies , 1996 .

[9]  Vahit Mermertaş,et al.  Preservation of the fundamental natural frequencies of rectangular plates with mass and spring modifications , 2004 .

[10]  Rakesh K. Kapania,et al.  Non-stationary random vibration analysis of structures under multiple correlated normal random excitations , 2017 .

[11]  Orhan Çakar,et al.  Determination of stiffness modifications to keep certain natural frequencies of a system unchanged after mass modifications , 2017 .

[12]  Qingguo Fei,et al.  Modal energy analysis for mechanical systems excited by spatially correlated loads , 2018, Mechanical Systems and Signal Processing.

[13]  Dario Richiedei,et al.  Concurrent Design of Active Control and Structural Modifications for Eigenstructure Assignment on a Cantilever Beam , 2017 .

[14]  Qingguo Fei,et al.  Using Sherman–Morrison theory to remove the coupled effects of multi-transducers in vibration test , 2019 .

[15]  Orhan Çakar,et al.  Mass and stiffness modifications without changing any specified natural frequency of a structure , 2011 .

[16]  M. Na,et al.  Structural dynamic modification of vibrating systems , 2007 .

[17]  Jimin He,et al.  Local structural modification using mass and stiffness changes , 1999 .

[18]  M. Gürgöze,et al.  Preserving the fundamental frequencies of beams despite mass attachments , 2000 .

[19]  Qingguo Fei,et al.  Prediction of uncertain elastic parameters of a braided composite , 2015 .

[20]  Youn-sik Park,et al.  STRUCTURE OPTIMIZATION TO ENHANCE ITS NATURAL FREQUENCIES BASED ON MEASURED FREQUENCY RESPONSE FUNCTIONS , 2000 .

[21]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .