Modal analysis of mdof system by using free vibration response data only

Conventional modal testing requires the actuator and sensor to perform FRF measurement so as to determine the structural modal parameters. This paper presents a new idea of experimental modal analysis by only using the structural free vibration response due to initial conditions. If the structural displacement can be measured, the displacement response matrices that are the discrete-time-domain data for all measured dofs can be formulated. The velocity and acceleration response matrices can then be calculated by finite difference methods. With the input of these response matrices to the developed algorithm, the system natural frequencies and their corresponding mode shapes can be determined simultaneously. Numerical examples for a 3-dof and 10-dof systems are presented, to show, respectively, the feasibility and effectiveness of the developed method. Results show the proposed method is very promising. Only the structural displacement response in free vibration condition need to be measured and as the input to the modal parameter extraction algorithm such that all of the structural modal frequencies and mode shapes of the system can be determined successfully. The presented idea can also be extended and applied to the general structure with non-proportional damping case. The proposed methodology can therefore enhance the structural modal analysis technique.

[1]  A. Vakakis,et al.  PROPER ORTHOGONAL DECOMPOSITION (POD) OF A CLASS OF VIBROIMPACT OSCILLATIONS , 2001 .

[2]  F. Shen,et al.  USING THE CROSS-CORRELATION TECHNIQUE TO EXTRACT MODAL PARAMETERS ON RESPONSE-ONLY DATA , 2003 .

[3]  G. Kerschen,et al.  Letter to the Editor Comments on ''Interpreting proper orthogonal modes of randomly excited linear vibration systems'' , 2004 .

[4]  Biswajit Basu,et al.  Identification of modal parameters of a mdof system by modified L–P wavelet packets , 2006 .

[5]  G. Kerschen,et al.  PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION , 2002 .

[6]  F.T.M.J.M. Huizinga,et al.  A practical approach to virtual testing in automotive engineering , 2002 .

[7]  E. C. Mikulcik,et al.  A method for the direct identification of vibration parameters from the free response , 1977 .

[8]  B. Feeny,et al.  Interpreting proper orthogonal modes of randomly excited vibration systems , 2003 .

[9]  Norris Stubbs,et al.  A new method to extract modal parameters using output-only responses , 2005 .

[10]  Prasenjit Mohanty,et al.  Modified SSTD method to account for harmonic excitations during operational modal analysis , 2004 .

[11]  Prasenjit Mohanty,et al.  Operational modal analysis in the presence of harmonic excitation , 2004 .

[12]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[13]  Palle Andersen,et al.  Modal Identification from Ambient Responses using Frequency Domain Decomposition , 2000 .

[14]  Wei-Xin Ren,et al.  EMD-based stochastic subspace identification of structures from operational vibration measurements , 2005 .

[15]  Brian F. Feeny,et al.  APPLICATION OF PROPER ORTHOGONAL DECOMPOSITION TO STRUCTURAL VIBRATION ANALYSIS , 2003 .

[16]  L. Meirovitch.  Principles and techniques of vibrations , 1996 .

[17]  S. Zaghlool,et al.  Single-station time-domain (SSTD) vibration testing technique: Theory and application , 1980 .