Measurements associated with smoothed frequency response, Part II: Identification of stiffnesses and masses in a dynamic structure

✍ Scribed by M.E. Gaylard

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 759 KB
• Volume: 113
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(87)80216-x

✦ Synopsis

Identification of a practical structure is accomplished by using an expansion for the frequency response function in a series of orthogonal polynomial functions of the mass and stiffness matrices M and K. In the preceding paper (Part 1) it has been shown how to evaluate the orthogonal polynomial quantities from measurements of dynamic response of a given structure. This paper (Part II) shows how the evaluated polynomials may be used to infer values for the matrices M and K. The polynomial approach originated as an alternative to the classic expansion in modes of vibration, with the purpose of deliberately approximate analysis of vibrations. However, in the present application to identification, there is no intention to approximate any further than obliged by errors of observation. Identification is possible without measuring vibrations at all recognized points on a structure which respond to excitation at each recognized point. By association with a sufficient range of polynomial functions with different polynomial degrees 0, 1, 2,..., etc., it is enough to measure a single column (or row) from the matrix of i,j response functions which relate velocities at points i to excitations at points j. By using polynomials of still higher degrees, there are further ways of identifying a structure from the same column (or row) of measured response functions. Such over-identification is exploited to reduce sensitivity to error. Damping is not identified. In contrast with some of the techniques in a more established group called "modal identification", there is little sensitivity to damping or to antiresonant-resonant detail in a frequency response function.

Tchebyshev orthogonal polynomials T2,,( ) of the first kind and of even degree are used in two examples. Ideal data is taken for simplicity in an introductory example, but in the second example practical measurements from a steel cantilever are used.