Theory of Structural Dynamic Testing Using Impedance Techniques. Volume I. Theoretical Development
KAMAN AEROSPACE CORP BLOOMFIELD CT
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It is shown that the mass, stiffness and damping parameters in Lagranges equations of motion of an n-degree-of-freedom damped linear elastic structure can be determined directly from impedance-type test data without prior assumption of an intuitive mathematical model. The damping is assumed to be such that the model vectors are orthogonal with respect to damping. A method is derived for determination of the exact modal eigenvector of the dominant mode at any forcing frequency by iteration on the damped impedance measurements in matrix form. A similar eigenvalue equation yields the vector in the inverse transpose of the modal matrix this vector called the gamma vector, is identified with the dominant mode. The generalized masses, stiffnesses and damping terms are related to the mass, stiffness and damping matrices of the equations of motion through products of the gamma vectors. Using the gamma vectors, obtained by iteration on test data, the natural frequencies and other modal parameters are determined. Natural frequencies which are not visible in response plots may be determined by this method. Computer experiments were conducted to test the sensitivity of the theory to errors in input data.
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