An Efficient Method for Compensating Truncated Higher Modes in Structural Dynamics Modification

Abstract

An efficient method for compensating the effects of the truncated higher modes in structural dynamics modification ( S D M ) is developed to predict the accurate modal parameters of locally modified structures. The effects of the truncated higher modes are represented by a fictitious, effective mode residing beyond the frequency range of interest. The modal parameters are then easily obtained by the iterative single degree-offreedom curve-fit tiny technique developed for lightly damped systems. A numerical example demonstrates the effectiveness of the improved SDM technique. NOTATION coefficients of D(o) coefficient of N ( o ) denominator of Hpqk(W) measured frequency response function ideal frequency response function frequency response function with only lower n modes frequency response function in the vicinity of the kth mode imaginary part of F , imaginary unit (= JT) stiffness modification quantity lower residual term (inertia restraints) mass modification quantity modal mass of the kth mode numerator of H,,,(w) response (displacement) measurement point system pole (= -nk + jw,) driving point complex residue ( r l k + j r 2 k )normalized residue w.r.t. mass matrix of the kth mode at point q effective residue of the truncated higher modes real part of F,, new rth eigenvalue of the modified structure original kth mode shape new rth eigenvector of the modified structure real residues of the kth mode at two points p and q respectively higher residual term (residual flexibility) ideal higher residual term approximation of Z,,(o) difference between H,,k(o) and Fpq(u) in the vicinity of the kth mode damping coefficient of the kth mode effective damping damped natural frequency of the kth mode lower and upper bounds of the kth mode effective natural frequency The M S was