Physical Modifications to Vibratory Systems With Assigned Eigendata

Modal Modification of Vibrating Systems: Some Problems and Their Solutions

“…In Section 6, we show how an approximate solution, which can be realised by an actual physical modi"cation, is determined. This result is due to Sivan and Ram [5]. Similar to Bucher and Braun [6], we show in Section 7 that if two truncated sets of left and right modal vectors are given, then the inverse problem can be solved without truncation error.…”

Viscously Damped Linear Systems Subjected to Damping Modifications

“…It is claimed that since the design sensitivities are calculated directly from the measured data, they are expected to be more realistic. Sivan and Ram [2] considered the backward problem: i.e., the problem of determining the structural modi"cation needed to prescribe some natural frequencies and mode shapes in the presence of model uncertainty. Mottershead and Lallement [3] investigated the relationship between the sensitivity of antiresonances (zeros) and sensitivities of the natural frequencies and mode shapes of structural systems.…”

Axial Vibration Confinement in Nonhomogenous Rods

“…Ram and Elhay have presented a method that constructs tridiagonal symmetric quadratic damping and stiffness matrices based on a given set of eigenvalues [17]. Sivan and Ram have treated the problem of determining structural alteration from a given set of eigenvalues and eigenvectors in the presence of model uncertainties [20]. Ram has synthesized control forces for shifting some poles of a vibrating rod to prescribed locations while keeping the other poles unchanged [16].…”