Differential and difference sensitivities of natural frequencies and mode shapes of mechanical structures

Autonomous Structural Health Monitoring—part Ii: Vibration-Based in-Operation Damage Assessment

“…Hence, the sensitivity of the natural frequencies will be more exact. Similar expressions can be written for the sensitivity of modal parameters to local changes in stiffness [7,10]. Moreover, damping can be taken into account by assuming a general viscous damped system.…”

“…Since we are usually interested in assessing the damage as soon as possible, this poses no problem. If the identification of severe structural defects (inducing large shifts in natural frequencies) should be of interest, higher order approximations [10] or iterative first-order approximations [16] can be used. By solving equation (6) in a least squares sense, for all N m considered modes simultaneously, damage indices can be obtained from DP.…”

Sensitivity-Based Operational Mode Shape Normalisation

“…As has been shown in literature [17][18][19][20][21], many methods are available for the calculation of the sensitivity (derivatives) of eigenvalues and eigenvectors (such as modal parameters). In the case of a general viscous damped system, the sensitivity of modal parameters to local changes in mass, stiffness or damping, can be calculated by means of the estimated poles and normalized mode shapes without the use of a finite element model [22][23][24]. As an example, the sensitivity of degree of freedom (dof) j of mode shape i to a local change in mass at dof k is given by…”

Eigenvalue based inverse model of beam for structural modification and diagnostics: theoretical formulation

“…The early works concerning the inverse eigenvalue problem [4,16] are based on Rayleigh's work and their authors utilize the first order terms of Taylor's series expansion. Such an approach was developed in the work [1], where the second order approximation in Taylor series expansion was used.…”