Flexible Boundary Method in Dynamic Substructure Techniques Including Different Component Damping

Abstract

There are various condensation methods for substructure techniques in structural dynamics. A generalized condensation method that comprises most of the classical condensation techniques and allows for arbitrary mode shapes within a standardized approach is described here. Within the framework of this method, a flexible boundary method is introduced that allows for elastic and mass-loaded boundaries for eigenmode determination, as well as for mode shapes that reflect the influence of damping. The relationship to other approaches taken from existing literature is examined. For damped structures, the flexible boundary method provides a condensation process that takes into account the influence of the complex eigenmodes of structures with nonproportional and high damping. To couple substructures with different component damping, the equivalent structural damping approach is provided. The problems associated with diagonal system damping of substructures and the full triple matrix product are overcome.Nomenclature A = attachment modes B = flexibility matrix C = structural damping matrix D = viscous damping matrix fFg = external force vector G = condensation matrix G = matrix of Ritz vectors K = stiffness matrix M = mass matrix P = projection matrix fqg = vector of generalized degrees of freedom R = residual flexibility T = transformation matrix fxg = vector of physical displacements = complex eigenmodes = static modes ' = real eigenmodes = frequency domain variable ! = eigenfrequency

Kineto-elastic analysis of modular robot systems with component model updating

“…(6.31) gives: further adjustments such as inertia-relief modes [95] for free-free component BCs. From the third [93] and Dieker et al [94] suggest using a non-singular flexibility matrix for free-interface attachment modes to obtain a secondar ro matrix in Eq. (6.26) can be readily inverted ained at the B interface DOFs) and does not require row in Eq.…”

“…More recently, the hybrid-interface CMS approaches for stationary structures have been improved by Majed et. al, [93] and Dieker et al [94] to allow for any set of interface BCs (all fixed, all free, or hybrid) to be used. Also, the component normal modes in these newer hybrid methods can be computed using any of the mentioned BCs.…”

“…Also, the component normal modes in these newer hybrid methods can be computed using any of the mentioned BCs. Further advantages of the methods in [93,94] Thus, the residual flexibility modes can effectively increase accuracy without increasing the number of kept normal modes.…”

Clarification about Component Mode Synthesis Methods for Substructures with Physical Flexible Interfaces

“…From this pioneering fundamental papers, several works have been published and among them, let us cite [28,29,30,31,32,33]. In this context, the Lagrange multipliers have also been used to write the coupling on the geometrical interface [23,34,35,36] As damping plays an important role in the prediction of the dynamical responses, substructuring techniques taking into account damping have been the subject of several investigations, for instance, [37,38,39,40,41,42,43,44,45,46,47]. In particular, the damping modeling is important in the medium-frequency range which has been analyzed in [48,49,50,51] in the context of substructuring techniques.…”