Higher order eigensensitivities‐based numerical method for the harmonic analysis of viscoelastically damped structures

Abstract

SUMMARYThis paper presents an efficient numerical method for the harmonic analysis of viscoelastically damped structural systems characterized by a frequency-dependent structural damping matrix, making use of the complex mode superposition method. Departing from the undamped eigensolution, the proposed numerical method updates the complex and frequency-dependent eigenpair avoiding the solution of a complex eigenproblem for each computational frequency. The complex eigenvalues and eigenvectors are updated within the desired tolerance by an adaptive step-size control scheme using the first-and higher order eigenderivatives. The influence on the computation time of the considered number of eigenderivatives and the tolerance is discussed, and the efficiency of the proposed numerical method for the harmonic analysis of viscoelastically damped large-ordered structural systems is proved. Finally, a practical application is presented where the harmonic response of a constrained layer damping cantilever beam subjected to a base motion is analyzed. The complex and frequency-dependent eigenvalues and eigenvectors are computed, the modal contributions to the total response are determined, and the total response is approximated by the complex mode superposition method. Finally, the approximated response is validated with the exact one computed by the direct frequency method and with that experimentally measured.

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…The analysis was performed using DDM due to changes in structural parameters and temperature variations. In [338], a method for calculating higher-order eigenvalues was presented to find the harmonic response of a structure.…”

Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads

“…Permoon et al [21] used the Galerkin method to discretize the motion equation into a set of linear ordinary differential equations and then studied the forced vibration of beams. Martinez-Agirre et al [22] studied the harmonic response of the constrained layer damped cantilever beam and analyzed the damping structure system by using the complex modal superposition method. Based on the constitutive relation in the form of genetic integral algorithm, Martin [23] established the mathematical model for the dynamic analysis of beams with viscoelastic properties by using Galerkin and variational iteration methods for both quasi-static and dynamic analysis.…”

Hob wear prediction based on simulation of friction, heat fluxes, and cutting temperature

“…The use of the second-order sensitivity can contribute to improving convergence in the optimization design and to increasing the accuracy of the approximation. The discussed methods have been extended to second-or higher-order analysis in [15,[18][19][20][21]. Three methods were proposed for the calculation of second-order sensitivity in [4]: DDM, AVM, and the hybrid method (HM).…”