An adjoint method of sensitivity analysis for residual vibrations of structures subject to impacts

• Published in: Journal of sound and vibration Vol. 418; pp. 15 - 35
• Main Authors: Yan, Kun, Cheng, Gengdong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 31.03.2018; Elsevier Science Ltd
• Subjects: Adjoint method; Dependence; Impact load; Impact loads; Load; Lyapunov equation; Performance indices; Residual vibration; Sensitivity analysis; Structural design; Structural engineering; Vibration; Vibration analysis; Vibration control; Vibration measurement; Adjoint method; Sensitivity analysis; Residual vibration; Lyapunov equation; Impact load
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2017.12.015

For structures subject to impact loads, the residual vibration reduction is more and more important as the machines become faster and lighter. An efficient sensitivity analysis of residual vibration with respect to structural or operational parameters is indispensable for using a gradient based optimization algorithm, which reduces the residual vibration in either active or passive way. In this paper, an integrated quadratic performance index is used as the measure of the residual vibration, since it globally measures the residual vibration response and its calculation can be simplified greatly with Lyapunov equation. Several sensitivity analysis approaches for performance index were developed based on the assumption that the initial excitations of residual vibration were given and independent of structural design. Since the resulting excitations by the impact load often depend on structural design, this paper aims to propose a new efficient sensitivity analysis method for residual vibration of structures subject to impacts to consider the dependence. The new method is developed by combining two existing methods and using adjoint variable approach. Three numerical examples are carried out and demonstrate the accuracy of the proposed method. The numerical results show that the dependence of initial excitations on structural design variables may strongly affects the accuracy of sensitivities.