Structural health monitoring through nonlinear frequency-based approaches for conservative vibratory systems

M. Bayat , I. Pakar , H.R. Ahmadi , M. Cao , A.H. Alavi

Abstract

This paper proposes a new approximate analytical solution for highly nonlinear vibration of mechanical systems called Hamiltonian Approach (HA) that can be widely use for structural health monitoring systems. The complete procedure of the HA approach is studied, and the precise application of the presented approach is surveyed by two familiar nonlinear partial differential problems. The nonlinear frequency of the considered systems is obtained. The results of the HA are verified with the numerical solution using Runge-Kutta\'s [RK] algorithm. It is established the only one iteration of the HA leads us to the high accurateness of the solution.

Key Words

Hamiltonian Approach (HA); nonlinear vibration; analytical solution; Runge-Kutta\'s algorithm

Address

M. Bayat — Department of Civil and Environmental Engineering, University of Pittsburgh, 3700 O\'Hara Street, 729 Benedum Hall, Pittsburgh, PA 15261, USA
I. Pakar — Department of Civil Engineering, Faculty of Engineering, Shomal University, Amol, Mazandaran, Iran
H.R. Ahmadi — Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh P.O. Box 55136-553, Iran
M. Cao — Jiangxi Provincial Key Laboratory of Environmental Geotechnical Engineering and Disaster Control, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, 341000, People\'s Republic of China ; Department of Engineering Mechanics, Hohai University, 210098 Nanjing, Jiangsu, People\'s Republic of China
A.H. Alavi — Department of Civil and Environmental Engineering, University of Pittsburgh, 3700 O\'Hara Street, 729 Benedum Hall, Pittsburgh, PA 15261, USA; Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

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