Extension of dual equivalent linearization to analysis of deterministic dynamic systems. Part 1: single-parameter equivalent linearization

Authors

• N. D. Anh, Vietnamese Academy of Science and Technology Institute of Mechanics
• Nguyen Ngoc Linh, Thuyloi University
• Tran Tuan Long, Vietnamese Academy of Science and Technology Institute of Mechanics
• Nguyen Cao Thang, Vietnamese Academy of Science and Technology Institute of Mechanics
• Anh Tay Nguyen, Robert R. McCormick School of Engineering and Applied Science
• Isaac Elishakoff, Florida Atlantic University

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Nonlinear Dynamics

Publication Status

Version of Record

Abstract

The paper develops the dual equivalent linearization with one weighting coefficient to nonlinear deterministic dynamic systems. The problem of equivalent replacement of a nonlinear function by a linear function is briefly revised using the dual approach that involves two forward and backward replacements. Further selecting a weighting coefficient connecting two objective functions is investigated using a semi-analytical analysis. The dual equivalent linearization with the selected weighting coefficient is then applied to the frequency analysis of nonlinear free vibrations, and some case studies are subsequently carried out in order to verify the accuracy and influence of nonlinearities on the effectiveness of the proposed technique. It is shown that the dual equivalent linearization provides the lowest maximal errors among the solutions obtained from several approximate methods for the rather large nonlinearities considered.

First Page

997

Last Page

1017

DOI

10.1007/s11071-022-07894-6

Publication Date

1-1-2023

Recommended Citation

Anh, N. D.; Linh, Nguyen Ngoc; Long, Tran Tuan; Thang, Nguyen Cao; Nguyen, Anh Tay; and Elishakoff, Isaac, "Extension of dual equivalent linearization to analysis of deterministic dynamic systems. Part 1: single-parameter equivalent linearization" (2023). Faculty Scholarship. 190.
https://digitalcommons.fau.edu/faculty_papers/190