Optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle considering the influence of concentrated mass

Bui Hai Le, Tran Minh Thuy
Author affiliations

Authors

  • Bui Hai Le Hanoi University of Science and Technology, Vietnam
  • Tran Minh Thuy Hanoi University of Science and Technology, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/6058

Keywords:

Eigen frequencie, optimal design, longitudinal bar, concentrated mass, Pareto front, Pontryagin's maximum principle

Abstract

In this paper, the problem of optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle (PMP) considering the influence of concentrated mass is presented. The necessary optimality condition when simultaneously maximizing system's eigen frequencies and minimizing system's weight considering the influence of concentrated mass is established by using Maier objective functional in order to control the final state of the objective functional. By considering eigen frequencies as state variables, the analogy coefficient k in the necessary optimality condition is explicitly determined. Numerical results obtained in this paper include: (1) the bar's optimal configurations as well as frequency responses in different cases of objective functions; (2) the Pareto front for the system's first eigen frequency and weight; (3) the influence of concentrated mass on the bar's optimal configuration.

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Published

28-03-2017

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Research Article