Purpose <p>This research proposes a novel equivalent continuum model capable of accurately predicting the dynamic behaviors of Warren girder with flexible joints by considering spring-dampers in six directions. Most of equivalent continuum modeling focuses on studying non-flexible jointed truss structures. The research on continuum modeling is in extreme lack of truss structures with flexible joints for now and needs to be furtherly investigated. </p> Methods <p>In this paper, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm for the parameter inversion analysis is integrated into the equivalent continuum modeling procedure, to identify unknown equivalent stiffnesses of Warren girder with flexible joints. The length-to-width ratio of the Warren girder is 30 with a relatively high slenderness ratio. The governing partial differential equations of established equivalent continuum model are obtained and solved utilizing the Galerkin method. Particularly, the mode shape functions of cantilevered equivalent continuum model are derived in analytical method, which is convenient to the low-order control law design and nonlinear mechanism analysis. </p> Results and Conclusion <p>The good agreements of mode shapes and dynamic responses show the equivalent continuum model can accurately captures the dynamic behaviors of the Warren girder with flexible joints by comparing results. Furthermore, the effect of stiffness of joints on the in-plane and out-of-plane vibration frequencies is discussed.</p>

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Equivalent Continuum Modeling of Warren Girder with Flexible Joints Using Parameter Inversion Method

  • Mei Liu,
  • De Li,
  • Zunbing Sheng,
  • Xiaoyun Zhang,
  • Dengqing Cao

摘要

Purpose

This research proposes a novel equivalent continuum model capable of accurately predicting the dynamic behaviors of Warren girder with flexible joints by considering spring-dampers in six directions. Most of equivalent continuum modeling focuses on studying non-flexible jointed truss structures. The research on continuum modeling is in extreme lack of truss structures with flexible joints for now and needs to be furtherly investigated.

Methods

In this paper, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm for the parameter inversion analysis is integrated into the equivalent continuum modeling procedure, to identify unknown equivalent stiffnesses of Warren girder with flexible joints. The length-to-width ratio of the Warren girder is 30 with a relatively high slenderness ratio. The governing partial differential equations of established equivalent continuum model are obtained and solved utilizing the Galerkin method. Particularly, the mode shape functions of cantilevered equivalent continuum model are derived in analytical method, which is convenient to the low-order control law design and nonlinear mechanism analysis.

Results and Conclusion

The good agreements of mode shapes and dynamic responses show the equivalent continuum model can accurately captures the dynamic behaviors of the Warren girder with flexible joints by comparing results. Furthermore, the effect of stiffness of joints on the in-plane and out-of-plane vibration frequencies is discussed.