Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

doi:10.1007/s10483-016-2137-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (10): 1361-1374.doi: https://doi.org/10.1007/s10483-016-2137-9

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

M. GRYGOROWICZ¹, E. MAGNUCKA-BLANDZI²

1. Institute of Applied Mechanics, Poznan University of Technology, Poznań 60-139, Poland;
2. Institute of Mathematics, Poznan University of Technology, Poznań 60-965, Poland

收稿日期:2016-01-04 修回日期:2016-05-05 出版日期:2016-10-01 发布日期:2016-10-01
通讯作者: M. GRYGOROWICZ E-mail:magdalena.grygorowicz@put.poznan.pl
基金资助:
Project supported by the Ministry of Science and Higher Education of Poland (Nos.04/43/DSPB/0085 and 02/21/DSPB/3464)

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

M. GRYGOROWICZ¹, E. MAGNUCKA-BLANDZI²

1. Institute of Applied Mechanics, Poznan University of Technology, Poznań 60-139, Poland;
2. Institute of Mathematics, Poznan University of Technology, Poznań 60-965, Poland

Received:2016-01-04 Revised:2016-05-05 Online:2016-10-01 Published:2016-10-01
Supported by:
Project supported by the Ministry of Science and Higher Education of Poland (Nos.04/43/DSPB/0085 and 02/21/DSPB/3464)

摘要/Abstract

摘要：

The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is formulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton’s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.

关键词: metal foam core with variable mechanical property, dynamic stability, angular frequency, static and dynamic equilibrium path, mathematical modelling

Abstract:

Key words: dynamic stability, static and dynamic equilibrium path, mathematical modelling, angular frequency, metal foam core with variable mechanical property

中图分类号:

70K20

M. GRYGOROWICZ, E. MAGNUCKA-BLANDZI. Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1361-1374.

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Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

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