The eigenvalue problem associated with the nonlinear buckling of a shear bending column

Isao Nishimura

doi:10.1117/12.880276

18 April 2011 The eigenvalue problem associated with the nonlinear buckling of a shear bending column

Isao Nishimura

Proceedings Volume 7981, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2011; 79815I (2011) https://doi.org/10.1117/12.880276
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2011, San Diego, California, United States

Abstract

This paper discusses the eigenvalue problem of a nonlinear differential equation that governs the stability of a shear bending column under extremely large deformation. What is taken into consideration is the geometrical nonlinearity while the material is supposed to be linear. The reason of a superbly stable buckling behavior of a slender rubber bearing is physically explained by pointing out the analogy that is similar to the nonlinear wave propagation expressed in KdV equation. The nonlinear boundary condition and the nonlinear term of the differential equation cancel each other and make the associated eigenvalue rather constant. In other words, as far as the material is supposed to be linear, the column does not buckle no matter how large the deformation is. This theoretical prediction is experimentally verified and successfully applied to a base isolation system of a lightweight structure.

Citation Download Citation

Isao Nishimura "The eigenvalue problem associated with the nonlinear buckling of a shear bending column", Proc. SPIE 7981, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2011, 79815I (18 April 2011); https://doi.org/10.1117/12.880276

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