ZHAO Yan-ping, LI Lin, JIN Ming. Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299
Citation: ZHAO Yan-ping, LI Lin, JIN Ming. Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299

Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support

doi: 10.21656/1000-0887.370299
  • Received Date: 2016-09-29
  • Rev Recd Date: 2016-12-01
  • Publish Date: 2017-08-15
  • Under Euler’s critical load, the stability of a slender compression rod with one end fixed and the other clamped in rotation but translationally restrained by a spring was studied. The potential energy of the system was expressed with the functional of the rod deflection angle; the disturbance was expanded into the Fourier series; the 2nd-order variation of the potential energy was expressed with a quadratic form. The 2nd-order positive semidefinite variation in the critical state was derived with the buckling mode and the critical load obtained. A further study of the positive definiteness of higher-order variations, including the 4th and 6th variations, indicates that the stability of the compression rod with a flexible support is related to the stiffness of the flexible constraint and may be stable or unstable, which is different from the case of a rigid constraint. In the stable and unstable critical states the ranges for the relative stiffness of the flexible support were also given.
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