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Supercritical equilibrium solutions of axially moving beams with hybrid boundary conditions

机译：混合边界条件下轴向运动梁的超临界平衡解

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摘要

In this paper supercritical equilibria and critical speeds of axially moving beams constrained by sleeves with torsion springs are deduced. Transverse vibration of the beams is governed by a nonlinear integropartial-differential equation. In the supercritical regime, the corresponding static equilibrium equation for the hybrid boundary conditions is analytically solved for the equilibria and the critical speeds. In the view of the non-trivial equilibrium, comparisons are made among the integro-partial-differential equation, a nonlinear partial-differential equation for transverse vibration, and coupled equations for planar motion under the hybrid boundary conditions.
机译：本文推导了带有扭簧的套筒约束的轴向运动梁的超临界平衡和临界速度。横梁的横向振动由非线性积分偏微分方程控制。在超临界状态下，针对混合边界条件的相应静态平衡方程通过解析求解了平衡速度和临界速度。考虑到非平凡的平衡，在混合边界条件下，对积分偏微分方程，用于横向振动的非线性偏微分方程以及用于平面运动的耦合方程进行了比较。

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