热冲击作用下轴向运动梁的振动特性研究

研究了两端简支不可移、轴向运动梁在热冲击作用下的横向振动特性,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,采用微分求积法求解了梁的横向振动问题,分析了热冲击和轴向运动效应对梁固有特性的影响。研究发现:热冲击引起的梁的等效热轴力、热弯矩和弹性模量变化三因素中,热轴力对梁固有频率的影响起主导作用,材料的弹性模量变化和热弯矩起次要作用;当热冲击载荷大于或等于梁的临界压力时,达到梁的第一阶失稳模态;热冲击和轴向运动效应都会降低梁的固有频率,它们的联合作用会导致模态之间的耦合现象,使梁更易达到失稳状态。

Vibration characteristics of an axially moving beam under thermal shocks

The transverse vibration characteristics of an axially moving beam immovably simply supported at both ends and subjected to a thermal shock were studied. Based on Timoshenko beam theory and Hamilton principle, the governing equations of its transverse vibration were established. The transverse vibration problem of the beam was solved by using the differential quadrature method. The effects of thermal shock and axially moving speed on its natural frequencies were analyzed. The results shwoed that among three factors including equivalent thermal axial force, equivalent thermal bending moment and changing of elastic modulus dut to thermal shock, equivalent thermal axial force plays a dominant role to affect natural frequencies of the beam, while changing of elastic modulus and equivalent thermal moment play a secondary role; when the thermal shock loads reach the critical load of the beam, the first order buckling mode is excited; thermal shock and axial moving speed can both reduce natural frequencies of the beam, and their joint action leads to the phenomenon of modal coupling to make the beam easily reach an unstable status.