两端固支热弹耦合运动梁的稳定性

Stability of the coupled thermoelastic moving beam with clamped ends

目的研究两端固支耦合热弹运动梁的稳定性。方法根据D′Alembert原理和考虑变形影响时的热传导方程,得出梁的耦合热弹运动微分方程,采用微分求积法得到特征方程。结果对两端固支耦合热弹运动梁的复频率进行了数值计算,分析了无量纲热弹耦合因子、无量纲运动速度对梁的临界速度和稳定性的影响。结论随着无量纲热弹耦合因子的增大,轴向运动梁的前三阶模态的复频率实部增大,一阶模态失稳的临界速度也增大。

Aim The stability of coupled thermoelastic moving beam with clamped ends are investigated. Methods The differential equation of motion of coupled thermoelastic moving beam is established based on the D′Alembert theory and the thermal conduction equation involving deformation effect,the characteristic equation is obtained by the differential quadrature method. Results The dimensionless complex frequencies of the axially moving beam with clamped ends are calculated numerically.The effects of the dimensionless coupled thermoelastic factor and the dimensionless moving speed on the critical speed and the stability of the beam are analyzed. Conclusion The real parts of the first three order dimensionless natural frequencies and the first order critical speed increase with the increase of the thermoelastic coupling factor.