导电梁在磁场中的磁弹性随机振动

根据磁弹性基本理论和连续体的随机振动理论，得到了在外加磁场中通有随机电流的梁的磁弹性随机振动方程。给出了导电梁在耦合场中的洛伦兹力及力矩，并将洛沦兹力的耦合项假设为梁的一种阻尼，另一部分假设为随机分布载荷，对梁的位移响应进行了分析。以简支梁为例，分别得到了外加磁场中通入平稳和非平稳随机电流时简支梁的位移响应的均值、自相关函数、功率谱密度函数等数字特征。最后以一个通有理想白噪声平稳随机电流的简支梁为实际算例，对其位移响应的功率谱密度函数进行了计算。图形形状的改变表明了耦合项对梁的功率谱密度函数的影响，据此可知通过控制随机电流和磁场可以达到控制梁的随机振动的目的。

MAGNETO-ELASTIC RANDOM VIBRATION OF AN ELECTRO-CONDUCTIVE BEAM IN MAGNETIC FIELD

On base of the electro-magneto-elastic theory and the theory of random vibraition of systems with distributed parameters, magnetoelastic random vibration equations of a random-current-carrying beam in magnetic field is obtained. And the Lorentz force and torque exerted on the beam are derived. The random displacement response of the beam on the assumption that one part Lorentz force is a kind of damping of the beam and the other part of Lorentz force is random distributing load is analyzed. As an example, the correlation function, the power spectral density function and the variance function of the random displacement response of a random-current-carrying simply supported beam are calculated.