论文标题
光链的结构稳定性,用于激光驱动的星际飞行
Structural Stability of a Lightsail for Laser-Driven Interstellar Flight
论文作者
论文摘要
在分析和数值上研究了星际飞行所需的激光通量下的轻型邮件的结构稳定性。正弦扰动被引入二维薄膜帆中,以确定帆是否保持稳定,或者扰动的幅度是否增长。在确定帆上产生的载荷时,假定了一种反射材料,尽管可以合并其他反射模型,但在确定帆上产生的载荷时假设了镜面反射。通过将辐射压力引起的弯曲矩与帆的强度以及在帆的边缘施加的张力引起的恢复矩所引起的弯曲力量,可以找到帆的稳定矩和不稳定性之间的临界点的准静态解决方案,从而使弹性模量和边界张力量的分析表达式允许出现航行型和数量的功能数量,以使弹性模量和边界张力范围均能找到启用型和wave的功能。这些表达也来自形式的变分能量方法。帆动力学的数值模型是通过将帆离散为有限元素而开发的。通过将元素之间的扭转和直线弹簧引入数值模型中,产生了模型的层次结构,可以结合弯曲和施加张力的影响。数值模型允许将驱动式帆的瞬时动力学与准静态分析的分析结果进行比较。分析表达式可以正确预测数值模拟中发现的稳定边界。证明已知材料对不受控制的扰动生长进行帆稳定所需的刚度被证明是不可行的。帆的适度张力(例如,通过充气结构或帆的旋转)可以在所有波长和扰动振幅下保持稳定的帆形状。
The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A reflective material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail and the tension applied at the edges of the sail, permitting analytical expressions for the elastic modulus and boundary tension magnitude to be found as a function of sail properties and the amplitude and wave number of the initial perturbation. These expressions are also derived from a formal variational energy approach. A numerical model of the sail dynamics is developed by discretizing the sail into finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed sail to be compared to the analytic results of the quasi-static analysis. The analytic expressions can correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a sail stable against uncontrolled perturbation growth is shown to be unfeasible for known materials. A modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) can maintain a stable sail shape under all wavelengths and amplitudes of perturbations.