Numerical and analytical investigations were performed to study the panel flutter generated by the coupling of elastic and aerodynamic loads with thermal loads. Based on large deflection theory and piston aerodynamic theory, the nonlinear dynamic differential equations of heated panels with pre-stretch displacement are derived. The Galerkin method is applied to transform the continuous partial differential equations into a nonlinear system of ordinary differential equations. The analytical expressions of the flutter critical dynamic pressure and flutter frequency, the static divergence stability boundary and the Hopf bifurcation fluttering stability boundary for the initial equilibrium of the panel can be obtained through the algebraic criterion of the Hopf bifurcation. The results show that, compared to the non-pre-stretch condition, when the pre-strain of the panel was merely 0.0328%, the flutter critical dynamic pressure and flutter frequency increased by 380.78% and 223.43%, respectively. Moreover, the pre-stretching method can significantly enhance the capacity of the supersonic panel to sustain temperature loads.

The weak intermolecular interactions between 2-F-tetrahydrofuran and imidazole, pyrimidine, adenine, and guanine were studied theoretically using density functional B3LYP/6-311++G** and HF/6-311++G** methods. The results showed that both conventional N...H hydrogen bond and C-F...H-C pseudohydrogen bond (PHB) structures coexist in the four complexes. The weak intermolecular interaction energies indicate that the relative stabilities of the four complexes are in the order guanine...F > imidazole ...F > adenine...F > pyrimidine...F. The characteristics of the four PHBs were determined using geometry optimizations, stretching vibrational frequencies, and natural bond orbital and electron density topological properties calculations. The most important result is that the F group of 2-F-tetrahydrofuran can activate the C-H to accept electrons from another molecule, and C-F...H-C PHB formation is relatively favorable.

Uncertainty caused by a parameter measurement error or a model error causes difficulties for the implementation of the control method. Experts can divide the uncertain system into a definite part and an uncertain part and solve each part using various methods. Two uncertainty problems of the control system arise: problem A for the definite part—how does one find out the optimal number and position of actuators when the actuating force of an actuator is smaller than the control force? Problem B for the uncertain part—how does one evaluate the effect of uncertainty on the eigenvalues of a closed-loop control system? This paper utilizes an interval to express the uncertain parameters and converts the control system into a definite part and an uncertain part using interval theory. The interval state matrix is constructed by physical parameters of the system for the definite part of the control system. For Problem A, the paper finds out the singular value element sensitivity of the modal control matrix and reorders the optimal location of the actuators. Then, the paper calculates the state feedback gain matrix for a single actuator using the receptance method of pole assignment and optimizes the number and position of the actuators using the recursive design method. For Problem B, which concerns the robustness of closed-loop systems, the paper obtains the effects of uncertain parameters on the real and imaginary parts of the eigenvalues of a closed-loop system using the matrix perturbation theory and interval expansion theory. Finally, a numerical example illustrates the recursive design method to optimize the number and location of actuators and it also shows that the change rate of eigenvalues increases with the increase in uncertainty.