A uni ed hypersonic -supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic in uence coef cient (AIC) matrix due to linear theory. Thus, this uni ed method can account for the effects of wing thickness and/or ow incidence, upstream in uence, and three dimensionality for an arbitrary lifting surface system in an unsteady ow, whereas piston theory fails to account for the latter effects. In particular, the present composite series renders the AIC matrix uniformly valid for all supersonic -hypersonic Mach numbers, thus extending the method applicability to cover both the Ackeret limit at the low supersonic end and the Newtonian limit at the hypersonic end. From various cases studied it is concluded that the present method makes a substantial improvement over the linear lifting surface theory and piston theory in terms of unsteady pressures, stability derivatives, and utter speeds. Among other theories it also predicts the most conservative utter boundary and it con rms that the supersonic thickness effect is to reduce the utter speed.

No abstract

No abstract

An accurate and effective method for calculations of unsteady three-dimensional supersonic flow has been developed. The present method is capable of handling general cases of planar, coplanar, and nonplanar wing planforms in the complete frequency domain. A harmonic-gradient potential model is provided for elementary doublet panels to be made compatible with the wave number generated. Consequently the number of panel elements required is least affected by the given Mach number and reduced frequency. Thus, the required panel number can be optimized to as few as 30, a fraction of the number required by the existing methods. To assess the accuracy and effectiveness of the present method, comparison with various available data is given. AC P h i L m M (x,y,z) (X,Y,Z) a. CO Subscripts J T.E. Nomenclature = lifting pressure coefficient = structural mode shapes = reference chord length = slope of leading or trailing edge of the panel element = freestream Mach number = wing-fixed coordinates; (x,y,z) = (X/$L, Y/L, Z/L) (see Fig. 1) = control point location in (x,y,z) coordinates = true physical coordinates = position of leading or trailing edge of the panel element at 77 = 0 = moving coordinates (see Fig. 1) = oscillatory potential = modified velocity potential = ^e ikMX = doublet solution of modified potential = circular frequency of harmonic motion = index of the number of chordwise element in the yth strip = index of the number of strip -trailing edge of the wing -wake

A developed transonic-aerodynamic-in uence-coef cient (TAIC) method is proposed as an ef cient tool for applications to utter, aeroservoelasticity, and multidisciplinary design/analysis optimization. Several plausible procedures for AIC generation are described. The modal-based AIC procedure is formally established as a general AIC scheme applicable to all classes of computational uid dynamics (CFD) methods. The present TAIC method integrates the previous transonic equivalent strip (TES) method with the modal AIC approach; its computer code ZTAIC has a similar input format to that of doublet lattice method (DLM) except with the additional steady pressure input. The versatility of ZTAIC is shown by two sets of cases studied: those cases with pressure input from measured data and those from CFD computation. Computed results of unsteady pressures and utter points are presented for six wing planforms. In contrast to the usual CFD practice, the effective use of the modal AIC in ZTAIC is clearly demonstrated by the utter calculations of the weakened and solid 445.6 wings, where the CPU time of a transonic utter point using warm-started AIC is less than 1 min on a SUN SPARC20 workstation. Moreover, the AIC capability allows ZTAIC to be readily integrated with structural nite element method (FEM). Hence, it is most suitable to be adopted in a multidisciplinary design (MDO) environment such as ASTROS.