Launch Vehicle Self-Sustained Oscillation from Aeroelastic Coupling Part 1: Theory

Launch Vehicle Buffeting With Aeroelastic Coupling Effects

“…The "rst term on the right-hand side of equation (3) represents the generalized force history for aeroelastic coupling. The two force resultants in this summation are de"ned by steady pressure pro"les for the alternating #ow states, and are described in further detail by Dotson et al (1998a). The alternating #ow forces are a function of the generalized displacement q RG , because the changes in #ow state occur when the de#ection angle of the payload fairing nose cone equals a critical value, as shown in Figure 1.…”

“…It was, furthermore, shown that this di!erence can be traced to the value of the time lag de"ned explicitly by Dotson et al (1998a) and implicitly by Ericsson (1967). There are two major implications of this "nding: "rst, the stability criterion concept can be misleading because a "nite limit-cycle amplitude always exists for structurally damped launch vehicles; second, it is essential that the estimate of the magnitude of the time lag be reasonable, otherwise the predicted launch vehicle responses and loads will be unrealistically large.…”

“…Ericsson (1967), in the "rst of these two semiempirical methods, assumed that the #ow state changes instantaneously after an implicit time lag and that the alternations occur on only one side of the payload fairing. More recently, Dotson et al (1998a) analyzed the e!ects of #ow state changes that occur linearly during an explicit time lag and on both sides of the payload fairing, as shown in Figure 2. Because most launch vehicles #y with an angle of attack close to zero degrees, and because most payload fairing shapes exhibit #ow state alternations for small angle-of-attack values, the two-sided alternations are generally representative of #ight conditions.…”

“…A stability criterion was next de"ned as the limit-cycle amplitude that corresponds to zero net system damping. Dotson et al (1998a), in contrast, established the steady-state behavior of the launch vehicle using analysis techniques for multifrequency periodic excitation. The frequency and amplitude of the limitcycle oscillations were derived directly, that is, without introducing an aerodynamic damping term.…”

“…Because most launch vehicles #y with an angle of attack close to zero degrees, and because most payload fairing shapes exhibit #ow state alternations for small angle-of-attack values, the two-sided alternations are generally representative of #ight conditions. One-sided and instantaneous #ow state changes can, however, also be analyzed using the techniques employed by Dotson et al (1998a). Ericsson (1967) linearized the equation of motion by converting the force from the #ow alternations into an aerodynamic damping term corresponding to harmonic response at the vehicle bending mode frequency.…”