This work explores deriving transmissibility functions for a missile from a measured location at the base of the fairing to a desired location within the payload. A pressure on the outside of the fairing and the rocket motor’s excitation creates an acceleration at a measured location and a desired location. Typically, the desired location is not measured. In fact, it is typical that the payload may change, but measured acceleration at the base of the fairing is generally similar to previous test flights. Given this knowledge, it is desired to use a finite-element model to create a transmissibility function which relates acceleration from the previous test flight’s measured location at the base of the fairing to acceleration at a location in the new payload. Four methods are explored for deriving this transmissibility, with the goal of finding an appropriate transmissibility when both the pressure and rocket motor excitation are equally present. These methods are assessed using transient results from a simple example problem, and it is found that one of the methods gives good agreement with the transient results for the full range of loads considered.
The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.
This work explores deriving transmissibility functions for a missile from a measured location at the base of the fairing to a desired location within the payload. A pressure on the outside of the fairing and the rocket motors excitation creates an acceleration at a measured location and a desired location. Typically, the desired location is not measured. In fact, it is typical that the payload may change, but measured acceleration at the base of the fairing is generally similar to previous test flights. Given this knowledge, it is desired to use a finite element model to create a transmissibility function which relates acceleration at the previous test flights measured location at the base of the fairing to acceleration at a location in the new payload. Three methods are explored for deriving this transmissibility, with the goal of finding an appropriate transmissibility when both the pressure and rocket motor excitation are equally present. A novel method termed the Harmonic method is introduced and unfortunately found not to be as accurate as standard methods. However, the standard methods also do not perform particularly well for the combined loading of aerodynamic pressure and rocket motor excitation.