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Differential equations play a prominent role in aerospace engineering by modeling aerospace structures, describing important phenomena, and simulating mathematical behavior of aerospace dynamical systems. Presently, aerospace systems have become more complex, space vehicle missions require more hours of simulation time to complete a maneuver, and high-performance missiles require more logical decisions in there phases of flight. Because of these conditions, a computationally efficient algorithm for solving these differential equations is highly demanded to significantly reduce the computing time. This paper presents an efficient method for solving the differential equations by using variational iteration method, which can be implemented into software package to dramatically reduce the computing time for simulating the aerospace systems thereby significantly improving computer's performance in real-time design and simulation of aircrafts, spacecrafts, and other aerospace vehicles.

The vibration response from undamaged and damaged polymer matrix composite beams at elevated temperatures is analyzed using the Hilbert-Huang Transform (HHT) technique. The HHT shows potential in identifying the nonlinear damaged response of the beams. Using empirical mode decomposition to separate superposed modes of signals, several intrinsic mode functions can be determined which can reveal more information about complex nonlinear signals than traditional data analysis techniques such as the Fourier Transform. The composite beams are fabricated from an out-of-autoclave uniaxial carbon/epoxy prepreg (CYCOM™-5320-1/T650). Delamination damage in the composite layups is introduced by insertion of mold release wax films during fabrication. A shaker-table fixture was used for the vibration testing of all beams in a vertical cantilever configuration. High temperature piezoelectric accelerometers were used to obtain the vibration data for a frequency range of 1-61 Hz.