Nonlinear vibration analysis of a complex aerospace structure

Technical paper presented at the 2016 Defence and Security Doctoral Symposium. Complex shaped aerodynamic structures such as deployable missiles are prone to exhibit some level of nonlinear phenomena due to their aerodynamic tailored design and application. Aside from the aeroelastic control challenges experienced by a missile, a fundamental challenge encountered by a deployable missile is the inevitable concentrated structural nonlinearities which are observed around the hinge of its fins. Due to the current design and manufacturing process, the hinge of the fin of a missile often consist of complex configurations, such as joints, friction and other nonlinear features which may lead to concentrated structural nonlinearities. Some of the nonlinearities encountered includes piecewise linearity, bilinear nonlinearity, hysteresis, coulomb friction and nonlinear damping mechanisms. These nonlinearities are frequently triggered at large vibration amplitudes, caused by high pressure loads during operational flight. Activation of these nonlinearities often affect the dynamic response of the missile and in some cases lead to structural failures in the major components of the air vehicle. In this context, identifying and predicting the vibration response of such aerodynamic structures with nonlinearities, may be of great advantage to the present structural dynamic community. In this paper, the nonlinear dynamic behaviour of a B61 prototype missile has been examined. A two-step methodology for integrating nonlinear system identification for estimating nonlinear stiffness and damping mechanism and nonlinear finite element modelling has been adopted in this investigation. The first step made use of acquired input and output data from random and sine sweep vibration test to derive a nonlinear experimental model for the missile, where the nonlinear experimental model was developed using a white box identification process, namely (detection, characterisation and parameter estimation). The second step implements the parameters of the identified nonlinear system into a finite element model (FEM) of the missile to develop a nonlinear FEM. The nonlinear dynamic response of the FEM was computed using the Harmonic balance method (HB) and pseudo-arclength continuation in the frequency domain. In addition, Force controlled stepped sine experiments at several excitation levels were conducted to validate the numerical solution obtained from the nonlinear FEM computation. The results obtained were used to understand the amplitude dependant behaviour of the missile under a vibration controlled environment and in addition predict the dynamic response of the missile in the existence of deployable hinge nonlinearity.