| The Volterra series is a mathematical description of the input/output relationship for nonlinear systems. The characterization of the system is based on an infinite sequence of kernels; the output is then predicted using higher order convolutions of such kernels with the input. Usually, the first few kernels are sufficient for a satisfactory representation of the system, thus providing a reduced order model. Such a methodology is applicable to a wide class of nonlinear problems. In particular, recent applications of this approach can be found in both nonlinear structural dynamics and nonlinear aeroelasticity.;A crucial part of the method is the identification of the kernels, either in the time or frequency domain. This work investigates the use of the impulsive method, in continuous time, to identify the Volterra kernels. It is shown how such an approach can be conveniently applied in an analytical, numerical or experimental setting, once the equivalence between impulsive forces and instantaneous changes in the states of the system is exploited. Furthermore, it is found that the amplitude of the excitation probing the system is an important parameter. Analytical and numerical examples are reported to highlight how different identified Volterra kernels are possible, according to the amplitude of the impulses. The use of imaginary inputs for the identification of the kernels in simulations is also presented.;The simplest paradigm in nonlinear structural dynamics---a spring-mass-damper nonlinear oscillator, with quadratic and cubic elastic terms---is analyzed in detail using the Volterra series approach. Analytical expressions for the first few kernels in the time domain have been derived using a perturbation method. Then, the same ideas have been successfully applied to two Multi-Degree-of-Freedom aeroelastic systems: a plunge and pitch airfoil with a nonlinear torsional spring, and an airfoil experiencing dynamic stall. |
