3 The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems 25 which has the property to be singular whenPhas a pair of complex conjugates crossing the imaginary axis, one can develop the following extra equation to track a NS bifurcation: jBˇjD0 (3.27) or, by using the bordering techniques as in (3.25): gNS D0 (3.28) withgNS obtained by solving Bˇ pNS q NS 0 w gNS D 0 1 (3.29) where pNS and qNS are chosen to ensure the nonsingularity of the matrix. 3.3 Validation of the Method on the Study of an Industrial, Complex Model with Strong Nonlinearities: The Smallsat In this section, the HB method is used to address the continuation of periodic solutions for a large-scale structure and the detection of their bifurcations. In addition, the study will illustrate how one can take advantage of the filtering features of the method to efficiently compute normal modes of the structure. 3.3.1 Case Study The example studied is referred to as the SmallSat, a structure represented in Fig. 3.2 and which was conceived by EADSAstrium as a platform for small satellites. The interface between the spacecraft and launch vehicle is achieved via four aluminum brackets located around cut-outs at the base of the structure. The total mass of the spacecraft including the interface brackets is around 64 kg, it is 1.2 m in height and 1 m in width. It supports a dummy telescope mounted on a Fig. 3.2 SmallSat spacecraft equipped with an inertia wheel supported by the WEMS device and a dummy telescope connected to the main structure by the SASSA isolators
RkJQdWJsaXNoZXIy MTMzNzEzMQ==