An Overview of ANSYS Harmonic Balance Method: Current Capabilities and Future Directions 73 Fig. 1 Solution to a case study from [11] obtained using Ansys-HBM. In this particular study, if solution vector scaling is not applied, the algorithm struggles to achieve convergence near the boundaries between the stable and unstable regions of the nonlinear frequency response functions (chart on the left). The chart on the right shows the solution after applying solution vector scaling, which significantly improves convergence. For more details on these techniques and their implementation, please refer to the Ansys-HBM Analysis Guide [10]. Application of the Ansys-HBM to a Benchmark Example In this benchmark example, the Harmonic Balance Method (HBM) is applied to a Brake-Reuss cantilever beam. This structure consists of two beams featuring a frictional contact surface between them, connected by three prestressed bolted joints. A point input force is applied to one beam, while the motion of the corner of the other beam is monitored. Since this example involves a Brake-Reuss cantilever beam, one end of the assembly is fixed. The geometry of the beam in this study is similar to that described in [12]. The specific geometry, boundary conditions, and loads are illustrated in Figure 2. Fig. 2 Geometry, boundary conditions, and load setup for the Brake-Reuss cantilever beam model used in this benchmark example. Figure 3 presents sample results obtained using the Ansys-HBM. The graph displays frequency responses (FRs) acquired near the second nonlinear bending mode of the cantilever beam, computed for various input force magnitudes. Notably, the
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