An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures

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The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems (2014, unknown): “, [11, 12]) and to the development of a continuation package manlab[13, 14].”
Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems (2017, background): “[10–13] and many improvements have been proposed, such as adaptive schemes that improve the performance by selecting only the harmonics of interest [14, 15] as well as methods to handle systems with many distinct states [16] and strong or non-smooth nonlinearities [17, 18].”
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems (2015, methodology): “sin ( NH ωt ν ) cos ( NH ωt ν ) ] (8) Velocities and accelerations can also be defined using the Fourier series [18], with ẋ(t) = ( Q̇(t) ⊗ In ) z = ((Q(t)∇) ⊗ In) z (9) ẍ(t) = ( Q̈(t) ⊗ In ) z = (( Q(t)∇(2) ) ⊗ In )”
A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes (2018, background): “Recent studies on the use of HBM for MDOF nonlinear systems in different areas include the application for joints [23, 24], rotor/stator contacts [25], bladed disks [26], geometrically nonlinear beams [27] and plates [28].”