Linear vibration measurement and analysis techniques have appeared to be sufficient with most vibration problems. This is partially due to the lack of proper identification of physical nonlinear dynamic responses. Therefore, as an example, a vehicle driveshaft exhibits a nonlinear super harmonic jump due to nonconstant velocity, NCV, joint excitation. Previously documented measurements or analytical predictions of vehicle driveshaft systems do not indicate nonlinear jump as a typical vibration mode. The nonlinear jump was both measured on a driveshaft test rig and simulated with a correlated model reproduced the jump. Subsequent development of the applied moments and simplified equations of motion provided the basis for nonlinear analysis. The nonlinear analyses included bifurcation, Poincare, Lyapunov Exponent, and identification of multiple solutions. Previous analytical models of driveshafts incorporating NCV joints are typically simple lumped parameter models. Complexity of models produce significant processing costs to completing significant analysis, and therefore large DOF systems incorporating significant flexibility are not analyzed. Therefore, a generalized method for creating simplified equations of motion while retaining integrity of the base system was developed. This method includes modal coupling, modal modification, and modal truncation techniques applied with nonlinear constraint conditions. Correlation of resonances and simulation results to operating results were accomplished. Previous NCV joint analyses address only the torsional degree of freedom. Limited background on lateral excitations and vibrations exist, and primarily focus on friction in the NCV joint or significant applied load. Therefore, the secondary moment was developed from the NCV joint excitation for application to the driveshaft system. This derivation provides detailed understanding of the vibration harmonic excitations due to NCV joints operating at misalignment angles. The model provides a basis for completing nonlinear analysis studying the system in more detail. Bifurcation analysis identified ranges of misalignment angles and speeds that produced nonlinear responses. Lyapunov Exponent analysis identified that these ranges were chaotic in nature. In addition, these analyses isolated the nonlinear response to the addition of the ITD nonlinear stiffness. In summary, the system and analysis show how an ITD installed to attenuate unwanted vibrations can cause other objectionable nonlinear response characteristics.

This paper presents the investigation of the nonlinear eigenvalue problem describing free vibrations of plates with elastically attached masses. We study properties of eigenvalues and eigenfunctions and prove the existence theorem. Theoretical results are illustrated by numerical experiments.

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