Vibration Suppression of a Harmonically Forced Oscillator Using a Passive Nonlinear Vibration Absorber

In this paper, the performance of a nonlinear vibration absorber with different nonlinearity is studied. The analytical solutions of periodic motions are obtained using the general harmonic balance method. As the nonlinear strength is weak, the effectiveness of the absorber is discussed. For strong nonlinearities, unstable parodic motions can be obtained and stabilities of the periodic motions are determined through the eigenvalue analysis. The Hopf and saddle bifurcations are observed. Numerical simulations are illustrated for both masses at the resonance peaks. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions.

The Influence of Additively Manufactured Nonlinearities on the Dynamic Response of Assembled Structures

Structural dynamic techniques have been proven accurate at predicting the vibrations of single parts (i.e., monolithic specimens), which are widely used in industrial applications. However, vibration analysis of such assemblies often exhibits high variability or nonrepeatability due to jointed interfaces. Inspired by advances in additive manufacturing (AM) and nonlinear vibration absorber theory, this research seeks to redesign jointed structures in an attempt to reduce the nonlinear effects introduced by the jointed interfaces. First, the nonlinear dynamics of a conventionally manufactured beam and an AM beam are measured in both a traditional (flat) lap joint assembly and also a “linearized” lap joint configuration (termed the small pad). Second, the internal structure of the AM beam is varied by printing specimens with internal vibration absorbers. With the two interface geometries studied in this experiment, the flat interface is found to be predominantly nonlinear, and introducing a vibration absorber fails to reduce the nonlinearities from the jointed interface. The small-pad responses are relatively linear in the range of excitation used in the analysis, and the nonlinear effects are further reduced with the presence of a center vibration absorber. Overall, the energy dissipation at the interface is highly dependent on the design of the contact interface and the internal vibration absorber. Adding a nonlinear vibration absorber alone is insufficient to negate the interfacial nonlinearity from the assembly; therefore, future work is needed to study the shape, location, and material for the design and fabrication of nonlinear vibration absorbers.