Session: VIB-08-01: Nonlinear Systems & Phenomena

Paper Number: 90221

90221 - Wave-Based Approaches for the Nonlinear Forced Response and Stability Analysis of Jointed 1d Structures 

This contribution presents two nonlinear wave-based approaches for the predictions of the forced responses of jointed 1D structures. The first approach is based on regular perturbations, and develops nonlinear scattering relationships of joints in a 1D model. These relationships are developed as a wave-based description of a discrete nonlinear connection in a continuous domain. The second approach is a multi-harmonic plane wave expansion technique that employs an Alternating Fourier-Time (AFT) domain approach to solve the governing equations of a wave-based model. Results are presented for systems consisting of 1D rods connected through nonlinear joints. The paper also develops two approaches based on Floquet theory for characterizing the stability of the solutions obtained from the above. The first one is a perturbation approach that develops a strained parameter formulation to obtain stability boundaries of the self-excited perturbed problem in terms of the solution amplitude. Qualitative analysis of stability is carried out by checking which region the perturbed system's parameters lie in the parameter space. The second approach proposes a novel approach based on properties of the residue of the perturbed system's eigenproblem. Specifically, it is shown that the sign of this residue switches across stability transition points, which can be used to evaluate stability after response computation has been carried out. All the results are compared against discretized finite element models for the illustrations.

Presenting Author: Nidish Narayanaa Balaji Rice University

Presenting Author Biography: Currently a Postdoctoral researcher at Rice university under Dr. Matthew Brake working in the area of nonlinear structural dynamics. <br/>Educational Background: PhD (Advisor: Dr. Matthew Brake) at Rice in 2021; MS, Rice University, 2019; BTech IIST, India, 2017

Authors:

Nidish Narayanaa Balaji Rice University
Matthew Rw Brake Rice University
Michael J Leamy Georgia Institute of Technology