Two-substructure, time-domain transfer path analysis of transient dynamic response of mechanical systems with nonlinear coupling.

Abstract

The traditional frequency domain transfer path analysis has become a popular method to detect and diagnose vehicle NVH problems. Unfortunately, due to its reliance on frequency transfer functions, the approach is strictly effective only for linear time-invariant system and steady-state response. This limitation prevents the method from being applied to transient and/or nonlinear behavior such as clunk, shudder, and tip-in and tip-out. In this paper, a novel time domain transfer path analysis is proposed to deal with a class of non-linear transient response problems. It combines the versatility of the transfer path analysis for tracking transmission of vibratory energy between substructures and generality of the time domain analysis for treating transient response that is also nonlinear in nature. The formulation that is derived by combining the spectral-based substructure method and a discrete, piecewise convolution theory is applied to a lumped parameter system, and the results are compared with output from a direct numerical integration of the nonlinear equations of motion. Comparison results show significant promise and appear to be usable for solving real-life vehicle problems that are highly transient with moderate level of nonlinearity present.

Time‐Domain Substructure Transient Vibration Transfer Path Analysis Based on Time‐Varying Frequency Response Functions under Operational Excitations

“…Applying the theory of superposition, an excitation input of the form f(t)δ(t − τ) dτ will yield the corresponding response given by f(t) h(t − τ)dτ. Finally, if f(t)δ(t − τ)dτ is equal to f(t), whose corresponding output is X(t) as noted above, then f(t) h(t − τ)dτ is equal to X(t), which is the fundamental basis for the convolution integration applied in this study [31][32][33]. We considered the example discussed in the introduction as the analysis object to obtain the following equation:…”

“…In the 2010s, a time-domain substructure transient vibration TPA method was studied by several researchers. e objectives of these studies were to expand applications of the spectral-based substructure method used under steady-state conditions to address the transient problems of a mechanical system with weak nonlinear coupling [31][32][33]. Time-domain convolution was used as the main theory to discretize input signals into time segments.…”