Effect of interfacial surface roughness condition on damping of riveted cantilever beams
Authors: Yemineni Siva Sankara Rao , Kutchibotla Mallikarjuna Rao , V.V. Subba Rao 
Published: August 2023

Purpose
This paper aims to analyze deeply the effect of surface roughness conditions of the common interface of the two-layered riveted cantilever beams on their frictional damping during free lateral vibration at first mode. Here, the product, (µ × α), and damping ratio, ξ, are the parameters whose variations are analyzed in this investigation. For this, the influencing parameters considered are the natural frequency of vibration, f; the amplitude of initial excitation, y; and surface roughness value, Ra.

Design/methodology/approach
For experimentally evaluating logarithmic damping decrement, d, the frequency response function analyzer for the case of free lateral vibrations was used. Later, for evaluating the product, µ × α (where µ is the kinematic coefficient of friction and α is the dynamic slip ratio), and then, the damping ratio, ξ, the empirical relation suggested for logarithmic damping decrement, d, of riveted cantilever beams was used. After this, the full and reduced quadratic models of the product, µ × α, ξ, response surface methodology (RSM) with the help of Design Expert 11 software was used. Corresponding main effects plots, surface plots and prediction comparison plots were obtained to observe the variations of the product, µ × α, ξ for the variations of influencing parameters: f, y and Ra. Finally, a machine learning technique such as artificial neural networks (ANNs) using “nntool” present in MATLAB R13a software was used to predict the ξ for the different combinations of f, y and Ra.

Findings
The full and reduced quadratic regression models for the product, (µ × α) and the damping ratio, ξ of riveted cantilever beams for free lateral vibrations of the first mode in terms of the parameters: f, y and Ra were obtained. In addition, the main effects plots, surface plots and prediction comparison plots for the product, µ × α, ξ, with the corresponding experimental values of the product, µ × α, ξ, were obtained. Also, the execution of ANNs using MATLAB R13a software is proved to be the more accurate tool for the prediction of damping ratios in comparison to quadratic regression equations obtained from Design Expert 11 software. In the end, the assumption that the effect of surface roughness value on the product, (µ × α), and the damping ratio, ξ, is negligible is proved to be true using the main effects plots for the product, (µ × α) and ξ obtained from the Design Expert 11 software.

Originality/value
Obtaining the full and reduced quadratic regression equations for the product, (µ × α), and ξ of the two-layered riveted cantilever beams in terms of parameters: f, y and Ra was done. In addition, the conditions for the corresponding minimum and maximum values of the product, (µ × α), and ξ were obtained. Later, the main effects plots, surface plots and comparison plots of the predicted product, (µ × α), and ξ versus experimental product, (µ × α), and ξ were also obtained. Finally, the predicted values of the product, (µ × α), and ξ using the ANNs tool are observed to be the more accurate values in comparison to that obtained from RSM using the Design Expert 11 software.