Vibrations + Contact = Quadratic Nonlinearity

Hello,

Studies of the vibration of a rod in contact with a surface are central to a range of applications from MEMS devices to flexible ocean risers. In our latest paper,

Nate N. Goldberg and Oliver M. O'Reilly Pervasive nonlinear vibrations due to rod-obstacle contact, Nonlinear Dynamics, 2021

we show how such contact inevitably induces a quadratic nonlinearity in the response of the rod. This nonlinearity is pervasive and can be directly attributed to the contact of the rod and the substrate. In the absence of a variable point of contact, the nonlinearity can be eliminated.

A freely accessible copy of the paper can be accessed here: https://rdcu.be/ce3KO

A graphical summary of the paper can be found here:

https://twitter.com/UCBDynamicsLab/status/1360066255214891011?s=20

Our work builds on the following papers

• Goldberg, N.N., O’Reilly, O.M.: On contact point motion in the vibration analysis of elastic rods. Journal of Sound and Vibration 487, 115579 (2020).
• Roy, A., Chatterjee, A.: Vibrations of a beam in variable contact with a flat surface. Journal of Vibrations and Acoustics 131(4), 041010 (2009). 
• Turnbull, P., Perkins, N., Schultz, W.: Contact-induced nonlinearity in oscillating belts and webs. Journal of Vibration and Control 1(4), 459–479 (1995).
• Majidi, C., O’Reilly, O.M., Williams, J.A.: On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling. Journal of Mechanics and Physics of Solids 60(5), 827–843 (2012).

Thanking you in advance for your interest in our work,

Sincerely,

Oliver O'Reilly