The school is investigating Meyer over what he did and didn't know about the alleged serial abuse committed by Smith against his ex-wife Courtney Smith.
Davidson has been appointed the chair, while Mary Jo White, former chair of the U.S. Securities and Exchange Commission, will lead the investigative team.
Any decisions resulting from the investigation will be made by Ohio State President Michael Drake in consultation with university trustees, the statement said.
Meyer's knowledge of the incidents came into question after college football insider Brett McMurphy reported that Smith had told Meyer's wife Shelley about the 2015 incidents and shared pictures of the injuries and text messages that she shared with McMurphy.
The petition was designated to Ohio State athletic director Gene Smith.
According to Hamms' post, the objective of the event is "to show our positive support for Ohio State Football players, coaches, Urban Meyer and their families".
A clause in Meyer's new contract, which raised his salary to $7.6 million this year and runs through 2022, also requires him to "report to Ohio State's Title IX athletics any known violations" of the sexual misconduct policy involving students, faculty or staff at the risk of being fired with cause.
Smith was sacked in July after his ex-wife obtained a protective order against him in court, and after veteran college sports reporter Brett McMurphy published reports to Facebook on the 2015 incidents, in addition to one from 2009 in which Smith was arrested for assaulting her while she was pregnant.
Meyer has gone 73-8 in six seasons at Ohio State, including a national championship in 2014 and two Big Ten titles after winning a pair of national titles at Florida.
Addazio hired Smith when he was the head coach of the Owls in 2011.