An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a traveling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T.R. Lin, J. Pan, A closed form solution for the dynamic response of finite ribbed plates, Journal of the Acoustical Society of America 119 (2006) 917–925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.

► An analytical solution is presented for the vibration response of a clamped ribbed plate. ► Vibration characteristics of the clamped ribbed plate were studied experimentally. ► Both free and forced vibration responses of the clamped ribbed plate were investigated. ► Mechanisms causing discrepancies between computation and experimental results were discussed.