Analysis of the forced response and radiation of a single-dimpled beam with different boundary conditions

Abstract

Beading and dimpling via the stamping process has been used for decades to stiffen structures (e.g., beams, plates, and shells) against static loads and buckling. Recently, this structural modification technique has been used as a means to shift a structure's natural frequencies and to reduce its radiated sound power. Most studies to date have modeled dimpled beams and dimpled/beaded plates using the finite element method. In this research, an analytical model is developed for a beam with any number of dimples using Hamilton's Principle. First, the natural frequencies and mode shapes are predicted for a dimpled beam in free transverse vibration. A comparison with those obtained using the finite element method shows excellent agreement. Second, the forced response of a dimpled beam is calculated for a given input force. Mode shapes properly scaled from the forced response are used in order to calculate the beam strain energy, thus demonstrating the effect of dimpling on beam natural frequencies. Finally, some preliminary results are presented on the changes in the radiation properties of dimpled beams.