Research on Nonlinear Vibration Control of a Slender Beam with Twin-Source Excitation and Spatially Distributed Nonlinear Energy Sinks Simultaneously

Slender beam structures, as core load-bearing components in fields such as aerospace, civil engineering, architecture, and mechanical equipment, have vibration characteristics that directly impact the system's dynamic performance, operational safety, and service life. To control vibrations in slender beam structures, scholars have designed nonlinear vibration absorption devices. The aforementioned studies primarily discuss the vibration control potential of single or double NESs on slender beam structures subjected to harmonic excitation. However, in practical engineering applications, slender beams are often exposed to multiple vibrational excitations. Moreover, these structures typically provide sufficient installation space, allowing for the implementation of multiple NESs. Motivated by these engineering backgrounds and the limitations of existing research, this work proposes a slender beam with twin-source excitation and spatially distributed NESs simultaneously. The governing formula of the slender beam with twin-source excitation and spatially distributed NESs simultaneously is derived and solved. Based on the correct numerical results, the influence of core parameters of NESs, the phase difference of external excitation, and the spatial distribution of NESs on the vibration response of slender beam structures is discussed. The spatially distributed NESs can effectively suppress the peak vibration response of the slender beam structure. Secondly, the differences can be observed in the vibration displacement response of the slender beam structure with spatially distributed NESs under different phase differences. Regardless of the phase difference, the spatially distributed NESs consistently demonstrate effective vibration suppression in the slender beam structure. The appropriate selection of positions for spatially distributed NESs can enhance their vibration control effect on the slender beam structure. Overall, rational use of spatially distributed NESs can suppress vibrations in slender beam structures subjected to multiple excitations.