Research and experimental verification of transverse vibration response characteristics of an axially compressed cantilever beam with concentrated mass at free end

Since cantilever beams have excellent stiffness characteristics and simple structure, they are widely used in civil engineering, construction, and machinery production. However, few studies focus on the influence of complex boundary and external load on the cantilever beams. To reveal the transverse vibration response mechanism of an axially compressed cantilever beam with concentrated mass at free end (CBCMFE), the theoretical analytical model of the vibration modal of the CBCMFE and axial load is firstly established, and the effects of critical parameters on the vibration modal are investigated. Secondly, the vibration response of an axially compressed CBCMFE under simple harmonic centralized force excitations is derived through the mode superposition methods. In addition, the vibration response of the cantilever beam under periodic concentrated force excitation is deduced using Fourier expansion. Finally, a cantilever beam with a concentrated mass vibration test platform is constructed, and the vibration response under concentrated force excitation is experimentally investigated under axial compression. The experimental results proved the correctness of the theoretical analysis.