Analytical solution and free vibration analysis for beams with step changes in stiffness

Purpose: This paper aims to investigate analytical solutions of natural frequencies and mode shapes of Euler-Bernoulli beams with step changes in the stiffness. Design/methodology/approach: In this work, analytical solutions for a beam with a single discontinuity was performed. Subsequently, based on an effective matrix formulation, the closed-form expressions of the single discontinuity beam could be conveniently extended to stepped beams with multiple stiffness discontinuities. Findings: The results of the study show that the natural frequency of the beam can be adjusted by the local stiffness variation, and step location plays a significant role in free vibration responses. Originality/value: The effects of the stiffness of the segment and step location on the natural frequencies of the stepped beams under different boundary conditions were examined using the proposed analytical scheme. This study provides insights into the design of variable-stiffness beam structures with the capability to adjust natural frequencies.