Dynamic behavior of pin-free beam with torsional spring and hub at pinned end

This paper described the free vibration of a Euler-Bernoulli beam and discovered the first five dimensionless natural frequencies and mode shapes of motion for the pin-free beam model with a helical spring and rotating mass on the pinned side of the beam. The effect of changing the dimensionless torsional stiffness ratios was investigated, as was the effect of changing the dimensionless rotational inertia torque ratios Concerning the vibration properties of the beam. The mathematical equations that regulate the pin-free beam model were constructed using the exact analytical solution, establishing the Admissible Function and the natural frequency equation for the basic pin-free beam system. The approximate Rayleigh-Ritz approach was then used to determine the first five dimensionless natural frequencies, as well as the movement pattern for the pin-free beam model with a helical spring and a rotating mass on the side of the hinge. The results demonstrated that modifying the beam's natural frequencies is dependent on the ratios of the additional torsional spring parameters as well as the ratios rotational moment of inertia. The threshold system frequencies increase when the spring parameters are the major factor, and decrease when the inertia moment parameters are the main factor. Both play a role in influencing natural frequency to varied degrees. Unifying the final distribution of parameters might lead to optimizing the impact of parameters on the natural frequencies of the system.