On the representation of a cantilevered beam carrying a tip mass by an equivalent spring–mass system

Vibration of a Rayleigh cantilever beam with axial force and tip mass

“…obtained previously, but only numerical results were given (see e.g. [1,9]). If considering the tip mass, axial force and rotatory inertia simultaneously, it is still capable of giving a formula for approximately determining the fundamental frequencies, and its expression is omitted here due to its complicated form.…”

“…For a cantilever beam carrying a tip mass, Fung et al [7] developed an electromagnetic actuator and analyzed its dynamic behavior. For a simple cantilever beam with a tip mass, Gurgoze [9] proposed an equivalent spring-mass system to solve it. De Rosa et al [8] analyzed free vibration of elastically restrained and tapered cantilever beams with concentrated viscous damping end mass.…”

Load case reduction for offshore wind turbine support structure fatigue assessment by importance sampling with two‐stage filtering

“…Note that the constant factor in front of m t is derived under specific assumptions and will in general depend on structural properties. However, this dependence is small enough that it can be neglected for the present purpose. If the dimensions of the support structure (meaning its element diameters and thicknesses) are scaled uniformly by a factor s , then the stiffness and mass will also be scaled.…”

“…Because the optimization itself is often time consuming, it has been a common practice to ignore the wider set of load cases when investigating optimization algorithms for support structure design, using only a few load cases for testing purposes. 23 Clearly, the presented method allows for approaches that use a small number of load cases without incurring high errors in the resulting fatigue estimates. While significant outliers were observed for large systematic design changes because of shifting eigenfrequencies, in the context of optimization, such situations could be avoided by enforcing eigenfrequency constraints.…”

Frequency Equation of Flexural Vibrating Cantilever Beam Considering the Rotary Inertial Moment of an Attached Mass

“…Laura [11] derived the frequency equation of a cantilever beam attaching an additional mass, which is considered as shear force acted on the free end of beam but did not consider the moment force generated by the mass. And recently, Gürgöze [12][13][14] studies the eigenfrequencies of a cantilever beam carrying a tip mass or spring-mass.…”