Corrigendum to “Vibration attenuation in wind turbines: A proposed robust pendulum pounding TMD” [Eng. Struct. 233 (2021) 111891] (Engineering Structures (2021) 233, (S0141029621000419), (10.1016/j.engstruct.2021.111891))
Document Type
Article
Publication Date
10-15-2021
Abstract
The authors regret that an earlier version of this paper had typos. In fact, the typos did not impact the simulation results or the scientific conclusions of the article in any way. The manuscript is updated, and the typos are corrected here. The authors would like to apologize for any inconvenience caused. The total kinetic energy is [Formula Presented] where [Formula Presented] is the moment of inertia of the pendulum PTMD about the center of mass. From Eq. (4) into Eq. (5), one obtains, [Formula Presented] The total potential energy is [Formula Presented] The Lagrangian of the system is written as [Formula Presented] The Lagrangian equation can be written as, [Formula Presented] One should pay attention to that the external excitation force, damping forces, and pounding force are non-conservative. These forces enter the Lagrangian formulation as a generalized force. Thus, the work done by the non-conservative force is given as [Formula Presented] Now we get [Formula Presented] Using Eqs. (8)–(12), one can obtain [Formula Presented] where [Formula Presented] is the mass, [Formula Presented] is the stiffness, and [Formula Presented] is the coefficient of damping of the primary structure. Similarly, [Formula Presented] and l are the mass and the distance from the center of mass of the pendulum to the hinge joint, g = 9.8 m/s2 is the acceleration due to gravity, F is the external force from excitation, and P is the pounding force. For the civil and energy infrastructure equipped with pendulum PTMD, the angle of rotation would be very small. Thus, Eqs. (13) and (14) can be simplified as follows. [Formula Presented] here, [Formula Presented] is the mass moment of inertia of the pounding mass about the hinge joint. Using the parallel axis theorem, it can be expressed as [Formula Presented] The equation becomes [Formula Presented], if the lumped mass is considered.
Publication Source (Journal or Book title)
Engineering Structures
Recommended Citation
Chapain, S., & Aly, A. (2021). Corrigendum to “Vibration attenuation in wind turbines: A proposed robust pendulum pounding TMD” [Eng. Struct. 233 (2021) 111891] (Engineering Structures (2021) 233, (S0141029621000419), (10.1016/j.engstruct.2021.111891)). Engineering Structures, 245 https://doi.org/10.1016/j.engstruct.2021.112889