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Moment of Inertia of Area
Published in M. Rashad Islam, Md Abdullah Al Faruque, Bahar Zoghi, Sylvester A. Kalevela, Engineering Statics, 2020
M. Rashad Islam, Md Abdullah Al Faruque, Bahar Zoghi, Sylvester A. Kalevela
For a rotating member, such as a shaft of motor, the polar moment of inertia is required to analyze the adequacy of the member. The polar moment of inertia (J) is the summation of the moment of inertia about two perpendicular axes passing through the centroid. It can be written as: J=I¯x+I¯y
Analytical solution for sheet-pile groin vibrations under tidal bore excitation
Published in Marine Georesources & Geotechnology, 2023
Tao Wu, Honglei Sun, Rubén Galindo Aires, Yuanqiang Cai, Juntao Wu, Yunpeng Zhang
Considering the flexural inertia effect of the sheet, it is simplified as a TB for which the governing equations for vertical vibration can be described as follows: where and are the polar moment of inertia and the shear modulus of the sheet, respectively; and are the vertical deflection and the bending rotation angle of the sheet, respectively. is the shear coefficient of the sheet with a rectangular cross section, and herein, (Rosinger and Ritchie 1977); and in which is the rotational damping coefficient (Doshi 1979).
Free vibration of a nanogrid based on Eringen’s stress gradient model
Published in Mechanics Based Design of Structures and Machines, 2022
Seyed Mojtaba Hozhabrossadati, Noël Challamel, Mohammad Rezaiee-Pajand, Ahmad Aftabi Sani
The nonlocal constitutive relation for shear stress in one-dimensional form can be expressed as (Murmu, Adhikari, and Wang 2011): where and denote the shear stress, shear strain, and shear modulus, respectively. Furthermore, the nonlocal torque relation with angular displacement has the next appearance in which and are the torque, angular displacement, and polar moment of inertia of the cross-section, respectively.
Motion modeling of cable-driven continuum robots using vector form intrinsic finite element method
Published in Journal of the Chinese Institute of Engineers, 2022
Mien-Li Wang, I-Hsuan Kuo, Jyh-Jone Lee
where Ea is Young’s modulus, Ga is the shear modulus, Aa is the area of the cross-section, and are the area moments of inertia, and is the polar moment of inertia. The remaining increments of force/moment components can be obtained via static equilibrium of the element as