Dynamic response of a space flexible arm with a moving mass

Abstract

The dynamic characteristic of a space rotating flexible arm with moving mass were investigated. The space arm with moving mass can rotate around the fixed end in horizontal and vertical planes simultaneously. And the lateral deflections of the arm in the two planes were considered. The equations of the structure were derived by the Lagrange’s equation with the assumed mode method. And a system of binary second order linear differential equations is gotten. Based on the central difference method, a conditionally stable algorithm for solving the equations is established. Due to the coupling of lateral displacements of the arm in horizontal and vertical planes, the increase of the angular velocity in one plane will increase the lateral displacements in the other plane. When the angle between the arm and the horizontal plane increases, the component of gravity along the normal direction of the beam will decrease, resulting in a decrease in lateral displacements in vertical plane, however, it will lead to a decrease in stiffness in horizontal plane and thus an increase in lateral displacements. Compared with moving mass, moving load ignores the influence of inertial force, so the calculation results of moving mass and moving load are different. The conclusions provide calculation basis for the design of similar structures.

Optimal Cluster Scheduling of Active–Reactive Power for Distribution Network Considering Aggregated Flexibility of Heterogeneous Building-Integrated DERs

“…Integration and quantification for the regulation capacity of flexible resources are regarded as effective means to take advantage of the flexibility of smart-building systems [4,[14][15][16][17][18]. Several important investigations have been reported on the virtual battery model [14], virtual synchronous machine model [15], flexible supply-and-demand balance model [16], and node power model [17] for the aggregation of flexible resources. A generic and scalable approach considering zonotopic sets for flexible energy systems was studied in [18] to describe their flexibility quantitatively.…”

Optimal Cluster Scheduling of Active/Reactive Power for Distribution Network Considering Aggerated Flexibility of Heterogeneous Building-Integrated DERs

“…Integration and quantification for the regulation capacity of flexible resources is regarded as an effective means to take advantage of the flexibility of the smart building system [4,[11][12][13][14][15]. Lots of inspiring works have been reported on the virtual battery model [11], virtual synchronous machine model [12], flexible supply and demand balance model [13], and node power model [14] for the aggregation of flexible resources. A generic and scalable approach considering zonotopic sets for flexible energy systems is studied in [15] to quantitatively describe their flexibility.…”