A numerical study of the dynamics of elastic articulated systems in a fluid

Abstract

We propose a method and an algorithm for computing the dynamics of elastic structures of articulated form in a fluid flow taking account of the weakening in certain structural elements. In describing the motion we use two sets of radius-vectors, which are approximated in the computations by parametric local splines of first degree. The possibilities of the proposed method are illustrated using the example of the study of the dynamics of transition processes m an articulated anchor-buoy structure, which arise when there is an abrupt change in the direction of the fluid flow velocity. We determine the kinematic and force characteristics of the structure under various changes in the direction of the flow velocity. We determine the structural elements in which the weakening occurs. Three figures. Bibliography: 7 titles.For the reliable and stable functioning of articulated systems in a flow and a disturbance, it is necessary to study the nonstationary dynamic behavior of such a system, both the structure as a whole and its individual parts.We consider an articulated system subject to hydrodynamic loads. We introduce a fixed coordinate system Oxtx2x3. We enumerate the joints in series P1-.-, PN, PN+I,.. P2N,---, P(M-1)N''. PMN. We shall assume that at some joints Pl(i) (i = 1, M_h/) there are bodies of compact shape regarded as material points; the dynamic conditions under which the concentrated forces F~(i)~~ = fro (~. k(i)~tj act (i = 1, MN) are -'o ~o (i 1, MN, re(i) prescribed at the joints Pk(0, and the kinematic conditions Rmd ) = Rm(o(t ) at Pro(O, = k(i)). During the motion solid and hydrodynamic surface forces act on the structure. The intensity of these forces depends on the orientation of the flexible elements in the flow, the parameters of the flow, and the parameters of the structure, and can be determined using the quasistationary semiempirical model [1].Any significant change in the shape of the structure during the motion leads to the need for a separate study of its extrinsic and intrinsic geometries using the approaches of Euler and Lagrange respectively to determine them. We shall study the extrinsic geometry in the fixed coordinate system Oxlx2x3 and the intrinsic geometry using the Lagrangian coordinate/--the length of the fiber measured from some fixed point P0 to the variable point P.The motion of the fiber that connects two joints Pi and Pi+l in the same row will be described using the radius-vector and the motion of the fiber connecting P~ and Pi+g will be described using the radius-vectorswhere ~'k are the unit vectors of the fixed coordinate system OXlX2X3; Rki and R~i are functions that express the connection between the length of a fiber and the coordinates of the joints that it connects. To describe the motion of a structural element we shall use a generalization of the principle of virtual work to dynamic problems [2] d OL OL __ _ Qj. dt Oqj OqjHere qj are generalized coordinates; L = K-P is the Lagrangian; and Qj are generalized forces corresponding to concentrated and distributed force...

Dynamics of deformable flexible systems in liquid

“…To analyze the distribution of stresses and strains due to the motion of the body, we will use the virtual-work principle [6,27,62,64]:…”