A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

Abstract

There are vast constraint equations in conventional dynamics analysis of deployable structures, which lead to differential-algebraic equations (DAEs) solved hard. To reduce the difficulty of solving and the amount of equations, a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements (SLEs) is presented. Firstly, a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation (ANCF), and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations. Secondly, according to features of deployable structures, the specification matrix method (SMM) is proposed to eliminate the constraint equations among SLEs in the frame of ANCF. With this method, the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently, especially on condition that there are vast nodal coordinates. So the element characteristic matrices can be added end to end circularly. Thus, the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation. Next, a new iteration procedure for the generalized-α algorithm is presented to solve the ordinary differential equations (ODEs) of deployable structure. Finally, the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements. The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure. The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

A Kind of Actuator for Shaft Torsional Vibration Active Control

“…These dynamic torques can be classified as the generalized rotational force of rigid body rotation (𝐐 e ) θ , and also the elastic generalized force (𝐐 e ) f or 𝐐 m . Equations (10) to (14) show that through the coupling effect between different coordinates in the mass matrix 𝐌 i and the elastic stiffness matrix 𝐊 i , the dynamic torques can cause vibration in translational directions, and at the same time, the vibration is transmitted to different parts of the shafting by way of the constraints between bodies.…”

“…The active control torque provided by a dynamic torque actuator can be arranged at the position where the influence of torque fluctuation has to be offset. Correspondingly this control torque is added into 𝐐 e and/or 𝐐 m in Equation ( 11) or (14). This can not only directly reduce the torsional vibration, but also effectively reduce the vibration in other directions with the help of the coupling effect.…”

“…So the element of 𝐀 i can be expressed as the function of elements of 𝛉 i . If the body is taken as an elastic one, the finite element mesh is divided for the purpose of analyzing the elastic deformation of body [14]. The body coordinate vector of any point P in the j th finite element of body i can be expressed as [13:275]…”

Design of Deployable Structures by Using Bistable Compliant Mechanisms

“…The first category is scissor-like deployable structures. The deployable structures, comprised of scissor-like elements (SLEs), are widely applied because of their high loading capacity and excellent equilibrium stability [ 8 , 9 , 10 ]. The second type of deployable structure is the tensegrity structure, where tensional and compressional members co-exist.…”

Geometric Constraints and Dynamic Behavior of a Deployable Footbridge

“…Responses of footbridges are calculated using a simple formula based on the dynamic loading due to one person, the response of a simple span at resonance, and limited duration of excitation. Tuned mass dampers can help reduce the resonant vibrations of the spans [16]. This study aims at predicting the dynamic properties of the structure during the conceptual design phase to enhance its safety.…”