Nonlinear Dynamics Analysis of Flexible Deployable Linkage Mechanisms Using the Finite Particle Method

Deployable mechanisms have notable applications in mechanical engineering, civil engineering, and space technology. Although often ignored, deployable linkage mechanism exhibits additional flexibility beyond rigid folding owing to the deformation of nonrigid components. The actual behavior of flexible deployable linkage usually involves the dynamic effect and geometric nonlinearity. Using the finite particle method (FPM), this study investigated the nonlinear responses of flexible deployable linkage mechanisms. As a particle method, the FPM is displacement based, explicit, and can avoid iterations to solve nonlinear equilibrium equations. It can be used for nonlinear analyses of structures with rigid body motion and infinitesimal mechanisms, and to determine the internal force and structural deformation. To investigate the nonrigid Bennett linkage and Bricard linkage, formulations of a three-dimensional beam element and revolute hinge element were derived for FPM analysis. Agreement between analytical solutions and numerical simulations demonstrated the efficiency of the proposed approach for nonlinear motion analysis of nonrigid mechanisms. The FPM results revealed that mechanism flexibility can cause deviation from rigid compatibility paths, and the internal force and deformation of mechanisms should be considered when designing nonrigid mechanisms.

Coherent Particle Structures in High-Prandtl-Number Liquid Bridges

Clustering of small rigid spherical particles into particle accumulation structures (PAS) is studied numerically for a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge. The one-way-coupling approach is used for calculation of the particle motion, modeling PAS as an attractor for a single particle. The attractor is created by dissipative forces acting on the particle near the boundary due to the finite size of the particle. These forces can dramatically deflect the particle trajectory from a fluid pathline and transfer it to certain tubular flow structures, called Kolmogorov–Arnold–Moser (KAM) tori, in which the particle is focused and from which it might not escape anymore. The transfer of particles can take place if a KAM torus, which is a property of the flow without particles, enters the narrow boundary layer on the flow boundaries in which the particle experiences extra forces. Since the PAS obtained in this system depends mainly on the finite particle size, it can be classified as a finite-size coherent structure (FSCS).