Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

Rational ANCF Thin Plate Finite Element

Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

In this paper, the nonlinear oscillations of a composite laminated circular cylindrical shell clamped along a generatrix and with the radial pre-stretched membranes at both ends are studied for the first time. The dynamic effect of membranes on the circular cylindrical shell is replaced by a nonlinear elastic excitation with the damping. Meanwhile, the parametric excitation of the changing temperature is also considered. Based on Reddy’s third-order shear deformation theory and von Karman-type nonlinear kinematics, the nonlinear partial differential equations of motion for the composite laminated circular cylindrical shell clamped along a generatrix are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The asymptotic perturbation method is applied to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Corresponding to several selected values of the parameters, the frequency–response curves are obtained by numerical method. It is found that the static bifurcations, the jump phenomena as well as the hardening-spring-type nonlinearity behaviors are exhibited and that different parameters change the frequency–response curve shape. The numerical results based on the averaged equations are obtained to exhibit some intrinsically nonlinear dynamic behaviors of the composite laminated circular cylindrical shell clamped along a generatrix using the bifurcation diagram, waveform, phase plots and Poincare maps. It is also found that there exist alternately the periodic and chaotic motions of the circular cylindrical shell clamped along a generatrix with the parameter excitation of temperature increases in a certain range.

Nonlinear dynamics of composite laminated circular cylindrical shell clamped along a generatrix and with membranes at both ends

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation

Mesh reflectors with large apertures have been used in many communication satellites. The performance of antenna reflectors crucially depends on the faceting error of the reflective surface, which is approximated by using meshes. The force density method (FDM) has been widely used for the form-finding analysis of mesh reflectors. However, after performing form-finding of some meshes, the effective reflective area will decrease. In addition, the form-finding of the auxiliary mesh has received little attention, and it cannot be achieved by using the FDM. Thus, in this study, an effective form-finding methodology that combines the iterative FDM and the minimum norm method (MNM) is proposed. To consider the flexibility of the reflector ring truss, a static analysis of the ring truss under the tension force actions is also performed in the form-finding processes. The reflector flexible parts are described by the absolute nodal coordinate formulation (ANCF). Finally, the form-finding analysis of the reflector with the standard configuration, the central hub configuration, and the circular configuration is performed to validate the proposed methodology. The influence of the mesh tension force on the reflector natural frequencies is also studied. After performing the form-finding analysis, the initial configuration of the reflector with tensioned meshes for the deployment dynamics study can be determined. Based on this paper, the deployment dynamics of a complex AstroMesh reflector will be studied in a successive paper “Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation.”

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis

In recent years, the space community has paid much attention to the development of the hoop truss antenna of satellite so as to improve the quality of telecommunication of high frequency. The antenna reflector is mainly composed of a mesh net and a deployable ring truss, which can be considered as a rigid-flexible multibody system. During the research process of the hoop truss antenna of satellite, an accurate and effective dynamics model has to be built. In order to describe the flexible components in this system accurately, the Absolute-Coordinate-Based (ACB) method combining the Absolute Nodal Coordinate Formulation (ANCF) and Natural Coordinate Formulation (NCF) is used to predict the deployment dynamics of the reflector antenna. Furthermore, the parallel computation methodology based on the multilevel decomposition method and the Schur Complement method is used to improve the computational efficiency. Using the parallel computation methodology, the dynamic simulation of a rigid-flexible multibody system is efficiently completed based on the Message Passing Interface. To analyze the asynchronous deployment phenomenon in the ground test, the decrease of the driving force is applied to the antenna reflector model. Finally, based on the above method, a computational program is developed via the Fortran language to analyze the deployment dynamics of the hoop truss mesh antennas. Using the program, the second phase of the deployment process of the hoop truss mesh antennas is simulated, and the computational results are verified by a deployment experiment on the 4 m aperture antenna reflector.

Deployment dynamics simulation and ground test of a large space hoop truss antenna reflector

The pillow effect is a key weakening factor in the surface accuracy of mesh antennas. Previous studies, however, have significant limitations in such antennas because they have been largely based on specific assumptions, which have failed to investigate the effects of mesh membrane material characteristics on the pillow effect. Thus, in this study, static analysis of a triangular membrane was performed using the weak form quadrature element method to explore the effects of material parameters in various directions on the pillow effect in polar coordinates. Because of its lack of central symmetry, the strain–displacement relations from Föppl–von Kármán membrane theory in polar coordinates were improved for calculations in triangular membranes. In polar coordinates, the triangular membrane domain was mapped into one sector for the discretion of integrals using bilinear interpolation. The convergence of the method results was examined, and the accuracy was demonstrated by comparing the computed deflections to those from the finite element method. Based on the present method, the effects of material properties on the pillow effect in different sections of a triangular membrane were examined, as was the influence of the shape of an isosceles triangle.

Analysis of pillow effect for isosceles triangular membranes of mesh reflector antenna by the weak form quadrature element method

Negative Gaussian curvature in deformed surface subjected to concentrated loads is a key weakening factor on the surface accuracy of umbrella antennas. The negative impacts can be mitigated by increasing the bending rigidity of the reflector surface. Thus, firstly, this paper is concerned with the effect of bending rigidity on Gaussian curvature based on the analysis of bending circular thin plate with large deflection. Exact expressions of Gaussian curvature for deformed circular thin plates are derived using the analytical solution of the von-Karman plate equation and the properties of positive and negative for Gaussian curvature is investigated. After solving the zeroes of Gaussian curvature using the Newton iteration method, Gaussian curvature distribution of the deformed surface is obtained.

https://iopscience.iop.org/article/10.1088/1742-6596/2338/1/012015/pdf

Yanping Song

Papers

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation

Deployment dynamics simulation and ground test of a large space hoop truss antenna reflector

Analysis of pillow effect for isosceles triangular membranes of mesh reflector antenna by the weak form quadrature element method

Analysis of the effect of bending rigidity on Gaussian Curvature for clamped and simply supported thin circular plates