Continuum Modeling of a Slewing ISAT (Innovative Space Antenna Technology)

2005 ◽  
Author(s):  
Armaghan Salehian ◽  
Eugene M. Cliff ◽  
Daniel J. Inman
Keyword(s):  
Continuum Model ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Space Antenna ◽  
Geometrical Properties ◽  
Strain Components ◽  
Equivalent Continuum Model ◽  
Equivalent Continuum ◽  
Very High ◽  
The Continuum

A simple approach is presented herein for obtaining the equivalent continuum model of an ISAT (Innovative Space Antenna Technology) truss structure in order to find the free vibration solutions for different coordinates of vibration. Kinetic and potential energy expressions are written in terms of the strain components of the elements and the nodal velocities. The Lagrangian approach is employed to find the governing partial differential equations of the structure which for the bending degrees of freedom lead to an equivalent Timoshenko beam. Finally, the physical characteristics of the continuum model are written in terms of the material and geometrical properties of the truss, which provide a simple tool for comparing dynamic characteristics of lattices with different properties. The natural frequencies are found for each of the bending, longitudinal, and torsional coordinates of vibration and are compared to those of a FEM solution for the purpose of validation. The analytical model shows very high accuracy in prediction of the natural frequencies of the original truss.

Vibration Modelling of String-Harnessed Beam Structures Using Homogenization Techniques

2014 ◽  
Author(s):  
Blake Martin ◽  
Armaghan Salehian
Keyword(s):  
Continuum Model ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Strain Tensor ◽  
Space Structures ◽  
Power Cables ◽  
Structural Elements ◽  
Equivalent Continuum Model ◽  
Lagrange Strain ◽  
Equivalent Continuum

Harnessing structural elements with strings, power cables, and signal cables increases the complexity in modelling the dynamic behaviour of such structures. Developing models capable of accurately predicting the dynamic behaviour of these systems is of great importance for space structures that cannot be tested prior to launch. The focus of this work is obtaining an equivalent continuum model for string-harnessed beam-like structures with periodic wrapping patterns. The tension in the string is assumed to vary as the beam deflects. The displacement field with second-order terms is determined and from which the Green-Lagrange strain tensor is obtained. After finding kinetic and potential energy expressions Hamilton’s principle is used to obtain the partial differential equation and boundary conditions. Numerical results for the shift in the natural frequencies are presented for various string properties to investigate their effects on the structure.

A Comparison of Continuum and Lumped-Mass Models for Hyper-Redundant Manipulator Mechanics

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Continuum Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Lumped Mass ◽  
Mass Model ◽  
Joint Torques ◽  
Lumped Mass Model ◽  
The Continuum

Abstract The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.

Dynamic Analysis and Experiment of Beamlike Space Deployable Lattice Truss

2011 ◽  
Vol 199-200 ◽  
pp. 1273-1280
Author(s):  
Hong Wei Guo ◽  
Rong Qiang Liu ◽  
Zong Quan Deng
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Continuum Model ◽  
Model Simulation ◽  
Element Model ◽  
Mode Shapes ◽  
Equivalent Continuum Model ◽  
Simulation Results ◽  
Equivalent Continuum ◽  
The Finite Element Model

The dynamic equivalent continuum model of beamlike space deployable lattice truss which is repetition of the basic truss bay is established based on the energy equivalence. The finite element model of the lattice truss is also developed. Free vibration frequencies and mode shapes are calculated and simulated based on equivalent continuum model and discrete finite element model. The analytical solutions calculated by equivalent continuum model match well with the finite element model simulation results. A prototype of deployable lattice truss consist of 20 truss bays is manufactured. The dynamic response of lattice truss with different truss bays are tested by dynamic vibration experiment, and natural frequencies of lattice truss with different length are obtained from acceleration response curves. The experiment results are compared with simulation results which verifies that the correctness of finite element model, which also validate the effectiveness of equivalent continuum model indirectly.

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