Natural Frequency Validation of a Homogenized Model of a Truss (original) (raw)
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Meccanica, 1990
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Continuum modeling of beamlike lattice trusses using averaging methods
Computers & Structures, 1999
A general procedure to determine the equivalent beam properties of beam-like lattice trusses is presented. The method is based on the energy equivalence. Its main features are the use of piecewise linear functions to represent the displacements, and the de®nition of the continuum stress and strain parameters by their average values over the continuum cell. This allows a unifying approach to be obtained to derive methods for computing the eective beam properties. It is shown that there is only one rigorous method, and this method takes the lattice periodicity into account. Moreover, the classical method based on static condensation is found to be only approximate. The procedure is applied to examples of planar lattice trusses in static analysis. The results prove the eectiveness and the reliability of the present approach, and comparisons are made with results obtained from other classical methods. #
The presented work is intended to develop a geometrically reduced order (homogenized) model for a large antenna space structure with flexible joints. An energy equivalence concept is employed to find the continuum model for the system. The kinetic and strain energy expressions of the fundamental elements are found based on the assumptions of the micropolar elasticity theory. Necessary assumptions are made to reduce the order of the strain variables while retaining the effects of the micro-rotations that are coupled to the primary strain terms. As a result, a micropolar-based continuum model is found for the structure with torsional joints. The vibrations equations of motion for various coordinates of the one dimensional equivalent model are presented. Subsequently, the relations between the physical parameters of the distributed parameter model and the radar structure are introduced. The effect of the asymmetric mass distribution as a result of the addition of the radar panel to the truss system is studied. For the purpose of the experimental validation of the suggested model a planar truss structure with Pratt Girder configuration was built and tested in the laboratory. The results for the experimental frequency response functions are shown to be in good agreement with the theory. Finally, the continuum model is used to quantify the effects of the thermally induced disturbances on the satellite system during the eclipse transition.
Dynamics Analysis of a Truss System Modelled by the Finite Element Method in the Frequency Domain
2020
The dynamic analysis of a truss system modelled by the finite element method in the frequency domain is studied. The truss system is modelled by 22 elements and has 44 degrees of freedom. The stiffness matrix and mass matrix of the truss system are obtained by using the finite element method. Differential equations of the truss system are obtained by using the obtained stiffness and mass matrix. By applying the Laplace transformation, the displacements of each node are calculated, and the equation is arranged in the frequency domain. The obtained differential equations are solved by using MATLAB. Eigen values are calculated and represented depending on the frequencies. Thus, static displacements, dynamic displacements, static reaction forces and dynamic reaction forces for each frequency are graphically obtained. Additionally, dynamic amplification factors are calculated and simulated depending on the frequencies. Dynamic displacements increased near the eigenvalues, and the dynamic...
Dynamic analysis of a lattice structure by homogenization: Experimental validation
Journal of Sound and Vibration, 2008
A homogenization method is presented for dynamic analysis of truss structures motivated by large satellite applications. The proposed method was previously compared to a full finite element procedure and the experimental verification of the homogenization approach is presented here. Local strains in a planar truss are found in terms of the strain components evaluated at the center of the repeating truss element. Kinetic and strain energy expressions are then derived in terms of the spatial and time derivative of the displacement components at the center of the truss element. Necessary assumptions are made to reduce the order of the strain field of the full model to a geometrically reduced order model. Hamilton's principle is employed to find the governing partial differential equations of motion for the equivalent continuum model. It is shown that the dynamic equations for this structure are similar to those of an anisotropic Timoshenko beam theory. Finally the natural frequencies of the structure are found using the one-dimensional homogenized model. A truss structure was fabricated and tested for the purpose of validation of the developed theory. The results for the frequency response functions and the natural frequencies from the continuum model are shown to be in good agreement with the experiment. As a result, the method shows promise as a tool for use in the analysis and design of lattice structures.
A continuum model for the nonlinear analysis of beam-like lattice structures
Computers & Structures, 1988
A simple equivalent continuum model has been developed for the geometrically nonlinear analysis of beam-like lattice structures. Two important features of the model are the simplicity of the calculation of the continuum properties and the ability of the continuum to accurately predict the behavior of rigid-joint as well as pin-joint lattices. The equivalence of the continuum and lattice is established by requiring the strain energy of the continuum to equal the strain energy of the lattice for a finite set of assumed deformation modes. It is shown that an additional strain energy term not found in classical Timoshenko beam theory must be included in the continuum strain energy function in order to accurately approximate the behavior of rigid-joint frames. A finite element discretization is applied to the continuum to obtain numerical solutions for the continuum model. By comparison with discrete finite element results for the lattice, the accuracy of the continuum methodology is demonstrated for both static and dynamical problems. For the nonlinear problems studied, the continuum solutions were found to require only a small fraction of the CPU time needed for the discrete finite element solutions.
Nonlinear Finite Element Analysis of Space Truss
2012
This paper presents an analytical investigation which includes the use of three dimensional nonlinear finite elements to model the performance of the space trusses by using (ANSYS 11.0) computer program. The numerical results show very good agreement (100%) with experimental results, while the graphical option reflects the behavior of the structure under the applied loads because of the ability of this option to simulate the real behavior of the structure under these loads. Also finite element models of the space truss simulate the lateral deflection of the top chord members especially at the corners, and the twisting of the bottom chords.
Dynamical Models Quality of Truss Supporting Structures
2011
The quality of the model used to describe a structure is the main value of the scientific selection of technical analyses. This theoretical-experimental analysis shows the quality of modern dynamic modeling when it comes to modeling structures using linear members (1D finite elements). A tower crane structure is observed as a representative of large structures. A FEM structure model is created and subjected to testing of its static and dynamic properties. Elastic displacements and forms of model oscillations are searched for. Numerically obtained theoretical solutions are compared to experimental results. The quality of modern structure modeling application has a deviation of less than 2%. At the locations of the pronounced bending of the lattice, in the structure of the cantilever type, the elastic displacement deviation is less than 3%. The differences in the results of theoretical models and of experimental studies indicate the sensitivity of modeling quality depending on the experience of the authors and the restrictions of theoretical models in the description of connections in the truss node. The paper points to the elements of quality modeling, the scope of the number of applied structure elements, the redundant detailedness of some descriptions, the importance of the finite element type selection, the experimental values of vibration damping and the tower cranes properties. On the basis of these analyses, it is possible to develop analogue models which assure the quality-precision in modeling responsible structures.
2000
wing-box chord vertical strut force (z-direction) horizontal strut force 0,-direction) strut vertical offset length freestream Mach number bending moment local lift distribution for element i wing-strut intersection (from wing root) unit step function Uah, Vab, Wabbackwash, sidewash and downwash velocity, respectively shear force bending deflection engine weight spanwise engine position (from root) spanwise coordinate lift coefficients at structural nodes wing sweep angle bending slope vortex strength However, along with the idea of the cantilever wing configuration with its aerodynamic advantages, the concept of the truss-braced wing configuration
Strain gradient elasticity theories in lattice structure modelling
GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry, 2017
The first and second strain gradient elasticity theories, resulting in higher-order governing equations, are studied in the framework of continualization, or homogenization, of lattice structures such as trusses in plane and space, with auxetic metamaterials as a special application. In particular, the role of length scale parameters and classical dimensions, such as the beam thickness, is addressed by parameter studies. Finite element and isogeometric methods are utilized for discretizations.