Abstract
A tensegrity structure is a structure which consists both of compressive and tensile elements without being restrained at the boundaries. The self-equilibrium state inside the tensegrity structure is the condition that builds the structure without any boundary condition necessity. The conventional Eigensystem solver cannot deal with this kind of structure since there are rigid body motions in the governing equations. The exact dynamic solution of tensegrity structure problems can only be obtained by using the frequency-dependent dynamic method. In this study, the free vibrational characteristics of a tensegrity structure which is modeled by a combination of the compressive strut and tensile cables elements are solved by using the Spectral Element Method (SEM). Natural frequencies of the tensegrity are tracked by using the Wittrick-Williams algorithm. Numerical calculations are given to show the effectiveness, efficiency, and accuracy of the SEM in solving the axially vibrating members of the tensegrity structures.
Highlights
Finite element method (FEM) is one of the major and common computational methods available in many fields of science and engineering
This sophisticated concept has directed to the so-called dynamic stiffness method (DSM) [1,2]
Because the dynamic shape functions are formulated by using exact dynamic stiffness matrix, they treat the mass in a structure member implicitly
Summary
Finite element method (FEM) is one of the major and common computational methods available in many fields of science and engineering. To obtain a sufficiently accurate dynamic response, all necessary high-frequency wave modes have to be considered in the analysis. Because the conventional FEM is formulated based on the frequency-independent polynomial shape functions, the FEM cannot accommodate all essential high-frequency wave modes without fine element discretization. The accuracy of the solution can be improved by using the shape functions, which depend on the natural frequency of the tensegrity. The dynamic shape functions can be considered as necessity in high-frequency wave modes, it is not necessary to refine the element. This sophisticated concept has directed to the so-called dynamic stiffness method (DSM) [1,2]. The exact natural frequencies of the free vibration tensegrity are investigated
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