Wave Propagation Characteristics Of Periodic Tensegrity Structure

Many physical systems appearing in different scientific fields such as optics,chemistry,crystallography,acoustics and mechanics can be modeled as periodic structures.Periodic structures have obvious characteristics of "passband" and "forbidden band",and are widely used to solve engineering problems such as cushioning,shock absorption,filtering and noise reduction.As a new type of vibration reduction and suppression structure with many excellent performances,the application of tensegrity structure in periodic structure has attracted more and more attention.In order to investigate the dynamic and wave propagation characteristics of the periodic prismatic tensegrity structure(PTS),the following studies are carried out:(1)The static stiffness evolution of the compressed PTS is studied.Firstly,based on the analytic geometry,the geometric model of tensegrity element posture is established,and the relationship between the bar length,cable length,height and rotation angle of tensegrity structure is deduced.Based on the nodal force balance equation,the influence model between the self-balancing position of the tensegrity element and the pre-tension of the cable segment is established.On this basis,the effective tangential stiffness and its feasible region of tensegrity structure are deduced by the principle of energy conservation.The numerical example results show that the effective axial stiffness of the tensegrity structure can be considered as linear when the height change of the tensegrity structure is less than 3% of the height at the self-balancing position;otherwise,the influence of non-linearity of stiffness should be considered.(2)The forbidden band characteristics and the localization of wave propagation of periodic tensegrity linear structures are studied.Based on the assumption of linear stiffness,the periodic tensegrity structures element is equivalent to the spring oscillator structure.The wave propagation equations of the periodic tensegrity linear structure is deduced for both monatomic and diatomic chains.With the help of Bloch's theorem,the wave transfer equation of periodic tensegrity linear structure is established.Considering the detuning of effective axial stiffness caused by the randomness of pre-tension of cable segments,the formula for calculating the localization factor of detuning periodical PTS is derived by Furstenberg limit theorem.The localization characteristics of monoatomic and diatomic chains show that both passband and forbidden band are localized,and this phenomenon is more obvious in the forbidden band than that of the passband.In addition,the localization factor increases with the increase of the detuning degree and the pre-tension level.Changing the pre-tension will result in changes of the energy band distribution characteristics of the periodically prismatic tensegrity structure.(3)The nonlinear frequency dispersion characteristics of the periodic tensegrity nonlinear structure are studied.First,considering the weak nonlinearity of effective axial stiffness,the nonlinear dynamic equation of tensegrity unit is established by using the small displacement hypothesis and the Taylor polynomial of nonlinear force between the tensegrity unit elements.Based on the Lindstedt-Poincare method and scaling principle,the multi-scale perturbation analysis of the dispersion relation under perturbation is carried out,and the analytical solution of the dispersion relation is obtained.Finally,the variation of nonlinear dispersion curves under different pretension levels is analyzed.The dispersion analysis results show that the periodic tensegrity nonlinear structure under weakly nonlinear condition is different from the traditional quadratic weakly nonlinear system.Because it has both stiffness softening and hardening characteristics at the same time.