Thermal Effect On Metamaterials And Tunable Topological States Based On Stewart Configuration

Thermal environment will significantly modify the elastic constants of materials,and will cause thermal deformation and thermal stresses,which will bring new challenge to noise-vibration control in thermal environments.Recently,as the development of elastic metamaterials and topologically metamaterials,the promising bandgap property and topologically protected edge states could offer a new way for noise,vibration and wave propagation control.Naturally,the effect of thermal environment on acoustic metamaterial and topologically tunable elastic metamaterials will definitely improve our understanding of the concept of metamaterial and can extend the application of metamaterials in engineering.In this paper,we investigate the effect of thermal environment on band structures of elastic metamaterials and topologically tunable elastic metamaterial designation.The main contents are as follows:(1)Analyzing the effect of thermal environment on band structures of elastic metamaterial.Firstly,based on Mindlin's plate theory,effect of thermal stresses on the band structure of elastic metamaterial plates has been investigated by developing a useful finite-element based method.It is demonstrated that the relative magnitudes between elastic properties and thermal stresses will lead to nonlinear effects on frequency band structures based on two different types of metamaterial plates made of single and double inclusions of square plates,respectively.Then,we validate the proposed approach by comparing the band structures with the frequency response curves obtained in finite periodic structures.We conduct sensitivity analysis and discuss in-depth the sensitivities of band structures with respect to temperature difference to quantitatively investigate the effect of thermal stresses on each band.In addition,the coupled effects of thermal stresses and temperature-dependent material properties on the band structure of Aluminum/ silicone rubber plate have also been discussed.The proposed method and new findings in this paper extends the ability of existing metamaterial plates by enabling tunability over a wide range of frequencies in thermal environments.Secondly,a theoretical investigation of the thermoelastic wave propagation in the phononic crystals in the context of Green-Nagdhi theory has been presented by taking thermoelastic coupling into account.The thermal field is assumed to be steady.For the 2D problem,we use plane wave expansion method to investigate the effect of various material,lattice type,and inclusion shape on the thermoelastic band structure.As for 1D metamaterial,we apply assumed mode method and transfer matrix method to obtain the thermoelastic band structure of Rayleigh wave.It is demonstrated that the band structure of thermoelastic band structure is composed of elastic and thermal bands and that the thermoelasticity can modify original elastic bands.For Rayleigh wave,the thermoelastic coupling will affect the transmission ability of band gaps as well as narrow down the band gap width,which is also remarkably influenced by the filling fraction ratio.The work presented here can expand the application of phononic crystals to the multi-physical field coupled with thermoelasticity.(2)Design and analysis of topologically tunable metamaterials.Specifically,we formulate topologically tunable metamaterial based on bistable Stewart platform which is regarded as the basic unit cell.Then we realize the tunability of topological waveguides.Firstly,considering the effect of base excitation,we obtain the nonlinear dynamic model of Stewart platform by using Kane's method.Then according to the micro-vibration assumption,we omit the nonlinear terms and get the linear dynamic equation.We verify the dynamic model by comparing the theoretically natural frequencies with the results of simulations and experiments.That a good agreement with them demonstrates the validation of the model.As the bistability property appeared in origami structures,we investigate the coupling relationship among various directions based on linear dynamic model and formulate a reduced model with three degree-of-freedoms.Then we analyze and design a bistable Stewart platform on the basis of principle of minimum potential energy.After that,a topological metamaterial system based on the bistable Stewart Platform has been proposed,which can not only guide mechanical waves robustly in a desired path,but also can be tuned in situ to change this wave path at will.Without resorting to any active materials,the current system harnesses bistability in its unit cells,such that tuning can be performed simply by a dial-in action.Consequently,a topological transition mechanism inspired by the quantum valley Hall effect can be achieved.We show the possibility of tuning in a variety of topological and traditional waveguides in the same system,and numerically investigate key qualitative and quantitative differences between them.We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range,topological waveguides are distinctive as they support robust,back scattering immune,one-way wave propagation.