Buckling Deformation And Surface Wave Modulation In Soft Materials With Periodic Surface Structures

Acoustic metamaterials are a kind of artificial composite structure with some orders,and possess a lot of superior physical properties that natural materials do not have.They can be used to modulate waves.One of the most basic characteristics is the existence of bandgaps,i.e.frequency range where waves attenuate rapidly and cannot propagate through the structures.Once being designed and fabricated,the geometric configuration of traditional acoustic metamaterials cannot be changed,and their operating frequencies are unchangeable.Compared with traditional acoustic metamaterials,tunable acoustic metamaterials have more extensive applications.To achieve the tunability,soft materials become a good choice because of their large deformation and instability.In this thesis,we mainly focus on the buckling deformation and surface wave bandgaps of the periodic soft structures.Based on buckling and energy band theory,the finite element method is employed to systematically study the buckling instability and wave characteristics of two-dimensional soft materials with periodic surface structures in theoretically and numerically.The main contents and conclusions include:1)A two-dimensional periodic surface structure is designed by drilling circular holes on the surface of homogeneous solid.Effects of geometric parameters of circular holes are studied with the fixed periodic constant.Based on the results of the buckling analysis,the difference between the buckling modes under different geometric parameters is explained.The numerical results show that the structure with circular holes has two buckling modes,depending on the ratio of holes depth to width between holes(termed as depth-to-width ratio).When the radius of holes is decreasing,the depth-to-width ratio causing the modal transformation is also decreasing.The critical strain of structure is positively correlated with the depth-towidth ratio and negatively correlated with the radius of the holes.The structure exhibits surface wave bandgaps which can be altered by applying a load to the structure or adjusting the geometric parameters of the structure.After buckling of the structure,the energy bands generally decrease and the number of surface wave modes increases.Some of the original bandgaps become narrow or disappear,but a new bandgap appears at low frequency.Before deformation,increasing the hole's depth of the structure can open a new bandgap.2)The periodic surface structures with elliptical,cross-like,square and triangular holes are designed by changing the shape of the circular holes.Effects of different shapes of the holes and geometric parameters are studied.Based on the results of the buckling analysis,the difference between the buckling modes under various shapes of the holes is explained.The numerical results show that the structures with elliptical and cross-like holes have two buckling modes depending on the depth-towidth ratio,which is similar to the structure with the circular holes.However,the structures with square and triangular holes have only one buckling mode.The shape of the holes does have a certain influence on the bandgaps,so it is possible to modulate elastic surface wave by altering the hole's shape.When the first instability mode occurs for elliptical and cross-like holes,the energy bands and bandgaps decrease,resulting in some new low-frequency bandgaps.When the second instability mode occurs,the bandgaps of the structure with elliptical,cross-like and square holes become narrow;but the bandgaps of the structures with triangular holes increase.3)The periodic surface structures with a double row of circular holes with or without hard inclusions are designed by adding an additional row of circular holes or filling some holes with hard inclusions.Effects of the additional row and the introduction of hard inclusions are studied.The numerical results show that the new structure with a double row of circular holes has two buckling modes depending on the depth of the holes in the first row,which is similar to the structure with a single row of circular holes.If some holes are filled by the hard inclusions,the first instability mode occurs,and it will not be affected by the depth of the holes.The buckling of the structures will lower their energy bands.The original bandgaps become narrow or disappear,resulting in a new low-frequency bandgap.After the introduction of hard inclusion,the composite structure has wider bandgaps with lower frequency.In conclusion,the present analysis shows that the buckling deformation and surface wave bandgaps of soft materials could be tuned by altering the holes' size,spacing,depth and shape,changing the loading,or introducing the inclusions.In these ways,the tunability of bandgaps is realized,which provide a useful reference for the design of specific acoustic devices.