| Phononic crystals(PnCs)are artificial periodic materials or structures which can exhibit elastic wave band gaps.Within the band gaps,the propagation of elastic waves can be effectively inhibited.PnCs have potential application in many fields like vibration control,acoustic isolation,acoustic function devices,micro-nano technology,intelligent robot,stealth technology and so on.The ultra-precise motion platform is the core component of the nanometer precision machining and measurement equipment.Inhibition of micro-vibration of the ultra-precision motion platform is the key issue to improve the level of nanometer processing precision.This thesis is oriented towards this major strategic needs of the country,focusing on the performance of PnCs on the suppression of low-frequency micro-vibration in ultra-precision motion platform.Based on the structural dynamics,wave mechanics and energy conservation,the study focuses on the two core problems of"reducing band gap frequency" and "widening band gap range",aiming at the PnCs with low-frequency and wide band gaps,and good vibration reduction performance.The main research content and results are as following:1.A folding beam-type piezoelectric PnC model is established.The characteristics and generation mechanism of low-frequency and wide band gaps are studied.Effects of the circuit parameters and geometrical parameters are revealed.The theoretical model is further verified with finite element method(FEM).The results show that the proposed PnC can not only generate better band gaps with low-frequency,wide range and strong attenuation,but also partially overcome the puzzle of size in practice.Two Bragg band gaps of 369 Hz to 1687 Hz and 2127 Hz to 4000 Hz can be obtained.In addition,between these two Bragg band gaps,a locally resonant band gap is induced by resonant shunting circuits.Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus,a low-frequency and broad band gap of 369 Hz to 4000 Hz is obtained.2.An axisymmetric type of PnC composed of a periodic alternation of circular cavity sandwich plates is established.The characteristics and generation mechanism of low-frequency and wide band gaps are studied.Effects of geometrical parameters and material paremeters are revealed.The theoretical model is further verified by FEM and experiment.Based on the PnC model,a vibration isolater with low-frequency and wide band gaps is invented.The results show that the proposed PnC can generate several wide low-frequency Bragg band gaps providing strong attenuation.Moreover,it has a small size,an easy processability and an excellent load-carrying capacity.Although a Bragg band gap,the first band gap can reach a lower frequency of 364 Hz,a value much smaller than the same type Bragg band gaps,and compares favorably with the locally resonant band gaps.Overall,the proposed PnC has a highly potential engineering application value.3.A two-dimensional PnC with combined convex and concave holes is established.Ultra-wide band gaps generated by this kind of PnC are investigated and the generation mechanism is analyzed.It is found that L-shaped connectors are the main reason for the formation of ultra-wide band gaps.Effects of geometrical parameters are revealed.The combination of convex and concave holes can be a new direction for the design of PnCs,especially the starting design for further topology optimization.Compared to other PnCs that have been discussed in the literature,this PnC has the following advantages:(1)ultrawide band gaps for both in-plane and out-of-plane waves,and a very broad complete band gap;(2)simple topology with regular holes that can be easily fabricated;(3)along with a significantly smaller filling fraction of the solid material,much thicker connectors and much lighter masses can induce ultra-wide band gaps that are useful to avoid stability and overweight problems;(4)ultra-wide band gaps can be obtained in a wide range of geometrical parameter that is not only beneficial to improve applicability,but also to enhance robustness to manufacturing errors.4.A silicon-based cross-like holey phononic crystal(PnC)strip is established.The characteristics and generation mechanism of low-frequency and wide band gaps are studied.Effects of the geometrical parameters are revealed.Compared with the published holey PnC strips,the following advantages of the proposed PnC strip are demonstrated:(1)broad band gap,(2)band gap with lower frequency,(3)smaller size,(4)broad band gaps can be obtained in a wide range of geometrical parameter and(5)intermediate filling fraction of the solid material.In summary,this traits make the PnC strip a powerful candidate for vibration isolation in the ultra-precision motion platform and MEMS.5.A cross-like two-dimensional phoxonic crystal(PxC)is established.The existence of simultaneously large complete photonic and phononic band gaps is investigated.The generation mechanism of dual large band gaps is analyzed.Effects of the geometrical parameters are revealed.The most silent trait is the large complete band gaps can exist over a wide range of geometrical parameters in the prerequisite of keeping simple topology.After optimization,photonic and phononic band gaps peak with gap-to-midgap ratios of 11.5%and 90.7%respectively.These profits enable the proposed topology to be a promising candidate in the phoxonic crystal devices.In this paper,the theoretical model,finite element model and experimental model are established.All efforts are try to address the limitations of the PnCs band gaps at this stage,focusing on lowering and widening the band gaps.Moreover,the requirements of practical application are also taken into consideration,such as miniature size,stability,load-carrying capacity,ease of manufacture and so on.The research results have important theoretical significance and engineering value to promote the research and application of PnCs on the suppression of low-frequency micro-vibration. |
