| Thin plate structures are widely used in transportation, aerospace, construction and other fields. Eliminating or reducing harmful structure vibration of thin plate structure has been one of the pop research topics in engineering and academic study. Thin phononic crystal plates combine vibration gaps of phononic crystal with thin plate structure. Good vibration isolating effectiveness can be achieved by reasonable design, which makes thin phononic crystal plates have an extensive application prospect in vibration isolation field. Comparing with the traditional passive and active vibration isolation, thin phononic crystal plate can realize the integrated design of structure and isolation system, meanwhile with the futures of light quality, wide isolation frequency and high reliability. The isolation characteristics of thin phononic crystal plates are significantly affected by its vibration gaps which depending on the structure parameters and material parameters. So research on vibration gaps and its influencing factors of PC plate is of great importance for the design of vibration isolation systems based on PC plate. Taking flat thin PC plate and pillared thin PC plate as research objects, the influences of structure parameters and material parameters on longitudinal vibration and flexural vibration gaps are investigated.Based on the thin plate theory and the improved plane wave expansion method, vibration band structures of flat PC plate with different lattices and scatterers are calculated and compared, and the change law of longitudinal vibration and flexural vibration gaps as a function of the scatterer filling fraction is investigated. A new complex square-like lattice based on the simple square lattice and a square-like Archimedes lattice is proposed. Take this new lattice as an example, the influences of filling fraction of each scatterer in the unit cell on the vibration gaps are investigated. Wider gaps can be obtained by this new lattice with an appropriate scatterer radius ratio. Twist of band structures is found when rotating square scatterers in this new lattice. A new proposed three-component grid plate structure is investigated by the finite element method, and the formation mechanism of its low-frequency locally resonant vibration gaps is revealed.From the basic longitudinal and flexural vibration equations based on the thin plate theory, material parameters which have the most significant influences on the gaps are obtained. Band structures of two kinds of two-component flat PC plates with diferrent structures are calculated by the improved plane wave expansion method. The interface between Bragg gaps and locally resonant gaps in the distribution range of material parameters are discovered during the investigation of the change law of relative width and location of different gaps as a function of the material parameters. The flexural vibration gaps of flat PC plate are validated by vibration experiments. Moreover, regulating effect of temperature on vibration gaps of flat PC plate with scatterers of shape memory alloy is discussed based on a simplified relationship of temperature and modulus of shape memory alloy.Finite element models of single-side single-vibrator pillared PC plate(SSPPCP), single-side double-vibrator pillared PC plate(SDPPCP) and double-side single-vibrator pillared PC plate(DSPPCP) are established. According to the band structures and eigenmodes, starting and cutoff of each vibration gap are analyzed. The existence of gaps are confirmed by finite element simulation and vibration experiment. Through the finite element simulation, the attenuation amplitude in the frequency range of the longitudinal vibration gaps is far less than that of the flexural vibration gaps, which makes the flexural vibration gaps of the pillared PC plate more useful. As such, the following investigation only focuses on the flexural vibration gaps. The analysis for the effect of the structure parameters on the flexural vibration gaps of these three kinds of pillared PC plates is conducted. Besides, more gaps are obtained by pillared PC plates with supercell composed by different pillars.Take SSPPCP as examples, the effects of material parameters of the three components on the flexural vibration gaps are investigated. Distribution law of the gaps is obtained when changing the materials of the base plate and the lateral layer of the pillars and the elastic modulus of the silicone rubber regarded as linear elastic material. According to the analysis results, SDPPCP and DSPPCP with four components are proposed and investigated. Based on the standard liner solid model, an iterative finite element method is proposed to calculate vibration band structures of pillared PC plates including viscoelastic materials. Using this method, the effects of the frequency dependent characteristic of the storage modulus of the rubber on the gaps are investigated, and loss factor band structures corresponding to the frequency band structures are obtained under different relaxation time.A new kind of one-directional spoke-like vibration isolator based on the flexural vibration gaps of pillared PC plates is obtained by a structure optimal design. Finite element simulation analysis of the vibration transmissibility of six spoke-like vibration isolators with single spoke-like DSPPCP is conducted. Combined frequency range of vibration gaps are realized by combination of different spoke-like DSPPCP. Experimental results show that the average vibration attenuation amplitudes of the proposed spoke-like isolators with one, two and three spoke-like DSPPCPs can reach 24 d B, 34 d B and 38 d B respectively. |
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