Band structures of transverse waves in nanoscale multilayered phononic crystals with nonlocal interface imperfections by using the radial basis function method

A radial basis function collocation method based on the nonlocal elastic continuum theory is developed to compute the band structures of nanoscale multilayered phononic crystals. The effects of nonlocal imperfect interfaces on band structures of transverse waves propagating obliquely or vertically in the system are studied. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interface. Furthermore, the influences of the nanoscale size, the impedance ratio and the incident angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface imperfections have significant effects on the band structures in the macroscopic and microscopic scale.

RBF collocation method and stability analysis for phononic crystals

The mesh-free radial basis function （RBF） collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric （MQ）, Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs. The choice of the shape parameter and the effects of the knot number are presented.

ELASTIC SH WAVE PROPAGATION IN PERIODIC LAYERED COMPOSITES WITH A PERIODIC ARRAY OF INTERFACE CRACKS

The interaction of anti-plane elastic SH waves with a periodic array of interface cracks in a multi-layered periodic medium is analyzed in this paper. A perfect periodic structure without interface cracks is first studied and the transmission displacement coefficient is obtained based on the transfer matrix method in conjunction with the Bloch-Floquet theorem. This is then generalized to a single and periodic distribution of cracks at the center interface and the result is compared with that of perfect periodic cases without interface cracks. The dependence of the transmission displacement coefficient on the frequency of the incident wave, the influences of material combination, crack configuration and incident angle are discussed in detail. Compared with the corresponding perfect periodic structure without interface cracks, a new phenomenon is found in the periodic layered system with a single and periodic array of interface cracks.

Band structures of elastic SH waves in nanoscale multi-layered functionally graded phononic crystals with/without nonlocal interface imperfections by using a local RBF collocation method

A meshless radial basis function （RBF） collocation method based on the Eringen nonlocal elasticity theory is developed to calculate the band structures of ternary and quaternary nanoscale multi-layered phononic crystals （PNCs） with functionally graded （FG） interlayers. Detailed calculations are performed for anti-plane transverse waves propagating in such PNCs. The influences of FG and homogeneous interlayers, component number, nonlocal interface imperfections and nanoscale size on cut-off frequency and band structures are investigated in detail. Numerical results show that these factors have significant effects on band structures at the macroscopic and microscopic scales.

A comparative study of wave localization in locally resonant Thue–Morse, Rudin–Shapiro and Period-Doubling aperiodic structures

The localization characteristics of the in-plane elastic waves in locally resonant aperiodic phononic crystals are examined in this study. In particular, the phononic crystals generated according to the Thue-Morse, Rudin-Shapiro and Period-Doubling sequences are theoretically investigated by using the extended transfer matrix method. For comparison, the binary and ternary locally resonant systems are considered, and their band structures are characterized by using the localization factors. Moreover, the influences of structural arrangement, material combination, incidence angle, number of components, length ratio, and random disorder on the band structures are also discussed. Some novel and interesting phenomena are observed and discussed.