Theoretical Modeling of Mechanical Waves in Periodic Phononic Structures

As an essential necessity for fundamental study and a broad variety of technological applications, it is important to control the propagation of mechanical waves and select particular vibration modes in phononic structures. In this thesis, the guiding of mechanical waves in engineered periodic phononic structures is demonstrated theoretically and numerically by using the finite element method. Controlling the phononic dispersion relation has lead to new insights in both fundamental research and applications. The band structures, transmission spectra, and displacement fields/acoustic pressure fields are calculated to characterize mechanical waves in periodic phononic structures. Phononic waveguides provide a convenient way to control phonon transport. Surface modes in the hypersonic regime generated by defects in a silicon pillar-substrate system are investigated in phononic crystal waveguides. Bandgaps are caused by the hybridization effect of band branches induced by local resonances and propagating modes in the substrate. The specific bands shift and localized modes emerge due to the local resonance effect induced by the defects. Moreover, being a kind of acoustic demultiplexer, channel drop waveguides are studied as an essential component of a possible acoustic communication system. The localized mode induced by the coupling elements in the channel drop waveguide is analyzed to achieve an efficient forward transfer or backward transfer signal of acoustic waves. Guiding of mechanical waves in a two-dimensional graded phononic crystal plate is examined. Mechanical waves can be focused or diffused in an infinite phononic crystal and inclusion-type graded phononic crystal plate. For an attachment-type graded phononic crystal plate the elastic waves can be guided along specific channels owing to the resonant coupling of attachments and matrix. Resonance frequencies of guided surface modes can be tuned by tailoring geometries and material properties of attachments, which shows the capability of spatially selecting different frequencies into designed channels. Acoustic directional waveguiding in a two-dimensional phononic crystal is simulated based on the analysis of equifrequency contours. Taking advantage of a self-collimation effect, acoustic beam splitting in a defect-free nanostructure is realized in the low Gigahertz range associated with relaxed limitations regarding the parameters of the excitation source. The influence factors of beam splitting quality are investigated to achieve potential super-resolution and construct an acoustic interferometer device at the nanoscale. As imperfect fabrication or environmental changes lead to defects and result in undesired coupled modes, it is of great value to realize robust designs and new functionalities by providing immunity to a variety of perturbations. A topological solid structure with protected phononic modes is achieved by appropriately engineering a phononic metamaterial based on a 2D pentamode structure. By separating the double accidental degeneracy Dirac point, a nontrivial bandgap is obtained and gapless edge states are constructed. Thereby, the elastic waves of the helical edge states, which are characterized by robust pseudospin-dependent edge phonon transport, can propagate unidirectionally with the characteristic of being backscatteringimmune.