The vibration of and wave propagation in periodic cellular structures are analyzed. Cellular structures exhibit a number of desirable multifunctional properties, which make them attractive in a variety of engineering applications. These include ultra-light structures, thermal and acoustic insulators, and impact amelioration systems, among others. Cellular structures with deterministic architecture can be considered as example of periodic structures. Periodic structures feature unique wave propagation characteristics, whereby elastic waves propagate only in specific frequency bands, known as "pass band", while they are attenuated in all other frequency bands, known as "stop bands". Such dynamic properties are here exploited to provide cellular structures with the capability of behaving as directional, pass-band mechanical filters, thus complementing their well documented multifunctional characteristics. This work presents a methodology for the analysis of the dynamic behavior of periodic cellular structures, which allows the evaluation of location and spectral width of propagation and attenuation regions. The filtering characteristics are tested and demonstrated for structures of various geometry and topology, including cylindrical grid-like structures, Kagom and eacute; and tetrhedral truss core lattices. Experimental investigations is done on a 2-D lattice manufactured out of aluminum. The complete wave field of the specimen at various frequencies is measured using a Scanning Laser Doppler Vibrometer (SLDV). Experimental results show good agreement with the methodology and computational tools developed in this work. The results demonstrate how wave propagation characteristics are defined by cell geometry and configuration. Numerical and experimental results show the potential of periodic cellular structures as mechanical filters and/or isolators of vibrations.

Because of their outstanding characteristics, micro/nano-mechanical (MM) structures have found a plethora of applications in wireless communications and sensing. Many of these MM structures utilize mechanical vibrations (or phonons) at megahertz or gigahertz frequencies for their operation. On the other hand, the periodic atomic structure of crystals is the fundamental phenomenon behind the new era of electronics technology. Such atomic arrangements lead to a periodic electric potential that modifies the propagation of electrons in the crystals. In some crystals, e.g. silicon (Si), this modification leads to an electronic band gap (EBG), which is a range of energies electrons can not propagate with. Discovering EBGs has made a revolution in the electronics and through that, other fields of technology and the society. Inspired by these trends of science and technology, I have designed and developed integrated MM periodic structures that support large phononic band gaps (PnBGs), which are ranges of frequencies that phonons (and elastic waves) are not allowed to propagate. Although PnBGs may be found in natural crystals due to their periodic atomic structures, such PnBGs occur at extra high frequencies (i.e., terahertz range) and cannot be easily engineered with the current state of technology. Contrarily, the structures I have developed in this research are made on planar substrates using lithography and plasma etching, and can be deliberately engineered for the required applications. Although the results and concepts developed in this research can be applied to other substrates, I have chosen silicon (Si) as the substrate of choice for implementing the PnBG structure due to its unique properties. I have also designed and implemented the fundamental building blocks of MM systems (e.g., resonators and waveguides) based on the developed PnBG structures and have shown that low loss and efficient MM devices can be made using the PnBG structures. As an example of the possible applications of these PnBG structures, I have shown that an important source of loss, the support loss, can be suppressed in MM resonators using PnBG structures. I have also made improvements in the characteristics of the developed MM PnBG resonators by developing and employing PnBG waveguides. I have further shown theoretically, that photonic band gaps (PtBGs) can also be simultaneously obtained in the developed PnBGs structures. This can lead to improved photon-phonon interactions due to the effective confinement of optical and mechanical vibrations in such structures. For the design, fabrication, and characterization of the structures, I have developed and utilized complex and efficient simulation tools, including a finite difference time domain (FDTD), a plane wave expansion (PWE), and a finite elements (FE) tool, each of which I have developed either completely from scratch, or by modification of an existing tool to suit my applications. I have also developed and used advanced micro-fabrication recipes, and characterization methods for realizing and characterizing these PnBG structures and devices. It is agued that by using the same ideas these structures can be fabricated at nanometer scales to operate at ultra high frequency ranges. I believe my contributions has opened a broad venue for new MM structures based on PnBG structures with superior characteristics compared to the conventional devices.