Dissipation is an inevitable property of a mechanical system and influences the dynamical behavior and device performance. It is, therefore, crucial to study and understand the sources of dissipation in mechanical systems in order to control the dissipation present in the system. These sources of dissipation can be broadly classified in two groups: extrinsic and intrinsic mechanisms. Extrinsic mechanisms are independent of material properties and influenced by the external properties of the system, such as geometry, pressure, and temperature. Intrinsic mechanisms on the other hand, are independent of external conditions and arise from the intrinsic properties of the device material, such as defects in the bulk and the surface of the material. In this work, we closely study two extreme limits of dissipation at the opposite ends of the spectrum. First, at the high dissipation limit where extrinsic mechanisms dominate dissipation, spectral properties of the thermal noise force giving rise to Brownian fluctuations of a continuous mechanical system — namely, a doubly clamped nanomechanical beam resonator — immersed in a viscous liquid are investigated. To this end, two separate sets of experiments are performed. The power spectral density (PSD) of the Brownian fluctuations of the resonator around its fundamental mode are measured at the center of the resonator. Then, the frequency-dependent linear response of the resonator is measured, again at its center, by driving it with a harmonic force, via an electrothermal transducer, that couples well to the fundamental mode. These two separate measurements are then used to determine the PSD of the Brownian force acting on the structure in its fundamental mode. The PSD of the force noise extracted from multiple resonators with varied lengths spanning a broad frequency range displays a ``colored spectrum'' and follows the viscous dissipation of a cylinder oscillating in a viscous liquid by virtue of the fluctuation-dissipation theorem. In the second application, which is at the ultra-low dissipation limit at low temperature where intrinsic mechanisms dominate dissipation, we design and fabricate high-frequency aluminum nitride (AlN) piezo-optomechanical resonators. Furthermore, an acoustic radiation shield consisting of periodic phononic crystals is designed and implemented to further decrease dissipation. Fabrication and design of both the optomechanical cavity and phononic crystals are discussed in detail. Room temperature characterization of the ring resonator is presented and out-of-plane thickness mode of the AlN resonators has been identified. With microwave mechanical frequency and high Quality factor mechanical response, these resonators can be cooled down to quantum ground state with direct cooling methods such as dilution fridge cooling. These type of resonators can achieve efficient conversion between electrical, optical, and mechanical signals which can be utilized for quantum information science and sensing applications in the field of nanoelectromechanical systems. / 2023-09-24T00:00:00Z