In the mammalian auditory system, specifically in the cochlea of the inner ear, the Basilar Membrane (BM) and hair cells are responsible for transducing incoming acoustic waves into electrical signals. These acoustic signals are carried as traveling waves by the BM and propagate from the base of the cochlea toward its apex where the helicotrema is located. An impressive feature of the mammalian auditory system is to prevent the propagated waves from reflecting which allows mammals to hear sounds without any reflection or overlap. This extraordinary characteristic of the inner ear is the main inspiration for this work. In the present study, the dynamic behavior of a beam structure with one or more attached spring-damper (SD) systems as passive absorbers is studied when excited by a harmonic force. The location of the spring-damper system divides the beam into two dynamic regions: one which exhibits non-reflecting traveling waves and the other with standing waves. In this work, the separation of traveling and standing waves is studied analytically, numerically, and experimentally. To the best of the author's knowledge, this is the first time in the literature that traveling and standing wave separation in a beam is realized experimentally using a single-point excitation and a spring-damper. Experimental results are used to validate the models of the system. Moreover, a parametric study is performed to gain a better understanding of the effect of different parameters on the quality of the generated waves in the structure. Furthermore, the effect of attaching the second spring-damper to the system is presented. Adding the secondary SD system results in increasing the excitation frequency range so that wave separation can be achieved. The results of this work can be used in various applications such as vibration suppression, energy absorption, particle transportation, and in exploring possible explanations for the BM and helicotrema functions in the cochlea. / Doctor of Philosophy / In the inner ear of the mammalian auditory system, the sound waves travel inside the cochlea where they are converted to electrical signals sent to the brain. A fascinating characteristic of the mammalian auditory system is that the sound waves traveling in the cochlea do not reflect when they reach its apex where the helicotrema is located. Therefore, we are able to hear sounds without any reflection or overlap. This work is inspired by the biological behavior of the inner ear and studies the dynamic behavior of a simple structure such as a beam with one (or two) attached spring-damper(s). In this work, the attached spring-damper system(s) prevents the waves traveling from the source to the beam's boundary from reflecting. This is similar to what happens in the inner ear. The location of the spring-damper divides the beam into two dynamic regions, one which exhibits non-reflecting traveling waves and the other with standing waves. The wave separation and parameters affecting the wave quality and its reflective or non-reflective features are studied analytically, numerically, and experimentally. To the best of the author's knowledge, the experiments carried out to generate the aforementioned wave types coexisting with each other on the beam are one of a kind. Furthermore, the results of this study showed a very good agreement between the experimental and theoretical results. The outcomes of this work can potentially be used in exploring possible explanations for the function of the cochlea and helicotrema and various applications such as particle transportation and suppression of unwanted vibrations.