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theses

In recent decades, noise pollution places increasing burden to people’s health and the ecological environment. In this dissertation, a general theory and a corresponding analytical model of a branch cavity are presented to analyze and predict the sound reduction frequency of the branch cavity. The vibrating air in the branch cavity is modeled as a continuous analog mass-spring system using the dynamic analogy method. The air inside the branch cavity is divided into many infinitesimal air layers. The physical properties such as pressure and density in each individual air layer are uniform within that air layer. Each air layer is modeled as a single mass-spring unit with mass and stiffness, and all the mass-spring units are converted into an effective mass-spring. Then, standing wave and the conservation of energy are employed to calculate the natural frequency of the effective mass-spring, which is also the sound reduction frequency of the branch cavity. Next, the concept of the serial-parallel mass-spring system is added to our proposed analog mass-spring system analytical model to analyze the asymmetric branch cavities. In terms of the asymmetric branch cavity, a branch cavity is modeled as two parallel effective mass-spring systems. The symmetric branch cavity is the special case of the asymmetric branch model. In addition, the idea of equivalence is applied to construct the equivalent single neck model for a branch cavity with multiple necks. Then, the analog serial-parallel mass-spring system analytical model is used to calculate the sound reduction frequency of the branch cavity with multiple necks. In addition, many two-dimensional and three-dimensional branch cavity models are simulated and analyzed in our study, including straight branch pipes, circular branch cavities, rectangular branch cavities, cylindrical branch cavities, combined shapes branch cavities, branch cavities with irregular shapes, asymmetric branch cavities and multiple necks branch cavities. The simulated and predicted results of these models indicate that our proposed analog mass-spring system analytical model is a general model for all kinds of branch cavities. Furthermore, our analog mass-spring system analytical model predicts sound reduction frequency accurately, and it has satisfying robustness. Lastly, we would present some design applications based on the analog mass-spring system analytical model. The design variables are some selected dimensional parameters of the branch cavity, and the value of the design variables can be solved as a constrained optimization problem based on the target sound reduction frequency or frequency band. The remarkable sound reduction effects of our branch cavity designs will be presented in the simulation results.

http://dissertations.umi.com/gsnb.rutgers:12333

Ph.D.

Includes bibliographical references

doi:10.7282/t3-dedk-kx02

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