Elements of Acoustics and Vibration

Catalog description

Vibrational acoustics including mechanical oscillation, forced and damped response, vibration of strings, membranes, rods, bars, and plates. ACS 501 Elements of Acoustics and Vibration (3) Acoustics is a broad subject that crosses and interacts with many engineering, science, mathematics, medical, and artistic disciplines. This course provides a thorough foundation necessary for studying structural acoustics and vibration problems and the exploration of acoustic waves in solids. A detailed analysis of the single-degree-of-freedom mechanical mass-spring system provides the building block for exploring lumped-element models of more complicated acoustic systems and the phenomena of resonance for forced and damped systems. Multiple-degree-of-freedom mechanical systems are used to investigate the coupled oscillation between oscillating systems, the design of vibration absorbers, and methods for modeling the low frequency behavior of guitars, violins, and vented-boxed loudspeakers. Extending the mass-spring model to an infinite number of degrees-of-freedom leads to a development of the wave equation and its solutions for longitudinal acoustic waves in elastic solids. Boundary conditions and the concept of mechanical impedance are used to explore standing waves in a bounded elastic medium and the transmission of waves between media with different elastic properties. Transverse waves on an elastic string, while fundamentally different from longitudinal waves, obey the same differential equation of motion and the same application of boundary conditions and mechanical impedance. For both longitudinal and transverse wave systems, the mechanical impedance approach and the method of separation of variables are used to study systems with specified boundary conditions. Longitudinal and transverse waves in structures with varying cross-section, density, or elastic properties are also explored. Torsional waves in elastic solids are explored with application to systems with various cross-sectional shapes. Membranes serve as a two-dimensional extension of transverse waves on an elastic string, and provide mode shapes which may be described using rectangular and cylindrical coordinates (with Bessel function solutions). The fourth-order differential equation of motion for flexural bending vibrations of thin beams is derived and solutions are explored using the separation of variables approach for boundary value problems. Finally, the flexural vibration of two-dimensional rectangular and circular plates are investigated. Homework problem sets will illustrate theory and applications to real world problems.