Dynamic response of a transducer mounted at one end of an acoustical cavity
Abstract
The dynamic response of a transducer mounted at one end of a one-dimensional acoustical cavity is determined. The cavity is filled with a compressible isentropic fluid, and the fluid at the open end of the cavity (i.e., the boundary at x = 0) is subjected to an axial displacement specified with respect to time. At the other end of the cavity the transducer is represented as a mass, spring, and damper system. Consequently, the boundary condition at x = 1 is also time dependent. The general solution to the boundary value problem is obtained as well as the steady state solution for harmonic excitation. Since the steady state response for harmonic excitation is of particular interest, an analytical or closed form solution is obtained for the displacement and pressure response functions. In addition, a simple and useful algebraic expression is obtained for the steady state pressure-frequency response function for harmonic excitation. An approximate solution is also obtained for the dynamic response of a transducer mounted at one end of a two-diameter or stepped-recessed cavity. Stepped-recessed pressure transducer cavities, which may be grease-filled, are suitable for measuring quasi-static pressures in solid propellant guns and regenerative liquid propellant guns (RLPGs), provided the frequencies contained in the quasi-static pressure pulse are low relative to the fundamental frequency for the empty stepped cavity.
- Publication:
-
Unknown
- Pub Date:
- April 1993
- Bibcode:
- 1993drtm.rept.....B
- Keywords:
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- Dynamic Response;
- Harmonic Excitation;
- Pressure Measurement;
- Pressure Sensors;
- Transducers;
- Boundary Value Problems;
- Cavities;
- Compressible Fluids;
- Displacement;
- Equations Of Motion;
- Partial Differential Equations;
- Pressure Pulses;
- Steady State;
- Acoustics