Abstract
In this chapter, the physical basics for active control of sound and vibration are presented. Some examples of the active control of one-dimensional acoustic pressure and structural–acoustic systems (such as beam, plate, and double plate) will be presented. It should be noted that we focus on the control performance due to the physical aspects in this chapter, so the disturbance sources are assumed tonal and constant. Sections 3.1 and 3.2 describe the control performance for a one-dimensional duct by using single or double control sources; then the control performance due to the different cost functions (such as cancellation of pressure or absorbing reflected wave) is discussed. Section 3.3 describes several active control strategies for structural–acoustic problems, such as minimization of the sound power, cancellation of the volume velocity, and cancellation of the first few radiation modes. Section 3.4 discusses the control performances for beam-type structures by using point forces as control sources. Section 3.5 discusses the control performances for plate-type structures by using the piezoelectric actuators and point forces as control sources. Section 3.6 discusses the sound transmission loss for double-plate structures by using different control sources.
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Problems
Problems
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P.3.1
Consider a rigid piston at x 0 separating the fluid-1 for x < x 0 from the fluid-2 at x > x 0 in an infinitely long pipe with cross section S. Assume that the piston vibrates with a frequency ω and an amplitude a. Calculate the force necessary to move the piston as a function of time.
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P.3.2
Consider a primary monopole source p p at x = 0 and a control monopole source p c placed downstream at x = L to control the downstream wave transmission, both sources being in an infinite duct, as shown in Fig. 3.3. Assume that L = λ/8 (λ is the acoustic wavelength). Calculate the amplitude of the pressure in duct due to the control source.
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P.3.3
Based on MATLAB
Fig. 3.33 
The vibration control and structural–acoustic control
GUI program shown in Fig. 3.17, please modify the boundary conditions of the beam as clamped at each end, and design a new GUI program to calculate the sound power and vibration energy for the clamped–clamped beam with different point forces.
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P.3.4
Design a MATLAB GUI program to calculate the control performance for a simply supported plate with different primary/control sources, the interface can be similar to Fig. 3.33.
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P.3.5
Derive Eq. (3.88).
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P.3.6
A simply supported, baffled, rectangular plate has an elastic modulus of 109 N/m2, a density of 700 kg/m3 and a thickness of 4 mm. The dimensions of the plate are 0.5 m × 0.6 m. Determine the transmission loss as a function of frequency range from 10 to 300 Hz. Assume that the plate is excited by the random indent acoustic wave (diffuse field).
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Mao, Q., Pietrzko, S. (2013). Introduction Examples on Control of Sound and Vibration. In: Control of Noise and Structural Vibration. Springer, London. https://doi.org/10.1007/978-1-4471-5091-6_3
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DOI: https://doi.org/10.1007/978-1-4471-5091-6_3
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