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Distributed Transducers by Using Smart Materials

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Control of Noise and Structural Vibration

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Abstract

In this chapter, we consider the design of piezoelectric sensors and actuators for structural vibration and sound control. Firstly, the robust stability analysis of the collocated sensor/actuator pair is discussed. Secondly, the design of modal sensors by using shaped PVDF films for beam-type structures is presented. Thirdly, the modal sensor by using a PVDF array is discussed. Finally, the design of 2-D modal sensor/actuator is also discussed.

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Author information

Authors and Affiliations

  1. School of Aircraft Engineering, Nanchang HangKong University, Nanchang, China, People’s Republic

    Qibo Mao PhD

  2. Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland

    Stanislaw Pietrzko DSc, Dr. sc. techn. ETH

Authors
  1. Qibo Mao PhD
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  2. Stanislaw Pietrzko DSc, Dr. sc. techn. ETH
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Problems

Problems

  1. P.4.1

    Consider a simply supported uniform beam with a collocated point force actuator and displacement sensor. The beam has an elastic modulus of 109 N/m2, a density of 2,700 kg/m3 and a thickness of 4 mm. The dimensions of the beam are 0.05 m × 0.6 m.

  1. (a)

    Calculate frequency response function (FRF) in frequency range 0–500 Hz when the collocated actuator/sensor pair is located at 0.1 m, 0.3 m and 0.4 m, respectively.

  2. (b)

    Draw the Pole/zero pattern and Nyquist diagram.

  1. P.4.2

    Consider a simply supported uniform beam covered with a PVDF patch as shown in Fig. 4.28. The beam’s physical parameters are the same as Problem 4.1. The mass and stiffness of the PVDF sensor is negligible.

  1. (a)

    If the beam is excited by a point force located at x a = 0.1 m, calculate the PVDF sensor charge output using Eq. (4.16).

  1. P.4.3

    Derive Eq. (4.38).

  1. P.4.4

    Calculate the shape of modal sensor for the third and fourth structural modes:

  1. (a)

    For a simply supported uniform beam

  2. (b)

    For a clamped–free uniform beam

  3. (c)

    For a clamped–clamped uniform beam

  1. P.4.5

    Consider the beam used in Problem 4.2. The beam is excited by a point force located at x a = 0.1 m.

  1. (a)

    Calculate the volume velocity for frequency below 1,000 Hz.

  2. (b)

    Why the even modes have no contribution to volume velocity?

  1. P.4.6

    Derive the shape function of the volume velocity PVDF sensor listed in Table 4.1 based on integration-by-parts approach.

  1. P.4.7

    Assume that there are n × n rectangular PVDF array with same size equally attached on a simply supported plate. To sense the first structural mode for the plate:

  1. (a)

    Calculate the weights of 8 × 4 PVDF array.

  2. (b)

    Calculate the weights of 8 × 8 PVDF array.

  3. (c)

    Calculate the weights of 16 × 8 PVDF array.

  4. (d)

    Calculate the weights of 20 × 10 PVDF array.

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Mao, Q., Pietrzko, S. (2013). Distributed Transducers by Using Smart Materials. In: Control of Noise and Structural Vibration. Springer, London. https://doi.org/10.1007/978-1-4471-5091-6_4

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  • DOI: https://doi.org/10.1007/978-1-4471-5091-6_4

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5090-9

  • Online ISBN: 978-1-4471-5091-6

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