Engineering Acoustics. Malcolm J. Crocker

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Название Engineering Acoustics
Автор произведения Malcolm J. Crocker
Жанр Техническая литература
Серия
Издательство Техническая литература
Год выпуска 0
isbn 9781118693827



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motion of an n‐degree‐of‐freedom undamped linear system excited by simple harmonic forces at some arbitrary angular forcing frequency ω (all excitation terms at the same phase) can be expressed in matrix form as

      where F is an n‐dimensional complex column vector of dynamic amplitude forces. We assume harmonic solutions of the form

      and

      (2.40b)equation

Schematic illustration of harmonically forced two-degree-of-freedom system.

      The particular solution is given by Eq. (2.36) as

      (2.41)equation

      Therefore, Eq. (2.37) becomes

      (2.42)equation

      which has to be simultaneously solved to find the displacement amplitudes A1 and A2.

      Example 2.6

      Let consider the two‐degree of freedom system of Example 2.5. Assume that a force F0 ejωt is applied to mass m1 and no force is applied to mass m2. Then, Eq. (2.37) becomes

      Solution

      (2.45)equation

      and the ratio

      (2.46)equation

      where images and images.

      Example

      Repeat the problem discussed in Example 2.6 but now assume that a force F0 ejωt is applied to the mass m2 and no force is applied to the mass m1.

      Solution

      Equation (2.37) becomes now

      (2.47)