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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alt="images"/>]. Equation (2.28) represents the superposition of all modes of vibration of the multi‐degree of freedom system.

      Example 2.5

      Solution

      The two‐coordinates x1 and x2 uniquely define the position of the system illustrated in Figure 2.11 if it is constrained to move in the x‐direction. The equations of motion of the system are:

      and

      (2.29b)equation

      (2.30)equation

      where q = images, images and images.

      Equation (2.26) gives the characteristic equation

      and

equation

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

Schematic illustrations of the mode shapes for the two-degree of freedom system (a) first mode, (b) second mode.

      

      2.4.2 Forced Vibration – Undamped

      By forced vibration, we mean that the system is vibrating under the influence of continuous (external) forces that do not cease. The total response of a multi‐degree of freedom system due to a force excitation is the sum of a homogeneous solution and a particular solution. The homogenous solution depends upon the system properties while the particular solution is the response due to the particular form of excitation. The homogenous solution is often ignored for a system subjected to a periodic vibration for being of lesser practical importance than the particular solution. For a general form of excitation, a closed‐form solution of a multi‐degree of freedom system can be very difficult to obtain and numerical methods are often used.

      The