Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 58

Equations (2.3) and (2.8) can be linearized if small changes around a certain equilibrium are considered:

(2.20)

(2.21)

(2.22)

Inserting (2.22) into the equation of continuity (2.3), neglecting all second order terms as far as source terms, and setting¹ v0=0 the linear equation of continuity is:

(2.23)

Doing the same for the equation of motion (2.8) leads to:

(2.24)

Using the curl(∇×) of this equation it can be shown that the acoustic velocity v′ can be expressed using a so-called velocity potential which will be useful for the calculation of some wave propagation phenomena.

(2.25)