Building Acoustics

40 Building acoustics 2 2 0or dd 0, d d ma cv k x xx mckx t t ⋅+⋅+⋅= ++⋅= (2.12) where x, v and a are displacement, velocity and ...

Excitation and response 41 ζ > 1 shows that the system is more than critically damped giving a solution 0 0021 xt() e−ξωt Aeω ...

42 Building acoustics 2 6 2 (0) 10 , () xt xt T = = = (2.23) and if further applied to Equation (2.21) we have 6 00 ln (10 ) 2.2 ...

Excitation and response 43 j 0 m d() () j (). d xt Fet vt xt tZ ω ω ⋅ == = (2.28) The quantity Zm is the mechanical impedance, t ...

44 Building acoustics Stiffness-controlled range, ω << ω 0 In this case, we have ω^2 << k/m = ω 02 and |Zm| ≈ k/ω. T ...

Excitation and response 45 2 0 0 1j2 . 1j2 F F ω ζ ω ωω ζ ωω +⋅ ′= −+⋅⎛⎞ ⎜⎟ ⎝⎠ ⋅ (2.32) If we only are interested in the ratio o ...

46 Building acoustics In the above model viscous damping was assumed, which will give a transmissibility dependent on damping al ...

Excitation and response 47 This transmissibility is shown in Figure 2.9 for four values of the loss factor η. These values are, ...

48 Building acoustics () 11 1j j M Z k m η ω ω == ⎛⎞+⋅ ⎜⎟− ⎝⎠ (2.39) and we must solve an integral, which after some rearranging ...

Excitation and response 49 2.5.1 Modelling systems using lumped elements The modelling of a system as a collection of lumped ele ...

50 Building acoustics For this case we have chosen to calculate the input point mobility and Figure 2.11 shows the result compar ...

Excitation and response 51 (machine), isolator and structure 2 (foundation) respectively, we may express the efficiency E as 2mf ...

52 Building acoustics We shall use the model shown in Figure 2.10 to illustrate the behaviour of the efficiency E given by Equat ...

Excitation and response 53 modes for a certain wave type we therefore have to rely on various approximate methods. Finite elemen ...

54 Building acoustics Meirovitch, L. (1997) Principles and techniques of vibration. Prentice-Hall International Inc., Thousand O ...

CHAPTER 3 Waves in fluid and solid media 3.1 INTRODUCTION This chapter is devoted to the fundamental properties of waves in flui ...

56 Building acoustics the acoustic fluctuating parts are relatively small; we may assume the phenomena to be linear. Also note, ...

Waves in fluid and solid media 57 3.2.1 Plane waves Using the notion plane wave implies a wave where the sound pressure varies i ...

58 Building acoustics adiabatically. This implies that the changes happen so fast that the temperature exchange with the surroun ...

Waves in fluid and solid media 59 At a temperature of 20 °C the characteristic impedance of air will be 415 Pa⋅s/m, which insert ...