Waveguides

Abstract

A waveguide is a system, which by means of its boundaries contains and directs the flow of energy in a construction. One such system is a structural waveguide typical of a ship construction. Aircraft and certain train constructions are also built up of frames and plates. Parallel frames mounted to plate elements guide the propagation of waves in a direction of the frames. A sandwich or honeycomb plate forms another type of waveguide. The laminates coupled to a core contain the energy flow in the structure. A third type of a waveguide system is a cylinder.

Problems

14.1

Determine the first five cut-on frequencies for an acoustic cylindrical waveguide.

14.2

A structural waveguide, Fig. 14.2, is excited by a bending moment $M\exp (i\omega t)$ at $x = 0$. The bending moment is constant along the y-axis. Determine the energy flow in the waveguide. The plate element is simply supported along the lines $y = 0$ and $y = L_y$. Assume the waveguide to be semi-infinite.

14.3

Assume that the elements in Fig. 14.5 are beam elements. Determine the coupling elements in the matrix $\left[ A \right]$ of Eq. (14.23) for this particular case.

14.4

Use Eq. (14.34) to prove the results given in Eq. (14.36).

14.5

Determine the matrix giving the natural frequencies of a sandwich beam with free ends.

14.6

Determine the response of a simply supported sandwich beam, length L, mass per unit length ${m}'$, and bending stiffness ${D}'$. The beam is extended along the x-axis of a coordinate system from $x = 0$ to $x = L$. The beam is excited by a force $F\exp (i\omega t)$ at $x_1$ where $0 < x_1 < L$.

14.7

Determine the point mobility of an infinite sandwich beam.

14.8

Determine the high frequency limits for the wavenumbers for waves propagating on a circular cylinder.

14.9

Use Eq. (14.100) to predict the sound transmission loss of a curved panel for $f > f_\mathrm{c}$ and well above the ring frequency.

14.10

Show that in a finite circular cylinder with an inside over pressure $\Delta p$ the tensions ${T}'_x$ and ${T}'_y$ are approximated by ${T}'_x = \Delta pR_y / 2$ and ${T}'_y = \Delta pR_y$.