Some Free Vibration and Dynamic Response Problems Associated with Centrifugally Stabilized Disk and Shell Structures Semiannual Progress Report, 15 Feb. - 15 Aug. 1966

Natural frequencies and normal modes for free vibrations of flat spinning annular and centrifugally stabilized disk and shell structure

Modeling the effects of wind tunnel wall absorption on the acoustic radiation characteristics of propellers

Finite element theory is used to calculate the acoustic field of a propeller in a soft walled circular wind tunnel and to compare the radiation patterns to the same propeller in free space. Parametric solutions are present for a "Gutin" propeller for a variety of flow Mach numbers, admittance values at the wall, microphone position locations, and propeller to duct radius ratios. Wind tunnel boundary layer is not included in this analysis. For wall admittance nearly equal to the characteristic value of free space, the free field and ducted propeller models agree in pressure level and directionality. In addition, the need for experimentally mapping the acoustic field is discussed

The transmission of sound in nonuniform ducts

The method of weighted residuals in the form of a modified Galerkin method with boundary residuals was developed for the study of the transmission of sound in nonuniform ducts carrying a steady, compressible flow. In this development, the steady flow was modeled as essentially one dimensional but with a kinematic modification to force tangency of the flow at the duct walls. Three forms of the computational scheme were developed using for basis functions (1) the no-flow uniform duct modes, (2) positive running uniform duct modes, with flow, and (3) positive and negative running uniform duct modes, with flow. The formulation using the no-flow modes was the most highly developed, and has advantages primarily due to relative computational simplicity. Results using the three methods are shown to converge to known solutions for several special cases, and the most significant check case is against low frequency, one dimensional results over the complete subsonic Mach number range. Development of the method is continuing, with emphasis on assessing the relative accuracy and efficiency of the three implementations

Fundamental investigations of the finite element solutions for acoustic propagation in ducts

The question of convergence of three finite element algorithms for the modelling of acoustic transmission in ducts carrying a nonuniform mean flow is addressed. The details of each algorithm are stated and example calculations in uniform and nonuniform ducts are made and assessed for accuracy and convergence. The algorithm based on the assumption of irrotationality is found to be highly convergent. This algorithm is the one used in current turbo-fan inlet acoustic radiation codes. A theoretical analysis indicating convergence is supported by example calculations. Two additional algorithms which do not require irrotationality are found to be less convergent, and perhaps not convergent at all for certain severely sheared velocity profiles. No theoretical convergence criteria can presently be established for these algorithms and convergence difficulties are shown here by example. Included in this class of algorithms is the duct analysis program ADAM which is known to display apparently nonconvergent solutions in certain cases

A comparison of the structureborne and airborne paths for propfan interior noise

A comparison is made between the relative levels of aircraft interior noise related to structureborne and airborne paths for the same propeller source. A simple, but physically meaningful, model of the structure treats the fuselage interior as a rectangular cavity with five rigid walls. The sixth wall, the fuselage sidewall, is a stiffened panel. The wing is modeled as a simple beam carried into the fuselage by a large discrete stiffener representing the carry-through structure. The fuselage interior is represented by analytically-derived acoustic cavity modes and the entire structure is represented by structural modes derived from a finite element model. The noise source for structureborne noise is the unsteady lift generation on the wing due to the rotating trailing vortex system of the propeller. The airborne noise source is the acoustic field created by a propeller model consistent with the vortex representation. Comparisons are made on the basis of interior noise over a range of propeller rotational frequencies at a fixed thrust

Application of steady state finite element and transient finite difference theory to sound propagation in a variable area duct: A comparison with experiment

Sound propagation without flow in a rectangular duct with a converging-diverging area variation was studied experimentally and theoretically. The area variation was of sufficient magnitude to produce large reflections and induce modal scattering. The rms (root-mean-squared) pressure and phase angle on both the flat and curved surface were measured and tabulated. The steady state finite element theory and the transient finite difference theory are in good agreement with the data. It is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations

Cut-on cut-off transition in flow ducts : comparing multiple-scales and finite-element solutions

The phenomenon of cut-on cut-off transition of acoustic modes in ducts with mean flow is examined using an analytical multiple-scales solution, and compared to solutions obtained from a numerical finite-element method. The analytical solution, derived for an arbitrary duct with irrotational mean flow, remains valid to leading-order throughout the duct. In other words, it is a composite solution, encompassing both the inner boundary-layer solution in the neighbourhood of the transition point and the outer slowly varying modal solution far upstream and downstream. Several test cases are defined and presented within a geometry representative of a high-bypass turbofan engine. The cases span a wide realistic range of frequencies and circumferential mode numbers both with and without mean flow, including one numerically-challenging investigation of cutoff cut-on transition of a mode. The agreement is in most cases remarkably good. Slight differences in position of the pressure pattern can be observed for cases with mean flow, which seem due to the slight variations in mean flow fields obtained from both methods. When cut-on cut-off transition occurs for high Helmholtz number and high radial mode number a certain amount of modal scattering is observed. An attempt is made to explain this by incorporating the presence of neighbouring modes in the asymptotic scaling arguments for the turning point region. The composite solution should enable designers to continue to use multiple-scales theory to examine flow pressure and noise transmission inside an engine duct, whilst now being able to include directly the contributions of modes undergoing transition without encountering singular behaviour