Chaotic Response of Panel Vibrations Forced by Turbulent Boundary Layer and Sound

Abstract

Experimental data are presented to show evidence of chaotic response of two adjacent aircraft panels forced by a turbulent boundary layer and pure tone sound. The experiments are a simulation of boundary-layer and fan noise loads on a fuselage sidewall with Reynolds number per meter of 2 :85 £ 10 5 . The response of the panels is purely random and assumed linear when forced by the turbulent boundary-layer e ow and clearly becomes nonlinear with the appearance of the interspersed periodic to chaotic motion when forced by the boundary layer with superimposed pure tone sound. The initial periodic response of two tori of two commensurate frequencies changes with an increase in pure tone sound level. The response of period-doubling bifurcations then makes a transition to chaos, which alternates with quasiperiodic response as the wave loses the spatial homogeneity. The objective is to demonstrate the existence of strong nonlinear effects on the structure response, which is not yet well understood. I. Background M OST studies of nonlinear deterministic and stochastic dynamic problems examine externally excited systems. A typical example of an externally excited system is an aircraft fuselage structure interacting with a turbulent boundary layer and jet engine noise. Periodic, aperiodic, and chaotic responses can occur along the sidewall of the fuselage structure during the acceleration from takeoff, as well as at cruise altitude. One type of load is the socalled buzz-saw noise in high-bypass-ratio turbofan engines. The present experiment is designed to simulate such loads, as well as structural nonlinear responses that result from turbulent boundarylayer e ow and high-intensity sound interaction. Such experiments must be conducted in a wind tunnel with an anechoic test section to prevent standing wave formation between the test panel surface and the opposite sidewall of the tunnel. As a rule, the panel tension and curvaturedependon theloading. Thistension, therefore, constitutes a coupling between the loading and the response. One manifestation of this coupling is the spontaneous surface deformation of the panel, giving rise e rst to the regular and then to the irregular spatial patterns as the load increases. In the previous experiments, panels with periodic nonlinear responses to sound and e ows of constant or accelerated speeds and their active control were considered. 1;2 The present study simulates the abnormal processes of e ow and sound loads, the unsteady loads of the boundary-layer pressure e uctuations coupled with the panel responses,andthesoundradiationbythepanel.Nonlinearbehaviors result fromincreasing levels of pure tone sound as evidenced by the response changes in the panel from periodic motions to broadband chaos. In the past, chaotic signals were not recognized as a physical behavior but were hidden in the broad view given by stochastic processes. At present, the interest is to distinguish between periodic, quasiperiodic,and nonperiodic responses. 3‐6 In the experiments reported herein, the input of the acoustic load superimposed on the turbulent boundary-layer e ow was gradually increased. First, the boundary-layer instability and then responses changing from periodic to quasiperiodic and e nally to chaotic were observed, analo