Aerospace Technic and Technology

This study develops a theoretical model of vibration-induced noise generation in helicopter blade elastic vibrations. Vibration and aerodynamic noises are generated during helicopter rotor rotation. Numerous studies have been conducted on aerodynamic noise, and a number of theories have been proposed.  However, vibration noise has been mainly studied experimentally or modeled only by the ordinary mechanical vibrations of the blade as a single body—a beam or plate. This does not consider the blade’s elastic deformations, which generate elastic sound waves inside the body. Until now, no model has mathematically described the transformation of elastic longitudinal and transverse waves arising inside an elastic blade into sound waves. These waves emerge from the blade and propagate into the air during elastic thickness vibrations, which are formed by variable deformations under the action of variable blade loads. The research methods are based on the analytical solution of the boundary value problem for the Navier-Cauchy equation, which is divided into four Helmholtz equations: one for the scalar potential and three for the vector potential. Elastic waves of the Love's wave type are studied, but for a finite-sized thin elastic plate. Limiting standing waves to only one direction is impossible for a helicopter rotor blade of finite sizes, since the blade has finite dimensions. Therefore, the following model of vibration noise generation was proposed: the blade is approximately replaced by a thin elastic plate, inside which elastic longitudinal and transverse waves arise, which are governed by Helmholtz equations. The general solution to these equations is found using the method of variable separation (Fourier method). The reflection and scattering issues of sound waves from the interface between an elastic body and air are not considered in this study. Results and conclusions. This paper proposes a new physical model of vibration-induced sound: vibration-induced sound is generated as a result of the emission of elastic longitudinal waves, which are emitted from inside an elastic blade outward into the air. An analytical solution of scalar and vector potentials in the form of standing sound waves was obtained for a boundary value problem with a known distribution of aerodynamic, time-harmonic loads on the blade surfaces. This solution allowed us to write expressions for normal stresses on the blade surface. Time-varying stresses transfer the energy of longitudinal standing sound waves, which emanate from the blade’s center outward into the air. They are the source of vibration-induced noise. The expression for normal stresses on the blade surface contains derivatives of both scalar and vector potentials, i.e., it considers the influence of both longitudinal and transverse waves. Thus, both wave types implicitly participate in the formation of normal stresses on the blade surface.  The periodic change in these stresses over time causes periodic blade thickness deformation, which is the source of air acoustic vibrations. The calculated data for the longitudinal wave potential on the blade surface coincide with the well-known Gutin’s theory of rotational sound: the maximum generated sound wave is located near the blade’s outer end. This indicates that the analytical solution obtained in this work physically describes the vibration-induced noise generation process.

vibration-induced noise model; aerodynamic load on helicopter blades; generation of elastic sound waves on helicopter blade surfaces

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