Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations

Abstract

Abstract Nonlinear differential equations are being used in many applied science fields such as engineering, there are more and more applications, such as musical instrumentation, chemistry, aerodynamics, cybernetics, signal and image processing, biophysics, complex media dynamics, etc. Mainly based on the analysis of the vibration and attenuation characteristics of piano strings, and on the theoretical basis of the discussion on the resonance effect of the resonance system, the model of the piano music simulation system is constructed, investigated a class of fractional nonlinear differential (integrative-differential) equations and systems of equations, fractional nonlinear differential equations on unbounded domains, and with multiple different fractional derivatives, and the existence of solutions to integral nonlinear impulse differential equations, uniqueness, multiple solutions, eigenvalue interval, as well as monotonic iterative sequences and error estimates that converge to the solutions of the corresponding equations. Finally, from the pitch frequency detection, formant point frequency estimation, and three aspects of spectrogram analysis, subjective evaluation experiments are carried out on the algorithm, and the experimental results verify the effectiveness of musical simulation.