Analytical solution and experiments in wave propagation problems (MS)

Abstract

Every disturbance in a continuum media generates a wave, which propagates through the space-time domain. Therefore, the study of waves and its propagation is of the utmost importance for all engineering problems. Various studies have been per formed in this domain. Analytical solutions exist for the simple cases and can be applied to most of the complex scenarios by using the superposition principle. A more complex problem can be solved using computational methods. But, each of them pertains to their own drawbacks. The response through a computational method needs the whole space and time domain to be analyzed. This approach provides good results but becomes inefficient when the solution is required at only a very distant time step. Also, some complex excitation become very cumbersome to be decomposed into superimposing components. Novel analytical methods are pro posed for wave propagation problems to overcome the above mentioned limitations A modified Laplace Transform approach is proposed to investigate the wave propagation/ vibration response of a stretched string. The vibration response is demonstrated using the proposed method for various initial and boundary conditions. The method is capable of calculating the vibration response of a moving impulse loading on the string. The method is compared with other methods such as Fourier analysis and finite difference method for accuracy and computational efficiency. A Dirac Delta function approximation is proposed to analyze the acoustic wave propagation through panel. Governing wave equation is modified to include the Dirac Delta function which represents the discontinuity in the wave propagation medium (air to panel). The expression for wave transmission, reflection, and absorption coefficients are evaluated for a single panel in terms of strength of the Dirac Delta. The obtained results are compared with Finite Element simulation results for a single-layered and multilayered panel materials. Finally, one-dimensional acoustic transmission line has been constructed to experimentally measure the strength of Dirac Delta function for various test materials of panel. For this purpose, a Two Microphone Impedance Tube experimental setup is designed and constructed. A statistical study has been performed on the developed setup to minimize the errors in measurements. The sample calculations has been demonstrated for acoustic testing of different materials using the developed experimental setup.