Suppression of time aliasing in the solution of the equations of motion of an impacted beam with partial constrained layer damping

Signal processing issues encountered when an analytical spectrum is converted in the time domain with an inverse discrete Fourier transform are investigated. In the analytical model of the transient time response of an impacted beam with partial constrained layer damping (PCLD) developed in Ref. [D. Granger, A. Ross, Effects of partial constrained viscoelastic layer damping parameters on the initial transient response of impacted cantilever beams: experimental and numerical results, Journal of Sound and Vibration 321 (1–2) (2009) 45–64, doi:10.1016/j.jsv.2008.09.039], noncausal effects were observed for lightly damped structures. As discussed in the present paper, the noncausal effects were due to time aliasing occurring when continuous frequency spectra were discretized. To suppress such errors, the numerical Laplace transform is introduced and applied to the previous model, which was based on Fourier transforms. The equations of motion of the system and the viscoelastic properties of the core are formulated in the Laplace domain. A window is used in the Laplace domain to avoid amplification of the Gibbs oscillations that are caused by the truncation of the spectrum. The new solution technique is compared to the previous method. It is shown that noncausal effects appearing in the first milliseconds of time signals with the use of discrete Fourier transforms are avoided with the Laplace transform solution method. Numerical results are validated for transient responses using experimental impact force signals. The results are in good agreement with experimental data.