Response of extended eulerbernoulli beam under impulse load using wavelet spectral finite element method

Abstract

Transform methods are some of those methods which are able to solve certain difficult ordinary and partial differential equation. The most commonly used transform for these solutions are Laplace and Fourier transforms. Wavelet transforms are new entrants in to this area, although
they are quite popular with electrical and communication engineers in characterizing and synthesizing the time signals. The utility of wavelet transforms is shown in structural engineering by addressing problems involving solutions of ordinary and partial differential equations
encountered in dynamical related problems.
Dynamical problems in structural engineering fall under two categories, one involving low frequencies, which is called structural dynamics problems, and the other involving very high frequencies, which is called the wave propagation problems. The most problems in structural engineering fall under the former category, wherein the response of the entire structural system is characterized using only the first few vibrational modes. The wave propagation is a multi-modal phenomenon involving vibrational modes of very high frequencies. Conventional analysis tools
such as finite element cannot handle these problems due to modeling limitations and extensive computational cost. The only alternative to such problems is the method based on transforms.Spectral finite element (SFE) method is one such transform method, which can be a viable alternative to solving problems involving high frequency excitations. SFE based on Fourier transform is quite well known and established. However, it has severe limitations in handling
finite structures and specifying non-zero boundary/initial conditions, and thus its utility in solving real world problems involving high frequency excitation is limited.
The aim of the present work is to show that the wavelet transform is very useful in solving ordinary differential equations by modeling the structure as a discrete system involving structural dynamic problems and it is to use wavelet transform to solve those problems involving partial
differential equations. In this work, the response of an cantilever Extended Euler-Bernoulli aluminum beam under impulse load applied axial and transverse at the free end is shown. The response is being obtained by coding programs in MATLAB.