Abstract

This paper focuses on responses of the free end of a cantilever beam made of two different materials under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin–Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange’s equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. It is seen in the numerical investigations that because of piecewise homogeneous character of the beam material, additional secondary waves appear between the primary waves. The relations between additional waves and location, physical properties of the part of different material are found. It is proved that the location and length of the part of different material can be obtained by investigating the additional secondary waves.

Key words: Wave propagation, additional wave, piecewise-homegenous cantilever beam.