Abstract
Abstract. The process of wave propagation in the discrete chain of bilinear oscillators subjected to several types of external harmonic excitation has been analysed. The phenomenon of sign inversion of the displacement is observed for tension–compression excitation. The solution for wave propagation in a continuous 1-D bimodular rod is developed and the numerical results are compared.
Highlights
We analyse the process of wave propagation in a chain of bilinear oscillators – discrete masses connected by springs having different stiffnesses in tension and compression
We focus on a conservative system; for the effects of damping in bilinear oscillators see Holmes (1983), Natsiavas (1990a, b), Liu et al (2015), Dyskin et al (2012), Klepka et al (2015), or Guzek et al (2016)
In order to compare the chain of bilinear oscillators with its homogenized counterpart, we considered a continuous 1-D bimodular rod and developed a solution for its wave equation
Summary
We analyse the process of wave propagation in a chain of bilinear oscillators – discrete masses connected by springs having different stiffnesses in tension and compression. A general case of a discrete chain of bilinear oscillators has never been studied with respect to the mechanical wave propagation, which is why it has been decided to numerically investigate the response of the bilinear system that could represent a continuous bimodular medium. The purpose of the present work is to study the response of a discrete system of bilinear oscillators loaded by an external harmonic force, especially for the case of the large difference between spring stiffnesses in tension and compression. We will not restrict ourselves to small difference in stiffnesses, providing a more general analysis than the ones presented in Naugolnykh and Ostrovsky (1998) and Gavrilov and Herman (2012)
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