Mono-coupled periodic systems with a single disorder: Free wave propagation

Abstract

A general method has been presented for analyzing free harmonic wave propagation through a mono-coupled periodic system with a single disorder. Expressions have been derived for the magnitudes of the waves transmitted and reflected by the disorder. These general expressions have then been used to study flexural wave motion through a periodic beam system into which three different types of disorder have been introduced: (i) a beam element of non-periodic length; (ii) a rotary mass at a support; (iii) a rotary spring at a support. The disorder always results in reduced transmission of the flexural wave when the frequency is in a frequency propagation zone of the periodic system but the first two disorders may lead to increased transmission in a frequency attenuation zone. Conditions have been identified under which the combined disorder plus periodic system can behave like a resonating spring-mass system, or as a spring-mass damper system. The adverse effects of resonating disorders are pointed out. Qualitative and quantitative analysis based upon computer studies have indicated how disorders can be used most effectively for vibration isolation in existing periodic systems or when designing new systems.