Dynamics of axially moving continua

• The first review on dynamics of axially moving plate-like systems.
• Observed for many years great interest in research dynamics of moving systems.
• Vviscoelastic properties significantly affect the dynamics of the moving continua.
• Many issues in this field should be examined in the future.

Dynamics of axially moving material continuum is investigated for over 60 years. Research interest in this subject is still high due to more and more new fields of application. Alongside traditional applications, such as band saws’ blades and axially moving paper webs, appeared as flat objects moving at high speeds in space. Recently many studies on the dynamics of axially moving beam-like and plate-like systems were published. Inclusion in analysis viscoelastic properties of broad moving continua is also the subject of research. The paper presents a review of research in this field with particular emphasis on the axially moving plate-like elastic and viscoelastic systems. Unlike the string-like and beam-like systems, such review on the plate-like systems has not been published yet. A brief overview of the most important studies on the dynamics of moving string-like and beam-like systems is presented as well. This paper also includes a comparative analysis of some results of studies published by the authors in the field of dynamics of axially moving viscoelastic systems. Some suggestions on the directions of further research in this field end the paper.