{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:06:34Z","timestamp":1782777994834,"version":"3.54.5"},"reference-count":48,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T00:00:00Z","timestamp":1586217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler\u2013Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.<\/jats:p>","DOI":"10.3390\/sym12040586","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T14:42:03Z","timestamp":1586443323000},"page":"586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters"],"prefix":"10.3390","volume":"12","author":[{"given":"Ali","family":"Shariati","sequence":"first","affiliation":[{"name":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9773-4884","authenticated-orcid":false,"given":"Dong won","family":"Jung","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Jeju National University, Jeju, Jeju-do 690-756, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3852-5473","authenticated-orcid":false,"given":"Hamid","family":"Mohammad-Sedighi","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1367-9609","authenticated-orcid":false,"given":"Krzysztof Kamil","family":"\u017bur","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1638-0338","authenticated-orcid":false,"given":"Mostafa","family":"Habibi","sequence":"additional","affiliation":[{"name":"Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran P.O. Box 11365-9567, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maryam","family":"Safa","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1115\/1.1849169","article-title":"Analysis and control of transverse vibrations of axially moving strings","volume":"58","author":"Chen","year":"2005","journal-title":"Appl. Mech. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.ijmecsci.2014.01.017","article-title":"Dynamics of axially moving continua","volume":"81","author":"Marynowski","year":"2014","journal-title":"Int. J. Mech. 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