On the vibration of functionally graded annular plate with elastic edge supports and resting on Winkler foundation

ABSTRACT

The current paper deals with the exact solution of vibration analysis of functionally graded (FG) annular plate elastically restrained boundary conditions and resting on Winkler foundation. Hamilton’s principle has been applied to derive the motion equations of FG annular plate and associated boundary conditions based on the classical plate theory (CPT). It is assumed that the material properties have been graded through the direction of plate thickness according to power law distribution. The effects of some key system parameters such as normalised inner radius, non-dimensional foundation stiffness, non-dimensional transverse and rotational spring constants of the elastic boundary, volume fraction index and number of nodal diameters on the frequency parameter have been assessed in tabular and graphical forms. The accuracy of the present work has been validated by comparing the present results with those computed by previously published literatures.

KEYWORDS:

• Vibration analysis
• annular plate
• functionally graded material
• elastic boundary conditions
• Winkler foundation

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this theory-based study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Soheil Hashemi

Soheil Hashemigraduated from the K. N. Toosi University of Technology in 2020 with Master of science’s degree in Mechanical Engineering. His current research focuses on the nonlinear vibrations, nonlinear dynamics, and plates and shells analysis. He is a adjunct professor at the University of Torbat Heydarieh. It should be noted that he has been the leader of the team of authors of the present article.

Farshad Zamani

Farshad Zamaniis currently a Researcher Engineer in the Research and Development unit in an Industrial Knowledge-based Company. He is a graduate of the Isfahan University of Technology and preparing for admission to the doctoral program. He has taught a number of courses on Technical drawing and statics as TA. His research and publication interests include analysis of buckling and vibration, particularly in micro and nanoscales and His research activities are currently continuous, the major research theme that he is pursuing is focused on the buckling analysis of the nanoplates with the Finite Element and Finite difference methods.

Arash Eftekhari

Arash Eftekharireceived his Bachelor of Science (BSc) in field of Aerospace Engineering from the Khajeh Nasir Toosi University of Technology, Iran, in 2016. He completed his Master of Science (MSc), in field of Mechanical Engineering, from the University of Tehran in 2020. He is currently a Doctor of Philosophy (PhD) candidate student in field of Mechanical Vibrations at the Khajeh Nasir Toosi University of Technology, Iran. His research interests lie in the areas of vibration of continuous systems, smart materials and energy harvesting from the nonlinear vibrations.

Yasser Rostamiyan

Dr. Yasser Rostamiyan is a Associated Professor  of Mechanical Engineering Department at Islamic Azad University. Dr. Rostamiyan has 13 years in research in Materials and Design. From prior to coming to Azad University in 2010 he was active in the following research field: Fatigue analysis of conventional materials, Mechanical Design, Failure Analysis for Applications, Composite Materials, Nano composite, Finite element simulation, Impact mechanics, Design of pressure vessels and piping, Design of energy absorption and crashworthy elements. He supervised several, Bachelor, Master and Ph.D. thesis. Also he has more than 50 scientific papers in these mentioned fields.

Himan Khaledi

Himan Khaledi is a PhD candidate student in mechanical engineer with six years of research experience alongside the executive team of laboratory in Azad University of Technology, Aliabad-e-Katul, Iran. He graduated from Azad University of Technology in 2014 with a Master's Degree in Mechanical Engineering.

Mohamadreza Rajabi Reza Abadi

Mohamadreza Rajabi Reza Abadihas graduated with a Ph.D. degree in solid mechanics in 2019 from the University of Birjand and he is currently a lecturer at Kar Higher education Institute and Vali-e-Asr University of Rafsanjan. His research interest includes solid design, fatigue and residual stress analysis and also dynamics and vibration analysis.