Abstract
In this paper, free vibration characteristics of stepped rectangular plates have been studied by using the dynamic stiffness method (DSM). The first-order shear deformation theory (FSDT) is used to obtain the governing differential equations of motions. Taking Levy-type plates into account, the displacements and the force boundary conditions are applied at the appropriate edges to develop a dynamic stiffness matrix. The Wittricks–Williams algorithm is used to solve the global dynamic stiffness matrix for computing the plate's natural frequencies with reasonably high accuracy. The complete analysis has been carried out in a computer program using MATLAB. The frequency results using the DSM are compared with the published results wherever possible. Finally, the effect of various plate parameters on the free vibration behavior of various stepped plates has been studied and important results are reported.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mori T, Hiramatsu T, Shamoto E (2011) Simultaneous double-sided milling of flexible plates with high accuracy and high efficiency–suppression of forced chatter vibration with synchronized single-tooth cutters. Precis Eng 35(3):416–423
Stone B (2014) Chatter and machine tools. Springer International, New York
Lee J, Bergman L (1994) The vibration of stepped beams and rectangular plates by an elemental dynamic flexibility method J Sound Vib 171(5):617–40
Takabatake H, Imaizumi T, Okatomi K (1995) Simplified analysis of rectangular plates with stepped thickness. J Struct Eng 121(1):28–38
Jaworski J, Dowell E (2007) Free vibration of a cantilevered beam with multiple steps: comparison of several theoretical methods with experiment. J Sound Vib 312(4):713–725
Wang G, Unal A (2013) Free vibration of stepped thickness rectangular plates using spectral finite element method. J Sound Vib 332(18):4324–4338
Chopra I (1974) Vibration of stepped thickness plates. Int J Mech Sci 16:337–344
Guo S, Keane A, Moshrefi-Torbati M (1997) Vibration analysis of stepped thickness plates. J Sound Vib 204(4):645–657
Boscolo M, Banerjee JR (2011) Dynamic Stiffness elements and their application for plates using first order shear deformation theory. Comput Struct 89(3):395–410
Wittrick WH, Williams FW (1971) A general algorithm for computing natural frequencies of elastic structures. Quart J Mach Appl Math 24(3):263–284
Banerjee JR (1997) Dynamic stiffness formulation for structural elements: a general approach. Comput Struct 63(1):101–103
Kumar S, Ranjan V, Jana P (2018) Free vibration analysis of thin functionally graded rectangular plates using the dynamic stiffness method. Comput Struct 197:39–53
Kumar S, Jana P (2019) Application of dynamic stiffness method for accurate free vibration analysis of sigmoid and exponential functionally graded rectangular plates. Int J Mech Sci 163:105–121
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kumar, R., Jana, P. (2022). Dynamic Stiffness Method for Free Vibration Analysis of Stepped Plate Using the First-Order Shear Deformation Theory. In: Maiti, D.K., et al. Recent Advances in Computational and Experimental Mechanics, Vol II. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-6490-8_4
Download citation
DOI: https://doi.org/10.1007/978-981-16-6490-8_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-6489-2
Online ISBN: 978-981-16-6490-8
eBook Packages: EngineeringEngineering (R0)