Abstract
Natural frequencies of different thick triangular plates subject to classical boundary conditions are found based on a proposed shear deformation plate theory in this chapter. The stress distribution needs no shear correction factor in this proposed plate theory. The numerical formulation is performed by means of Rayleigh–Ritz method to obtain the generalized eigenvalue problem. The aim of this study is to find the effect of different physical and geometric parameters on natural frequencies. New results along with 3D mode shapes have been evaluated after the test of convergence and validation with the available results.
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Notes
- 1.
Boundary Conditions.
References
Ansari R, Torabi J, Hassani R (2019) A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates. Eng Struct 181:653–669
Aydogdu M (2009) A new shear deformation theory for laminated composite plates. Compos Struct 89:94–101
Bhat RB (1987) Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables. J Sound Vib 114(1):65–71
Cheng ZQ, Batra RC (2000) Exact correspondece between eigenvalues of membranes and functionally graded simply supported polygonal plates. J Sound Vib 229(4):879–895
Cheung YK, Zhou D (2002) Three-dimensional vibration analysis of clamped and completely free isosceles triangular plates. Int J Solids Struct 39:673–687
Gorman DJ (1983) A highly accurate analytical solution for free vibraion analysis of simply supported right triangular plates. J Sound Vib 89(1):107–118
Gorman DJ (1986) Free vibration analysis of right triangular plates with combinations of clamped-simply supported boundary conditions. J Sound Vib 106(3):419–431
Gorman DJ (1989) Accurate free vibration analysis of right triangular plate with one free edge. J Sound Vib 131(1):115–125
Hosseini-Hashemi S, Fadaee M, Taher HRD (2011) Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third order shear deformation plate theory. Appl Math Model 35:708–727
Kang SW, Lee JM (2001) Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type functions. J Sound Vib 242(1):9–26
Lv X, Shi D (2018) Free vibration of arbitrary-shaped laminated triangular thin plates with elastic boundary conditions. Results Phys 11:523–533
Mirza S, Bijlani M (1985) Vibration of triangular plates of variable thickness. Comput Struct 21:1129–1135
Pradhan KK, Chakraverty S (2016) Natural frequencies of equilateral triangular plates under classical edge supports. In: Symposium on Statistical & Computational Modelling with Applications (SymSCMA—2016), Nov 2016, pp 30–34
Sakiyama T, Huang M (2000) Free-vibration analysis of right triangular plates with variable thickness. J Sound Vib 234(5):841–858
Saliba HT (1990) Transverse free vibration of simply supported right triangular thin plates: a highly accurate simplified solution. J Sound Vib 139(2):289–297
Shimpi RP, Patel HG (2006) Free vibrations of plates using two variable refined plate theory. J Sound Vib 296:979–999
Shimpi RP, Patel HG, Arya H (2007) New first-order shear deformation plate theories. J Appl Mech 74:523–533
Singh B, Chakraverty S (1992) Transverse vibration of triangular plates using characteristic orthogonal polynomials in two variables. Int J Mech Sci 34(12):947–955
Singh B, Saxena V (1996) Transverse vibration of triangular plates with variable thickness. J Sound Vib 194(4):471–496
Thai CH, Ferreira AJM, Bordas SPA, Rabczuk T, Nguyen-Xuan H (2014) Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory. Eur J Mech A Solids 43:89–108
Wanji C, Cheung YK (1998) Refined triangular discrete Kirchoff plate element for thin plate bending, vibration and buckling analysis. Int J Numer Meth Eng 41:1507–1525
Xiang S, Wang K, Ai Y, Sha Y, Shi H (2009) Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories. Compos Struct 91:31–37
Zhong HZ (2000) Free vibration analysis of isosceles triangular Mindlin plates by the triangular differential quadrature method. J Sound Vib 237(4):697–708
Acknowledgements
The first author is thankful for the funding provided by NPIU (TEQIP-III) against TEQIP-009582 and also Parala Maharaja Engineering College, Berhampur for permitting smooth progress in terms of official provisions.
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Pradhan, K.K., Chakraverty, S. (2020). Transverse Vibration of Thick Triangular Plates Based on a Proposed Shear Deformation Theory. In: Chakraverty, S., Biswas, P. (eds) Recent Trends in Wave Mechanics and Vibrations. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0287-3_1
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DOI: https://doi.org/10.1007/978-981-15-0287-3_1
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