Analytical modeling and vibration analysis of internally cracked rectangular plates

Joshi, P.V.; Jain, N. K.; Ramtekkar, Gangadhar

doi:10.1016/j.jsv.2014.06.028

Cited by 45 publications

(28 citation statements)

References 25 publications

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“…The equation of motion of an isotropic plate with two perpendicular continuous line cracks is presented by Joshi et al [15] which can be stated as…”

Section: Governing Equation Of Cracked Platementioning

confidence: 99%

“…y M and x M are the bending moments due to the crack length 2a and 2b respectively [15]. The work of Ismail and Cartmell [37] shows that the twisting moment xy M = yx M appears in the equation of motion of cracked plate only when the crack is inclined to the edges of the plate, hence it is neglected in Fig 3. Taking moment equilibrium about the x and the y axis one obtains …”

Section: Governing Equation Of Cracked Platementioning

confidence: 99%

“…They also calculated compliance coefficients for bending and tension considering crack depth to plate thickness ratio of 0.6 and concluded that with an increase in crack length the fundamental frequency decreases. Line spring model has also been used by Joshi et al [15] where the authors presented results for vibration analysis of isotropic plate containing two perpendicular continuous line cracks.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Gupta

Jain

Salhotra

et al. 2015

International Journal of Mechanical Sciences

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“…The equation of motion of an isotropic plate with two perpendicular continuous line cracks is presented by Joshi et al [15] which can be stated as…”

Section: Governing Equation Of Cracked Platementioning

confidence: 99%

Section: Governing Equation Of Cracked Platementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Gupta

Jain

Salhotra

et al. 2015

International Journal of Mechanical Sciences

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“…In this proposition, the free and forced vibration analyses of uniform and multipoints supported laminated rectangular plate resting on the Winkler and Pasternak foundations are studied in this paper. As we all know, there are many structural forms of plate in engineering applications, like stiffened plates [31][32][33][34], cracked rectangular plates [35][36][37][38], corroded plates [39][40][41][42][43], and so on. As the most common basic model, the rectangular plate structure is widely studied.…”

Section: Introductionmentioning

confidence: 99%

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Shi

Zhang

Wang

et al. 2017

Shock and Vibration

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An improved Fourier series method (IFSM) is applied to study the free and forced vibration characteristics of the moderately thick laminated composite rectangular plates on the elastic Winkler or Pasternak foundations which have elastic uniform supports and multipoints supports. The formulation is based on the first-order shear deformation theory (FSDT) and combined with artificial virtual spring technology and the plate-foundation interaction by establishing the two-parameter foundation model. Under the framework of this paper, the displacement and rotation functions are expressed as a double Fourier cosine series and two supplementary functions which have no relations to boundary conditions. The Rayleigh-Ritz technique is applied to solve all the series expansion coefficients. The accuracy of the results obtained by the present method is validated by being compared with the results of literatures and Finite Element Method (FEM). In this paper, some results are obtained by analyzing the varying parameters, such as different boundary conditions, the number of layers and points, the spring stiffness parameters, and foundation parameters, which can provide a benchmark for the future research.

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“…Stahl and Keer, 24 Huang and Leissa, 25 Huang et al, 26 Bachene et al, 27 and Liew et al 31 studied the vibration of cracked rectangular and square plate with central crack, side crack and inclined crack under different boundary conditions by different methods that include the Ritz method, Rayleigh-Ritz method and finite element method. Recently, Israr et al, 28 Ismail and Cartmell, 29 and Joshi et al 30 presented closed form solution for the vibration of cracked rectangular plate. This paper deals with the effect of central crack on natural frequencies of skew plate under six different combinations of edge conditions by the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rhombic Plate with Central Crack

Azam¹,

Ranjan²,

Kumar³

2017

IJAV

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In this paper, free vibration analysis of rhombic plate with pre-existing central crack has been done using the finite element method. The Mindlin theory of plate has been used in the process of investigation. The following six boundary conditions at the edges of the plate have been considered. They are simply supported at all edges (SSSS), clamped at all edges (CCCC), free at all edges (FFFF), clamped-simply supported (CSSC), clamped-free (CFFC), and clamped-free-simply supported (CSFS). Effects of crack length on natural frequencies of rhombic plate with different skew angles i.e. 15• , 30• , 45• , 60• have been studied. It is observed that percentage drop in fundamental frequency due to presence of central crack in the rhombic plate increases with an increase in skew angle for CCCC, SSSS, and CSSC edge conditions at a given crack ratio (non-dimensional crack length). Under the CFFC, CSFS, and FFFF edge conditions, percentage drop in natural frequency of rhombic plate is very small for crack ratio of 0.2 at different skew angles. In case of the CFFC edge condition of the rhombic plate, percentage drop in fundamental frequency is within 0.7% at all skew angles and with all crack ratios considered. Some of the results obtained by the present method have been compared with the published results. Most of the results obtained are novel for rhombic crack plate.

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Analytical modeling and vibration analysis of internally cracked rectangular plates

Cited by 45 publications

References 25 publications

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Free Vibration Analysis of Rhombic Plate with Central Crack

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