Free vibration of circular plates with elastic or rigid interior support

Azimi, Sajjad

doi:10.1016/0022-460x(88)90333-1

Cited by 34 publications

(8 citation statements)

References 5 publications

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“…The numerical results for fundamental frequencies of elastically supported circular plates are presented in Tables 1 and 2 with comparison to the results by Azimi (1988), Ding (1994), Wang and Wang. (2003).…”

Section: Resultsmentioning

confidence: 89%

Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Żur

2017

jtam

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Free vibration analysis of homogeneous and isotropic thin circular and annular plates with discrete elements such as elastic ring supports is considered. The general form of quasi--Green's function for thin circular and annular plates is obtained. The nonlinear characteristic equations are defined for thin circular and annular plates with different boundary conditions and different combinations of the core and support radius. The continuity conditions at the ring supports are omitted based on the properties of Green's function. The fundamental frequency of axisymmetric vibration has been calculated using the Newton-Raphson method and calculation software. The obtained results are compared with selected results presented in literature. The exact frequencies of vibration presented in a non-dimensional form can serve as benchmark values for researchers to validate their numerical methods when applied for uniform thin circular and annular plate problems.

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Section: Resultsmentioning

confidence: 89%

Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Żur

2017

jtam

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“…Azimi [12] used the modal expansion technique and the recptance method (essentially the same as the Green function method) for the free vibration analysis of circular plates with elastic or rigid interior supports on concentric circles in the plate.…”

Section: Analytical Formulationmentioning

confidence: 99%

“…In the present study, we follow the methods of Nicholson and Bergman [10,11] and Azimi [12]. The response of the system to harmonic forces applied by the three actuators is expressed in terms of the Green functions obtained by the modal analysis.…”

Section: Analytical Formulationmentioning

confidence: 99%

A Tip-Tilt Adaptive Optics System for Amateur Astronomers and Optimum Placement of Actuators

Chakraborty¹,

Behdinan

Tabarrok

1999

Journal of Sound and Vibration

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“…[1][2][3][4] Several researchers reviewed the literature on vibrations of circular plates with basic edge conditions and internal strengthening. [5][6][7][8][9] Detection of structural damage through analytical and experimental investigations of vibration characteristics of cracked plates has become essential for solving design analysis problems of various types of mechanical systems. The natural frequencies and mode shapes of cracked elastic circular plates considerably differ from their healthy counterparts.…”

Section: Introductionmentioning

confidence: 99%

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

Rao¹,

Rao²

2017

IJAV

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A thin circular plate with generally restrained periphery and weakened along an internal concentric circle due to a crack, is considered in this paper for studying its vibration characteristics. The frequency for first six modes of plate vibration is computed for varying values of radius of crack, elastic rotational and translational restraints, and the extent of weakening duly simulated by considering the crack as a rotational restraint on the plate. From the results obtained, it is observed that for a plate with translation and rotational restraints, the internal weakening decreases the fundamental frequency by around 31 per cent.

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Free vibration of circular plates with elastic or rigid interior support

Cited by 34 publications

References 5 publications

Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

A Tip-Tilt Adaptive Optics System for Amateur Astronomers and Optimum Placement of Actuators

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

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