Free vibration of cantilever quadrilateral plates

Srinivasan, R.; Babu, B.J.C.

doi:10.1121/1.389054

Cited by 24 publications

(14 citation statements)

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“…Consider now a sectorial plate domain having unit radius ( r ) , included angle ( a ) and polar co-ordinate origin at the reentrant corner of the skew plate shown in Figure 1 (12) Given that the power terms in r are non-zero, equation (1 1) reduces to which may be factored into…”

Section: Theoretical Formulation Shown Inmentioning

confidence: 99%

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Vibrations of cantilevered skewed plates with corner stress singularities

McGee¹,

Leissa²,

Huang³

1992

Numerical Meth Engineering

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SUMMARYAccurate natural frequencies of skewed cantilevered thin plates are determined using the Ritz method. The present work is the first known vibrational study of the effects of stress singularities at the reentrant corner of skewed plates. In conjunction with classical thin plate theory, the Ritz trial space of assumed transverse displacement functions consists of algebraic polynomials, which are mathematically complete, and corner functions, which account for the singular behaviour of bending stresses at the reentrant corner. The corner functions were derived approximately four decades ago to study the nature of the stress singularities which occur at sharp interior corners or crack tips of typical plane elasticity and plate bending problems. Accurate non-dimensional frequencies are calculated for thin plates having various side ratios and arbitrary degrees of skewness. Detailed numerical studies show that augmenting the Ritz trial space of polynomials with corner functions, having a co-ordinate origin at the reentrant corner, enhances the convergence of the upper-bound frequencies. The importance of using corner functions in skew plate vibrations is found to increase as the skew angle increases and as the side ratio decreases. Results obtained using the present method are compared with those obtained by other investigators using both theoretical and experimental methods.

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Section: Theoretical Formulation Shown Inmentioning

confidence: 99%

“…and F,(& A,) is now expressed as the general solution of the fourth-order differential equation (12), as follows:…”

Section: Theoretical Formulation Shown Inmentioning

confidence: 99%

Vibrations of cantilevered skewed plates with corner stress singularities

McGee¹,

Leissa²,

Huang³

1992

Numerical Meth Engineering

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show abstract

“…In acidic slurry a high Cu/SiO 2 polish rate can be easily achieved. Hence, most of the copper CMP studies have focused on acidic slurries [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. However, a disadvantage of the acidic slurries is the possible corrosion of the polishing equipment by the slurry [5].…”

Section: Introductionmentioning

confidence: 98%

Chemical mechanical planarization of copper in alkaline slurry with uric acid as inhibitor

Prasad

Ramanathan

2007

Electrochimica Acta

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“…Most of them propose chemical interaction between the ceria abrasive and the silicon dioxide surface [5,[7][8][9], while in situ frictional force measurements seem to indicate that the effect may be mainly mechanical [10]. Various additives have been used in ceria-based slurries to suppress the silicon nitride polish rate and maintain a high or moderate silicon dioxide polish rate, thus enhancing the selectivity [11][12][13]. The mechanism of action of these high selective slurries is not understood well.…”

Section: Introductionmentioning

confidence: 99%