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Free vibration and thick generally laminated cantilever quadrilateral plates
An approximate approach has been developed to analyze the natural frequencies of generally laminated, thick, skew, trapezoidal plates with various edge supports. In this method, Chebychev polynomials are used as trial functions in the Rayleigh-Ritz method as applied to an first-order shear deformation theory (FSDT) formulation. Although the present method is applicable to any edge-supported plate, in the current study, skew, trapezoidal, cantilever plates are compared with published results when possible, and results for thick plates are presented. Since laminated plate vibrations are dependent upon a great number of variables, including angular stacking sequence and material stacking sequence, the frequency parameters presented are not as useful in design as those for isotropic plates. It is not the intent of this study to present design information but to make available data for comparative purposes with other methods, data that are not available at this time in the literature. Lastly, since this simple approach yields accurate results for a large variety of plates without the necessity of choosing functions that satisfy the essential boundary conditions, it can be easily implemented for design or optimization calculations. The collection of results, representing a large variation of planforms for both symmetrically and unsymmetrically laminated, thick, skew, trapezoidal, cantilever plates clearly show some general qualitative trends for the frequency. They are as follows: 1) as the value of q, a measure of span, increases, the frequency decreases; 2) as the sweep angle beta moves away from 0 deg in either the positive or negative direction, the frequency generally tends to increase; 3) as the taper ratio increases, the frequency decreases; 4) for bending modes, the value of the frequency decreases as the fiber orientation angle Theta moves away from 0; and 5) for torsional modes, the value of the frequency as a function of the fiber orientation angle Theta is dependent upon the geometric parameters.
Free vibration and thick generally laminated cantilever quadrilateral plates
An approximate approach has been developed to analyze the natural frequencies of generally laminated, thick, skew, trapezoidal plates with various edge supports. In this method, Chebychev polynomials are used as trial functions in the Rayleigh-Ritz method as applied to an first-order shear deformation theory (FSDT) formulation. Although the present method is applicable to any edge-supported plate, in the current study, skew, trapezoidal, cantilever plates are compared with published results when possible, and results for thick plates are presented. Since laminated plate vibrations are dependent upon a great number of variables, including angular stacking sequence and material stacking sequence, the frequency parameters presented are not as useful in design as those for isotropic plates. It is not the intent of this study to present design information but to make available data for comparative purposes with other methods, data that are not available at this time in the literature. Lastly, since this simple approach yields accurate results for a large variety of plates without the necessity of choosing functions that satisfy the essential boundary conditions, it can be easily implemented for design or optimization calculations. The collection of results, representing a large variation of planforms for both symmetrically and unsymmetrically laminated, thick, skew, trapezoidal, cantilever plates clearly show some general qualitative trends for the frequency. They are as follows: 1) as the value of q, a measure of span, increases, the frequency decreases; 2) as the sweep angle beta moves away from 0 deg in either the positive or negative direction, the frequency generally tends to increase; 3) as the taper ratio increases, the frequency decreases; 4) for bending modes, the value of the frequency decreases as the fiber orientation angle Theta moves away from 0; and 5) for torsional modes, the value of the frequency as a function of the fiber orientation angle Theta is dependent upon the geometric parameters.
Free vibration and thick generally laminated cantilever quadrilateral plates
Freie Schwingungen von dicken, allgemein üblich laminierten Krag-Rechteckplatten
Kapania, R.K. (author) / Lovejoy, A.E. (author)
AIAA Journal ; 34 ; 1474-1486
1996
13 Seiten, 12 Bilder, 9 Tabellen, 36 Quellen
Article (Journal)
English
Platte (Bauteil) , Schichtstoff , freie Schwingung , Rechteck , Schichtdicke , Scherspannung , Querrichtung , Polynom , Verlagerung , Verformung , Trägheit , Randbedingung , Feder (Federungselement) , mathematisches Modell , Integralgleichung , Differenzialgleichung , Resonanzfrequenz , Leitwerk (Flugzeug) , Variationsrechnung , Optimierung , Pfeilflügel , Biegebeanspruchung , Torsion , Näherungsverfahren , Konvergenz , Schwingungsform
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