FUNDAMENTAL FREQUENCY OF TRANSVERSE VIBRATION OF ORTHOTROPIC PLATES OF REGULAR POLYGONAL SHAPE CARRYING A CONCENTRATED MASS

1999 ◽  
Vol 221 (1) ◽  
pp. 175-179 ◽  
Author(s):  
P.A.A. Laura ◽  
R.H. Gutierrez
Keyword(s):  
Fundamental Frequency ◽  
Transverse Vibration ◽  
Orthotropic Plates ◽  
Concentrated Mass ◽  
Polygonal Shape

scholarly journals Free Transverse Vibration of Rectangular Orthotropic Plates with Two Opposite Edges Rotationally Restrained and Remaining Others Free

2018 ◽  
Vol 9 (1) ◽  
pp. 22 ◽  
Author(s):  
Yuan Zhang ◽  
Sigong Zhang
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Integral Transforms ◽  
Mode Shapes ◽  
Alternative Formulation ◽  
Orthotropic Plates ◽  
Engineering Structures ◽  
Current Design ◽  
Classical Boundary ◽  
Finite Integral

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications.

Mobility power flows of thin circular plate carrying concentrated masses based on structural circumferential periodicity

2016 ◽  
Vol 230 (17) ◽  
pp. 2996-3011
Author(s):  
Jun-hong Zhang ◽  
De-sheng Li
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Transverse Vibration ◽  
New Method ◽  
Concentrate Mass ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Parametric Effect ◽  
Analytical Results ◽  
Concentrated Masses

A new method was presented by utilizing the structural circumferential periodicity of the inertia excitation due to the concentrated masses to compute the transverse vibration for thin circular plate carrying concentrated masses. Comparison between the calculated fundamental frequency coefficients and those from other approaches validates the method. And then, the point mobility matrices and the power flows were solved on the basis of modal function solutions and the analytical results of simply supported case were presented. Finally, the parametric effect of the single concentrate mass on the power flows was investigated.

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