Transverse vibration of a circular plate with unidirectional quadratic thickness variation

1996 ◽  
Vol 38 (4) ◽  
pp. 423-430 ◽  
Author(s):  
Bani Singh ◽  
Vipin Saxena
1979 ◽  
Vol 22 (167) ◽  
pp. 642-647 ◽  
Author(s):  
Kosuke NAGAYA ◽  
Yoshitaro HIRANO ◽  
Katsutoshi OKAZAKI

2020 ◽  
Vol 60 (2) ◽  
pp. 127-144
Author(s):  
Saheed Salawu ◽  
Gbeminiyi Sobamowo ◽  
Obanishola Sadiq

The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration.


2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Desheng Li ◽  
Junhong Zhang

When calculating the vibration or sound power of a vibration source, it is necessary to know the point mobility of the supporting structure. A new method is presented for the calculation of point mobility matrix of a thin circular plate with concentrated masses in this paper. Transverse vibration mode functions are worked out by utilizing the structural circumferential periodicity of the inertia excitation produced by the concentrated masses. The numerical vibratory results, taking the clamped case as an instance, are compared to the published ones to validate the method for ensuring the correctness of mobility solution. Point mobility matrix, including the driving and transfer point mobility, of the titled structure is computed based on the transverse vibration solution. After that, effect of the concentrated masses on the mechanical point mobility characteristics is analyzed.


Author(s):  
Jun-hong Zhang ◽  
De-sheng Li

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.


2020 ◽  
pp. 107754632092688
Author(s):  
Reeta Bhardwaj ◽  
Naveen Mani ◽  
Amit Sharma

Time period of natural transverse vibration of a nonhomogeneous skew (parallelogram) plate with variable thickness and temperature field has been investigated on clamped CCCC and combination of clamped and simply supported CSCS edge conditions. The thickness variation on the plate is assumed to be linear in two dimensions, and the temperature variation on the plate is considered to be parabolic in two dimensions. For nonhomogeneity, authors considered circular variation in density. The Rayleigh–Ritz technique is applied to solve the differential equation of motion. A comparative analysis of frequency modes of the present study with the available published result is also given to support the present findings. The convergence study of obtained results is also presented with the help of figures.


2018 ◽  
Vol 8 (12) ◽  
pp. 2542 ◽  
Author(s):  
Abhijeet Chatterjee ◽  
Vinayak Ranjan ◽  
Mohammad Azam ◽  
Mohan Rao

This paper compares the vibroacoustic behavior of a tapered annular circular plate having different parabolic varying thickness with different combinations of rectangular and concentric stiffener patches keeping the mass of the plate and the patch constant for a clamped-free boundary condition. Both numerical and analytical methods are used to solve the plate. The finite element method (FEM) is used to determine the vibration characteristic and both Rayleigh integral and FEM is used to determine the acoustic behavior of the plate. It is observed that a Case II plate with parabolic decreasing–increasing thickness variation for a plate with different stiffener patches shows reduction in frequency parameter in comparison to other cases. For acoustic response, the variation of peak sound power level for different combinations of stiffener patches is investigated with different taper ratios. It is investigated that Case II plate with parabolic decreasing–increasing thickness variation for an unloaded tapered plate as well as case II plate with 2 rectangular and 4 concentric stiffeners patches shows the maximum sound power level among all variations. However, it is shown that the Case III plate with parabolically increasing–decreasing thickness variation with different combinations of rectangular and concentric stiffeners patches is least prone to acoustic radiation. Furthermore, it is shown that at low forcing frequency, average radiation efficiency with different combinations of stiffeners patches remains the same, but at higher forcing frequency a higher taper ratio causes higher radiation efficiency, and the radiation peak shifts towards the lower frequency and alters its stiffness as the taper ratio increases. Finally, the design options for peak sound power actuation and reduction for different combinations of stiffener patches with different taper ratios are suggested.


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