scholarly journals INVESTIGATION OF THE DYNAMIC BEHAVIOUR OF NON-UNIFORM THICKNESS CIRCULAR PLATES RESTING ON WINKLER AND PASTERNAK FOUNDATIONS

2020 ◽  
Vol 60 (2) ◽  
pp. 127-144
Author(s):  
Saheed Salawu ◽  
Gbeminiyi Sobamowo ◽  
Obanishola Sadiq
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Analytical Solutions ◽  
Dynamic Behaviour ◽  
Circumferential Stress ◽  
Thickness Variation ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Weighted Residuals ◽  
Elastic Foundations

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.

Primary Resonance of MEMS/NEMS Circular Plate Biosensors

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Dna Detection ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Van Der Waals Forces ◽  
Electrostatic Actuation ◽  
Circular Plates ◽  
Saddle Node Bifurcation ◽  
Saddle Node

This investigation deals with M/NEMS circular plates under electrostatic actuation. Such structures can be used as resonator sensors for medicine and biology applications such as virus, bacteria or DNA detection. The system consists of a clamped circular plate over a ground. The actuation of the plate is done through an AC voltage whose frequency is near half natural frequency of the plate. This produces a primary resonance to be used afterwards for sensing purposes. It is showed that a saddle-node bifurcation occurs. The effects of damping, voltage, Casimir, and van der Waals forces are predicted.

Parametric Resonance of MEMS Circular Plate Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Circular Plate ◽  
Parametric Resonance ◽  
Elastic Plate ◽  
Electrostatic Force ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate

This paper investigates parametric resonance of electrostatically actuated MEMS circular plates for resonator sensing applications. The system consists of a clamped circular elastic plate over a ground plate. Soft AC voltage of frequency near natural frequency of the plate gives the electrostatic force that leads the elastic plate into vibration, more specifically into parametric resonance which can be used afterwards for biosensing purposes. Frequency response and corresponding bifurcations are reported. The effects of damping and voltage are predicted.

Bending of fibre-reinforced composite circular plates of non-uniform thickness

1973 ◽  
Vol 8 (4) ◽  
pp. 253-259 ◽  
Author(s):  
H V Lakshminarayana ◽  
H Srinath
Keyword(s):  
Analytical Solutions ◽  
Epoxy Composite ◽  
Plate Theory ◽  
Composite Plates ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Classical Plate Theory ◽  
Varying Thickness ◽  
Reinforced Composite ◽  
Plate Equations

By use of classical plate theory complete analytical solutions are obtained for the bending of thin fibre-reinforced composite circular plates of radially varying thickness exhibiting rectangular orthotropy. The plate equations are solved for three specific cases of axisymmetric loading and boundary conditions. The solutions are presented in non-dimensional form. Numerical results are presented graphically for glass-epoxy composite plates.

Axi-Symmetric Buckling of Orthotopic Circular Plates with Variable Thickness

1967 ◽  
Vol 71 (675) ◽  
pp. 218-223 ◽  
Author(s):  
Sharad A. Patel ◽  
Franklin J. Broth
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Material Properties ◽  
Radial Direction ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Edge ◽  
Simply Supported

Axi-symmetric buckling of a circular plate having different material properties in the radial and circumferential directions was analysed in ref. 1. A plate with constant thickness and subjected to a uniform edge compression was considered. The plate edge was assumed clamped or simply-supported. The analysis of ref. 1 is extended to include plates with thickness variation in the radial direction.

Buckling of Orthotropic Circular Plates

1965 ◽  
Vol 69 (652) ◽  
pp. 279-280 ◽  
Author(s):  
K. A. V. Pandalai ◽  
Sharad A. Patel
Keyword(s):  
Circular Plate ◽  
Material Properties ◽  
Orthotropic Plate ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Axisymmetric Buckling

This Note is concerned with the axisymmetric buckling of orthotropic circular plates. A circular plate fabricated with radial and/or circumferential reinforcements may be idealised as an orthotropic plate of uniform thickness h having different material properties in the radial and circumferential directions.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

scholarly journals Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

2018 ◽  
Vol 38 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Yongqiang Yang ◽  
Zhongmin Wang ◽  
Yongqin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Coupling Coefficient ◽  
Inertial Force ◽  
Angular Speed ◽  
Circular Plates ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Friction Clutch

Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

The Method of Finite Differences in Solutions Concerning Circular Plate

2011 ◽  
Vol 490 ◽  
pp. 305-311
Author(s):  
Henryk G. Sabiniak
Keyword(s):  
Circular Plate ◽  
Finite Differences ◽  
Machine Building ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Technical Problems ◽  
Theory Of Plates ◽  
Worm Gearing ◽  
Mixed Derivatives ◽  
Plate Deflection

Finite difference method in solving classic problems in theory of plates is considered a standard one [1], [2], [3], [4]. The above refers mainly to solutions in right-angle coordinates. For circular plates, for which the use of polar coordinates is the best option, the question of classic plate deflection gets complicated. In accordance with mathematical rules the passage from partial differentials to final differences seems firm. Still final formulas both for the equation (1), as well as for border conditions of circular plate obtained in this study and in the study [3] differ considerably. The paper describes in detail necessary mathematical calculations. The final results are presented in identical form as in the study [3]. Difference of results as well as the length of arm in passage from partial differentials to finite differences for mixed derivatives are discussed. Generalizations resulting from these discussions are presented. This preliminary proceeding has the purpose of searching for solutions to technical problems in machine building and construction, in particular finding a solution to the question of distribution of load along contact line in worm gearing.

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