A simplified plate theory for vibration analysis of composite laminated sector, annular and circular plate

2019 ◽  
Vol 143 ◽  
pp. 106252 ◽  
Author(s):  
Hong Zhang ◽  
Rupeng Zhu ◽  
Dongyan Shi ◽  
Qingshan Wang
Keyword(s):  
Circular Plate ◽  
Vibration Analysis ◽  
Plate Theory

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

2020 ◽  
Vol 36 (4) ◽  
pp. 465-484
Author(s):  
Ankur Gupta ◽  
Shashank Soni ◽  
N. K. Jain
Keyword(s):  
Governing Equation ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Multiple Cracks ◽  
Arbitrary Orientation ◽  
Response Curves ◽  
Classical Plate Theory ◽  
Orientation Gradient

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

On the Existence of a Solution for a Solid Circular Plate Bilaterally Supported Along Two Antipodal Boundary Arcs and Loaded by a Central Transverse Concentrated Force

2000 ◽  
Vol 68 (5) ◽  
pp. 809-812 ◽  
Author(s):  
G. Monegato ◽  
A. Strozzi
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Reaction Force ◽  
Mechanical Analysis ◽  
Square Root ◽  
Existence Of A Solution ◽  
Concentrated Force ◽  
Boundary Constraints ◽  
Title Problem ◽  
The One

A purely flexural mechanical analysis is presented for a thin, solid, circular plate, deflected by a central transverse concentrated force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. This problem is modeled in terms of a singular integral equation of the Prandtl type, which possesses a unique solution expressed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the requested boundary constraints. It is therefore concluded that, within the framework of the purely flexural plate theory, the title problem cannot admit the weighted L2 solution here examined. It cannot, however, be excluded that a solution to the title problem exists, which possesses stronger endpoint singularities than those examined in this paper, or is of a more general form than the one considered here.

A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

2002 ◽  
Vol 02 (02) ◽  
pp. 163-184 ◽  
Author(s):  
A. CHAKRABARTI ◽  
A. H. SHEIKH
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Higher Order ◽  
Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

Axisymmetric vibration analysis of isotropic circular plate with attached annular piezoceramic plate

2012 ◽  
Vol 8 (4) ◽  
pp. 302 ◽  
Author(s):  
Syed Noh Syed Abu Bakar ◽  
Mostafa M. Abdalla ◽  
Waleed F. Faris ◽  
Sany Izan Ihsan
Keyword(s):  
Circular Plate ◽  
Vibration Analysis ◽  
Axisymmetric Vibration ◽  
Piezoceramic Plate

Semi-Active Control of Sound Radiated From an Elastic Circular Plate Integrated With Adaptive Tuned Vibration Absorbers

2016 ◽  
Author(s):  
Masoud Hemmatian ◽  
Ramin Sedaghati
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Integral Approach ◽  
Shear Mode ◽  
Transverse Displacement ◽  
Vibration Absorbers ◽  
Classical Plate Theory ◽  
Low Frequencies ◽  
Control Applications ◽  
Radiated Sound

While adaptive tuning of vibration absorbers (ATVA) have been widely studied for vibration control applications, limited studies have been done to explore their potential for noise control applications. This study aims to utilize magnetorheological elastomer (MRE)-based ATVA to control the radiated sound from an elastic plate excited by a plane wave especially at low frequencies. Radiated sound from a clamped circular plate integrated with MRE-based ATVA is analytically studied using classical plate theory. Rayleigh integral approach is, then, used to express the transmitted sound pressure in terms of the plate’s displacement modal amplitude. A MRE-based ATVA under shear mode is investigated. The semi-active Skyhook controller is proposed to attenuate the transverse displacement of the plate and subsequently reduce the radiated sound. The controller determines the current input to the electromagnet and tunes the MRE-based ATVA with the desired stiffness.

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