Fundamental frequency and buckling load of circular plates with variable profile and non-uniform boundary conditions

1981 ◽  
Vol 78 (1) ◽  
pp. 147-153 ◽  
Author(s):  
G.M. Ficcadenti ◽  
P.A.A. Laura
Keyword(s):  
Boundary Conditions ◽  
Fundamental Frequency ◽  
Buckling Load ◽  
Circular Plates

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.

Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge

2007 ◽  
Author(s):  
George Weiss
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Bessel Functions ◽  
Unit Area ◽  
Continuous System ◽  
Modified Bessel Functions ◽  
Circular Plates ◽  
Numerical Parameter ◽  
Elliptical Plate ◽  
Distributed Load

Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate itself. Considering the mass per unit area of the plate, and substituting it in Dunkerley’s equation rearranged, we obtain a numerical parameter K02, related to the fundamental frequency of the plate, which has to be evaluated for each particular case. In this paper, have been evaluated the values of K02 for thin circular plates clamped or pinned at edge. An elliptical plate clamped at edge is also presented for several ratios of the semi–axes, one of which is identical with a circular plate.

A Unified Modeling Method for Dynamic Analyses of FGP Annular and Circular Plates with General Boundary Conditions

2021 ◽  
Author(s):  
J. Lu ◽  
X. Hua ◽  
C. Chiu ◽  
X. Zhang ◽  
S. Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Modeling Method ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Circular Plates ◽  
Unified Modeling ◽  
Dynamic Analyses ◽  
Vibration Responses

The porous material is an emerging lightweight material, which is able to reduce structural weight and also keeps the superiority of the structure. Therefore, this work is devoted to the investigation of the functionally graded porous (FGP) annular and circular plates with general boundary conditions. The unified modeling method is proposed by combining the first-order shear deformation theory, the virtual spring technology, the multi-segment partition method, and the semi-analysis Rayleigh–Ritz approach. Afterwards, the convergency and correctness of the proposed method are verified, respectively. The frequency parameters, modal shapes, and forced vibration responses are uniformly calculated based on the proposed method. Finally, the dynamic analyses of the FGP annular and circular plates with different parameters, such as the porosity distribution types, porosity ratios, boundary condition types, geometry parameters, and load types, are conducted in detail. It is found that the reasonable porous design is able to keep the dynamic stability of the structure under different parameter variations.

scholarly journals Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks

Materials ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1412 ◽  
Author(s):  
Meifung Tam ◽  
Zhicheng Yang ◽  
Shaoyu Zhao ◽  
Jie Yang
Keyword(s):  
Fundamental Frequency ◽  
Slenderness Ratio ◽  
Weight Fraction ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Reinforced Composite ◽  
Edge Cracks ◽  
Open Edge

This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young’s modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson’s ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.

Sign in / Sign up

Export Citation Format

Share Document