Stress and Deflection Analysis of a Glass Window (Circular Plate) Elastically Restrained Along Its Edge in a Photonic Device

2002 ◽  
Author(s):  
John H. Lau ◽  
Steve Erasmus ◽  
Yida Zou
Keyword(s):  
Circular Plate ◽  
Spring Constant ◽  
Engineering Practice ◽  
Thermal Coefficient ◽  
Circular Plates ◽  
Rotational Spring ◽  
Optical Coefficient ◽  
Deflection Analysis ◽  
Linear Spring ◽  
Elastically Restrained

An exact analysis is presented for the stresses and deflections of circular plates (glass windows) elastically restrained along its edge in a photonic device’s housing subjected to the pressure and temperature loadings. Dimensionless curves and charts are also provided for engineering practice convenience. These charts show the interactions of the deflection, stress, temperature, pressure, linear spring constant, rotational spring constant, geometry of the glass windows, and the Young’s modulus, Poisson’s ratio, thermal coefficient of expansion, geometry, stress-optical coefficient, and birefringence of glass materials. The results presented herein should be useful for designing glass windows for shipping, storing, handling, functioning, and reliability.

Thermal Stress and Deflection Analysis of a Glass Window (Circular Plate) Elastically Restrained Along its Edge in a Photonic Device

2003 ◽  
Vol 125 (4) ◽  
pp. 602-608
Author(s):  
John H. Lau ◽  
Steve Erasmus ◽  
Yida Zou
Keyword(s):  
Thermal Stress ◽  
Circular Plate ◽  
Spring Constant ◽  
Engineering Practice ◽  
Thermal Coefficient ◽  
Circular Plates ◽  
Optical Coefficient ◽  
Deflection Analysis ◽  
Linear Spring ◽  
Elastically Restrained

An exact analysis is presented for the stresses and deflections of circular plates (glass windows) elastically restrained along its edge in a photonic device’s housing subjected to the pressure and temperature loadings. Dimensionless curves and charts are also provided for engineering practice convenience. These charts show the interactions of the deflection, stress, temperature, pressure, linear spring constant, rotational spring constant, geometry of the glass windows, and the Young’s modulus, Poisson’s ratio, thermal coefficient of expansion, geometry, stress-optical coefficient, and birefringence of glass materials. The results presented herein should be useful for designing glass windows for shipping, storing, handling, functioning, and reliability.

Modal Analysis of Circular Plates

2014 ◽  
Vol 611 ◽  
pp. 245-251
Author(s):  
Jozef Bocko ◽  
Peter Sivák ◽  
Ingrid Delyová ◽  
Štefánia Šelestáková
Keyword(s):  
Circular Plate ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Engineering Practice ◽  
Structural Elements ◽  
Circular Plates ◽  
Structural Element ◽  
Thin Circular Plate ◽  
Outer Periphery ◽  
Modes Of Vibration

In engineering practice, some of the structural elements take the form of a thin planar plate. For such elements, it is sometimes important to consider dangerous condition of resonance. A structural element cannot operate in the range of resonant frequencies. It is therefore necessary to determine natural frequencies and normal modes of vibration of such structural elements. Parts of the paper are the results of the analysis of natural frequencies and normal modes of vibration using FEM program Cosmos. The subject of the analysis was a thin flat circular plate considered in three modifications, i.e. free thin circular plate without hole, a thin circular plate without hole, clamped on the outer periphery, a thin circular plate with a hole, clamped on the outer and inner circumference. At the same time, Chladni patterns were obtained. They were created using the Matlab system and extraction of the outputs of the Cosmos program.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

Elasto-Plastic Large Deflection Analysis of a Copper Film

1992 ◽  
Vol 114 (2) ◽  
pp. 221-225
Author(s):  
J. H. Lau
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plastic Strain ◽  
Mechanical Behavior ◽  
Effective Stress ◽  
Large Deflection ◽  
Applied Pressure ◽  
Copper Film ◽  
Engineering Practice ◽  
Deflection Analysis

The ductility of a copper film has been determined by an elastoplastic large deflection finite element method. The effective stress and incremental plastic strain and pressure-deflection curves of the copper film have also been provided for a better understanding of its mechanical behavior. Furthermore, for engineering practice convenience, the ductility and effective stress of the copper film have been plotted as functions of measurable variables, i.e., applied pressure and deflection at the center of the bulge.

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.

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.

Circular Plates Under Hard Excitations to Include Casimir Effect: Amplitude-Voltage Response of Superharmonic Resonance of Second Order

2020 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Jonathan Perez
Keyword(s):  
Circular Plate ◽  
Casimir Effect ◽  
Second Order ◽  
Peak Amplitude ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Circular Plates ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated

Abstract This paper deals with voltage-amplitude response of superharmonic resonance of second order of electrostatically actuated clamped MEMS circular plates. A flexible MEMS circular plate, parallel to a ground plate, and under AC voltage, constitute the structure under consideration. Hard excitations due to voltage large enough and AC frequency near one fourth of the natural frequency of the MEMS plate resonator lead the MEMS plate into superharmonic resonance of second order. These excitations produce resonance away from the primary resonance zone. No DC component is included in the voltage applied. The equation of motion of the MEMS plate is solved using two modes of vibration reduced order model (ROM), that is then solved through a continuation and bifurcation analysis using the software package AUTO 07P. This predicts the voltage-amplitude response of the electrostatically actuated MEMS plate. Also, a numerical integration of the system of differential equations using Matlab is used to produce time responses of the system. A typical MEMS silicon circular plate resonator is used to conduct numerical simulations. For this resonator the quantum dynamics effects such as Casimir effect are considered. Also, the Method of Multiple Scales (MMS) is used in this work. All methods show agreement for dimensionless voltage values less than 6. The amplitude increases with the increase of voltage, except around the dimensionless voltage value of 4, where the resonance shows two saddle-node bifurcations and a peak amplitude significantly larger than the amplitudes before and after the dimensionless voltage of 4. A light softening effect is present. The pull-in dimensionless voltage is found to be around 16. The effects of damping and frequency on the voltage response are reported. As the damping increases, the peak amplitude decreases. while the pull-in voltage is not affected. As the frequency increases, the peak amplitude is shifted to lower values and lower voltage values. However, the pull-in voltage and the behavior for large voltage values are not affected.

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