RESEARCH ON THE TYMPANIC MEMBRANE FREE VIBRATION MODEL BASED ON THIN PLATE THEORY

2017 ◽  
Vol 17 (05) ◽  
pp. 1750079
Author(s):  
CAN WU ◽  
JING NI ◽  
XIAO YANG ◽  
JIANRONG LANG
Keyword(s):  
Free Vibration ◽  
Tympanic Membrane ◽  
Natural Frequency ◽  
Plate Theory ◽  
Fundamental Solutions ◽  
Anatomic Structure ◽  
Vibration Model ◽  
Thin Plate Theory ◽  
Natural Vibration Mode ◽  
Analytical Expressions

Myringoplasty is one of the routine surgeries in the treatment of tympanic membrane (TM) perforation. Since the anatomic structure of the middle ear cannot be simulated in clinical treatment, the surgery is mainly directed by experiences. Based on the mechanical properties of TM in the anatomy, four hypotheses are presented and TM is simplified as a sectorial annulus plate with fixed boundary condition. This paper proposes a free vibration model of TM. Its natural frequencies of free vibration are obtained by variables separation method and Bessel function. The system of fundamental solutions of fourth-order homogeneous equations can be solved for the analytical expressions of corresponding natural vibration mode. The theoretical model is proved to be valid since the natural frequency of the model is consistent with the experimental data. The effect of geometric parameters and material parameters on TM natural frequency is subsequently discussed in the numerical examples. Especially, the diameter and thickness of TM will cause different natural frequency errors above 40%, while the Young’s modulus and density of TM cause errors below 15% as well.

Prediction of Vibration Properties of Sandwich Panel Using Thick Plate Theory

2001 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Free Vibration ◽  
Thick Plate ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Vibration Properties ◽  
Proposed Model ◽  
Thin Plate Theory

Abstract The vibration of a sandwich panel with two identical isotropic facesheets and an orthotropic core was studied. The governing partial differential equation was derived using variational principle. Kirchhoff’s theory was applied to describe the deformation of the panel, and the rotational effect was taken into consideration. The frequencies of free vibration of a rectangular panel can be predicted based on the proposed analytical model. Results based on the proposed model were compared with those from thin plate theory. The effect of orthotropic core on frequencies was also discussed.

scholarly journals Free vibration model and theoretical solution of the tympanic membrane

2016 ◽  
Vol 21 (sup1) ◽  
pp. 61-68 ◽  
Author(s):  
Can Wu ◽  
Ying Chen ◽  
M. S. H. Al-Furjan ◽  
Jing Ni ◽  
Xiao Yang
Keyword(s):  
Free Vibration ◽  
Tympanic Membrane ◽  
Theoretical Solution ◽  
Vibration Model

An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates

2017 ◽  
Vol 24 (18) ◽  
pp. 4130-4144 ◽  
Author(s):  
AS Rezaei ◽  
AR Saidi
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Geometrical Parameters ◽  
Inviscid Fluid ◽  
Interconnected Network ◽  
Various Boundary Conditions ◽  
Annular Sector

An exact analytical approach based on Mindlin plate theory is considered for free vibration analysis of fluid-saturated porous annular sector plates. The interconnected network of pores is saturated by inviscid fluid and the fluid is trapped in the network. The plate’s radial edges are considered to be simply supported and four auxiliary functions are used to evaluate the natural frequencies of porous plates under undrained condition. The mechanical properties of the material are considered to vary through the thickness by expressing shear modulus and density in terms of a simple cosine rule in case of plates with pores free of fluid. The present method is validated by comparing it with the results of other accurate solutions found in the literature. The influence of the coefficient of plate porosity, geometrical parameters as well as the effect of fluid on natural frequency response of porous annular sector plates under various boundary conditions are comprehensively investigated. It is found that the presence of fluid in the interconnected network of pores causes the fundamental natural frequency to increase. The method proposed in this paper may provide useful information for the future assessments of the dynamic response of porous structures when fluid–solid interaction effects are fully taken into account.

Free Vibration Analysis of a PEMFC Using the Finite Element Method

2010 ◽  
Author(s):  
Hasnet E. U. Ahmed ◽  
Jean W. Zu ◽  
Aimy Bazylak
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Gas Diffusion ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Maximum Displacement

In this study, a free vibration analysis of a polymer electrolyte membrane fuel cell (PEMFC) is performed by modelling the PEMFC as a composite plate structure. The membrane, gas diffusion electrodes, and bi-polar plates are modelled as composite material plies. Energy equations are derived based on the Mindlin plate theory, and natural frequencies and mode shapes of the PEMFC are calculated using finite element modelling. A parametric study is conducted to investigate how the natural frequency varies as a function of thickness, Young’s modulus, and density for each component layer. It is observed that increasing the thickness of the bi-polar plates has the most significant effect on the lowest natural frequency, with a 25% increase in thickness resulting in an 11% increase in the natural frequency. The mode shapes of the PEMFC provide insight into the maximum displacement exhibited as well as the stresses experienced by the material under various vibration conditions.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

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.

Investigation of Strength and Dynamic Characteristics for the Rolling Mill

2013 ◽  
Vol 706-708 ◽  
pp. 1405-1408
Author(s):  
Xi Ping Guo ◽  
Shuang Zhou
Keyword(s):  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Rolling Mill ◽  
Maximum Stress ◽  
Weak Link ◽  
Deformation Analysis ◽  
Vibration Model ◽  
Strength And Stiffness ◽  
Stress And Deformation ◽  
Diagram Analysis

Stress and deformation analysis of 950 mill housing was done by means of ANSYS to calculate the maximum stress and deformation. Strength and stiffness of the mill roll were checked to meet requirements. Carries on the modal analysis to the rolling-mill housing, obtains its first 10 steps the natural frequency and the mode of vibration, through the vibration model diagram analysis frame of the weak link,and it is significant for similar mill housing designs.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

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