scholarly journals Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

2019 ◽  
Vol 110 ◽  
pp. 01045 ◽  
Author(s):  
Dadakhon Khodzhaev ◽  
Bakhodir Normuminov ◽  
Yazdan Mustapakulov ◽  
Angela Mottaeva
Keyword(s):  
Variable Thickness ◽  
Viscoelastic Properties ◽  
Shallow Shell ◽  
Dynamic Instability ◽  
Rheological Parameters ◽  
Periodic Load ◽  
Weakly Singular Kernel ◽  
Initial Shape ◽  
Aspect Ratios ◽  
Parametric Oscillations

The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.

scholarly journals To Calculation of Rectangular Plates on Periodic Oscillations

2018 ◽  
Vol 245 ◽  
pp. 01003 ◽  
Author(s):  
Rustamkhan Abdikarimov ◽  
Dadakhan Khodzhaev ◽  
Nikolay Vatin
Keyword(s):  
Variable Thickness ◽  
Dynamic Instability ◽  
Rheological Parameters ◽  
Problem Solution ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Weakly Singular Kernel ◽  
Parametric Oscillations ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

Geometrically nonlinear mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic plate of variable thickness is developed using the classical Kirchhoff-Love hypothesis. The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric oscillations of viscoelastic orthotropic plates of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors are taken into account. The results obtained are in good agreement with the results and data of other authors.

Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance

2017 ◽  
Vol 24 (19) ◽  
pp. 4419-4432 ◽  
Author(s):  
Airong Liu ◽  
Zhicheng Yang ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Damping Ratio ◽  
Analytical Investigation ◽  
Engineering Practice ◽  
Test Results ◽  
Periodic Load ◽  
Shallow Arches ◽  
Excitation Frequencies ◽  
Critical Regions

When an arch is subjected to a periodic load, it may lose in-plane stability dynamically owing to parametric resonance. Previous investigations have been concentrated on in-plane dynamic buckling of pin-ended shallow arches. However, in engineering practice, fixed arches with different rise-to-span ratios are often encountered. Little research on in-plane dynamic instability of deep fixed arches has been reported in the literature. This paper is concerned with experimental and analytical investigations for in-plane dynamic instability of fixed circular arches with rise-to-span ratios 1/8–1/2 under a central periodic load owing to parametric resonance. Experiments are carried out to determine the in-plane frequency and damping ratio of arches, to investigate critical regions of frequencies and amplitudes of the periodic load for in-plane dynamic instability of arches, and to explore effects of the rise-to-span ratio and additional weights on dynamic instability. The analytical method for determining the region of excitation frequencies and amplitudes of the periodic load causing in-plane instability of the arch is established using the Hamilton’s principle by accounting for effects of additional concentrated weights. Comparisons of analytical solutions with test results show that they agree with each other quite well. These results show that the rise-to-span ratio significantly influences the bandwidth of regions of critical excitation frequencies for in-plane dynamic instability of arches. The critical frequencies of the periodic load and their bandwidth increase with a decrease of the rise–span ratio of the arch, whereas the corresponding amplitude of the periodic load decreases at the same time. It is also found that the central concentrated weight influences in-plane dynamic instability of arches significantly. As the weight increases, the critical frequencies of excitation and their bandwidth for in-plane dynamic instability of arches decreases, whereas the corresponding amplitude of excitation increases.

VIBRATION AND DYNAMIC INSTABILITY OF STIFFENED PLATES SUBJECTED TO IN-PLANE HARMONIC EDGE LOADING

2002 ◽  
Vol 02 (02) ◽  
pp. 185-206 ◽  
Author(s):  
A. K. L. SRIVASTAVA ◽  
P. K. DATTA ◽  
A. H. SHEIKH
Keyword(s):  
Dynamic Instability ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Element Analysis ◽  
Aspect Ratios ◽  
Stiffness Properties ◽  
Edge Loading ◽  
Instability Regions ◽  
Varying Mass ◽  
Good Agreement

The vibration and dynamic instability behavior of a stiffened plate subjected to uniform in-plane edge loading is studied using finite element analysis. The method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Rectangular stiffened plates possessing different boundary conditions, aspect ratios, varying mass and stiffness properties and varying number of stiffeners have been analyzed for dynamic instability. The results are obtained considering the bending displacements of the plate and the stiffener. Eccentricity of the stiffeners give rise to axial and bending displacement in the middle plane of the plate. The results show that the principal instability regions have a significant effect considering and neglecting in-plane displacements. Comparison with published results indicates good agreement.

scholarly journals Slender metal web stability analysis: Impact of initial imperfection on the mode of buckling

2020 ◽  
Vol 313 ◽  
pp. 00006
Author(s):  
Martin Psotný
Keyword(s):  
Initial Imperfection ◽  
Iteration Algorithm ◽  
Initial Shape ◽  
Aspect Ratios ◽  
Nonlinear Approach ◽  
Linearized Problem ◽  
Nonlinear Equilibrium ◽  
Post Buckling ◽  
Ansys System ◽  
Raphson Iteration

The post buckling of a rectangular slender web in compression has been analyzed. Shapes of a buckling area obtained from the nonlinear analysis have been compared with buckling modes from the linearized problem for various aspect ratios. Effects of initial shape imperfections upon the analysis have been investigated using nonlinear approach. To trace the complete nonlinear equilibrium curves, specialized code based on FEM was created. The Newton-Raphson iteration algorithm was used, load versus displacement control was changed during the process of calculation. Obtained results were verified using Ansys system, in this case arc-length method was activated for overcoming critical points.

Study on Effect of Viscoelastic Properties on Surface Roughness Uniformity in Abrasive Flow Machining for Plate Surface

2016 ◽  
Vol 1136 ◽  
pp. 131-134 ◽  
Author(s):  
Xuan Ping Wang ◽  
You Zhi Fu ◽  
Hang Gao
Keyword(s):  
Viscoelastic Properties ◽  
Material Removal ◽  
Flow Direction ◽  
Dominant Role ◽  
Machining Process ◽  
Rheological Parameters ◽  
Process Conditions ◽  
Abrasive Flow Machining ◽  
Surface Polishing ◽  
Viscoelastic Constitutive Model

Abrasive flow machining is a suitable technique for surface polishing due to its rheological characteristics, however, it's difficult to achieve uniform roughness for polished surfaces as the material removal mechanism is still ambiguous. In this paper the viscoelastic properties of abrasive flow media are incorporated to explore the phenomena of inconsistent material removal in the AFM polishing process, where the material removal near the edges is obviously higher than that in the middle along the flow direction. The rheological parameters of the viscoelastic constitutive model adopted are varied to study the polishing effectiveness under different process conditions. The results of numerical analysis reveal that there exist distinct differences of viscoelastic stress fields between the edges and the middle regions, which leads to the material removal near the edges is higher than that in the middle. It could be concluded that the viscoelastic properties of abrasive media play the dominant role for the inconsistent material removal in abrasive flow machining process.

The Fractional derivative rheological model and the linear viscoelastic behavior of hydrocolloids

2012 ◽  
Vol 33 (1) ◽  
pp. 141-151 ◽  
Author(s):  
Magdalena Orczykowska ◽  
Marek Dziubiński
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Properties ◽  
Rheological Model ◽  
Xanthan Gum ◽  
Viscoelastic Behavior ◽  
Rheological Parameters ◽  
Rice Starch ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
The Impact

The Fractional derivative rheological model and the linear viscoelastic behavior of hydrocolloids This study was aimed at evaluating the possibility to use the Friedrich-Braun fractional derivative rheological model to assess the viscoelastic properties of xanthan gum with rice starch and sweet potato starch. The Friedrich-Braun fractional derivative rheological model allows to describe viscoelastic properties comprehensively, starting from the behaviour characteristic of purely viscous fluids to the behaviour corresponding to elastic solids. The Friedrich-Braun fractional derivative rheological model has one more virtue which distinguishes it from other models, it allows to determine the relationship between stress and strain and the impact of each of them on viscoelastic properties on the tested material. An analysis of the data described using the Friedrich-Braun fractional derivative rheological model allows to state that all the tested mixtures of starch with xanthan gum form macromolecular gels exhibiting behaviour typical of viscoelastic quasi-solid bodies. The Friedrich-Braun fractional derivative rheological model and 8 rheological parameters of this model allow to determine changes in the structure of the examined starch - xanthan gum mixtures. Similarly important is the possibility to find out the trend and changes going on in this structure as well as their causes.

Hygrothermal Effects on Dynamic Instability of Hybrid Composite Plates

2017 ◽  
Vol 17 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Chun-Sheng Chen ◽  
An-Hung Tan ◽  
Jin-Yih Kao ◽  
Wei-Ren Chen
Keyword(s):  
Layer Thickness ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Dynamic Instability ◽  
Composite Plates ◽  
Thickness Ratio ◽  
Fiber Volume ◽  
Periodic Load ◽  
Moisture Concentration ◽  
Layer Thickness Ratio

The dynamic characteristics of hybrid composite plates under an arbitrary periodic load in hygrothermal environments are investigated. The material properties of the plate are assumed to be dependent on the temperature and moisture. The governing equations of motion of the Mathieu-type are established based on the Galerkin method with reduced eigenfunction transforms. The periodic stress is taken to be a combination of the pulsating axial and bending stress in the example problems. Based on Bolotin’s method, the dynamic instability behaviors of hybrid composite plates are determined. The effects of layer thickness ratio, fiber volume fraction, temperature rise, moisture concentration and dynamic load on the instability regions of hybrid composite plates are studied, along with the dynamic instability index discussed. The results reveal that the layer thickness ratio and hygrothermal conditions have a significant impact on the dynamic instability of hybrid composite plates.

scholarly journals Study of parametric oscillations of viscoelastic cylindrical panel of variable thickness

Vestnik MGSU ◽  
2018 ◽  
pp. 1315-1325 ◽  
Author(s):  
R. A. Abdikarimov ◽  
D. A. Khodzhaev ◽  
B. A. Normuminov ◽  
M. M. Mirsaidov
Keyword(s):  
Variable Thickness ◽  
Cylindrical Panel ◽  
Parametric Oscillations

Multiscale Finite Element Modeling of the Viscoelastic Behavior of Sportswear Under Periodic Load

2020 ◽  
pp. 0887302X2093779
Author(s):  
Ali Sajjadi ◽  
Seyed Abdolkarim Hosseini ◽  
Saeed Ajeli ◽  
Mohammad Mashayekhi
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Viscoelastic Properties ◽  
Viscoelastic Behavior ◽  
Tensile Load ◽  
Periodic Load ◽  
Unit Cells ◽  
Multiscale Finite Element ◽  
Optimum Sample ◽  
Good Agreement

The aim of this study was to investigate the influence of different stitch factors on the mechanical behavior of the seam section of sportswear under periodic load. Multiscale finite element (FE) modeling was then utilized to predict the mechanical behavior of the samples under periodic tensile load. The unit cells of the fabric and the stitched section were modeled in the mesoscale. Elastic and viscoelastic properties of the yarns were assigned to the model. In order to obtain the mechanical properties of the sample, periodic boundary conditions were applied to the unit cell. Elastic and viscoelastic properties calculated from the mesoscale were then used for the macromodel. FE results had a good agreement with the experimental ones in predicting the mechanical behavior of the seam section under the periodic tensile load. By using Taguchi method, the optimum sample was found.

scholarly journals Viscoelasticity of Quartz and Kaolin Slurries in Seawater: Importance of Magnesium Precipitates

Metals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 1120 ◽  
Author(s):  
Matías Jeldres ◽  
Eder Piceros ◽  
Pedro A. Robles ◽  
Norman Toro ◽  
Ricardo I. Jeldres
Keyword(s):  
Yield Stress ◽  
Phase Angle ◽  
Viscoelastic Properties ◽  
Structural Changes ◽  
Rheological Parameters ◽  
Viscoelastic Moduli ◽  
Alkaline Conditions ◽  
The Difference ◽  
Solid Complexes

In this study, the viscoelastic properties of quartz and kaolin suspensions in seawater were analysed considering two distinct conditions: pH 8 and 10.7. Creep and oscillatory sweep tests provided the rheological parameters. An Anton Paar MCR 102 rheometer (ANAMIN Group, Santiago, Chile) was used with a vane-in-cup configuration, and the data were processed with RheoCompassTM Light software (ANAMIN Group, Santiago, Chile). The outcomes were associated with the formation of solid species principally composed of magnesium precipitates. The magnesium in solution reduced in the presence of quartz (68 wt %), from 1380 to 1280 mg/L. Since the difference was not large regarding the solid-free seawater, the disposition of solid complexes at pH 10.7 was expected to be similar. The jump in pH caused both yield stress and viscoelastic moduli to drop, suggesting that the solid precipitates diminished the strength of the particle networks that made up the suspension. For the kaolin slurries (37 wt %), the yield stress raised when the pH increased, but unlike quartz, there was significant adsorption of magnesium cations. In fact, the concentration of magnesium in solution fell from 1380 to 658 mg/L. Dynamic oscillatory assays revealed structural changes in both pulps; in particular, the phase angle was greater at pH 8 than at pH 10.7, which indicates that at more alkaline conditions, the suspension exhibits a more solid-like character.

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