scholarly journals Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 586 ◽  
Author(s):  
Ali Shariati ◽  
Dong won Jung ◽  
Hamid Mohammad-Sedighi ◽  
Krzysztof Kamil Żur ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Critical Velocity ◽  
Natural Frequencies ◽  
Longitudinal Direction ◽  
Variable Density ◽  
Functionally Graded ◽  
Dynamic Configuration ◽  
Stability Maps ◽  
Gradient Parameter ◽  
The Stability

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

scholarly journals On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1707 ◽  
Author(s):  
Ali Shariati ◽  
Dong won Jung ◽  
Hamid Mohammad-Sedighi ◽  
Krzysztof Kamil Żur ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Critical Velocity ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Dynamical Behavior ◽  
Functionally Graded ◽  
Fine Tuning ◽  
Dynamical Response ◽  
Power Law Distribution ◽  
Axially Moving ◽  
The Stability

In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

Stability analysis of a two-segment constructed nanotube embedded in an elastic matrix

2019 ◽  
Vol 26 (3-4) ◽  
pp. 241-252
Author(s):  
Guo-jun Tong ◽  
Yong-shou Liu ◽  
Qian Cheng ◽  
Jia-yin Dai
Keyword(s):  
Elastic Modulus ◽  
Natural Frequency ◽  
Critical Velocity ◽  
Dynamic Stiffness ◽  
Elastic Matrix ◽  
Length Ratio ◽  
Mass Ratio ◽  
Modulus Ratio ◽  
Elastic Coefficient ◽  
The Stability

In this paper, the dynamic stiffness method is used to study the stability of a two-segment constructed nanotube embedded in an elastic matrix. The influences of the length ratio, elastic modulus ratio, mass ratio, and elastic coefficient on the stability of the nanotube are investigated. It can be concluded that a change in the elastic coefficient, length ratio, and elastic modulus ratio has no effect on the form of instability of the two-segment constructed nanotube, but a change in the mass ratio has a significant influence on the form of instability of the nanotube. The elastic coefficient of the elastic matrix mainly affects the natural frequency and the critical velocity of the nanotube of the first mode. The change in the length ratio and elastic modulus ratio mainly affects the natural frequency and the critical velocity of the second mode. The mass change in the two materials mainly affects the natural frequency of the nanotube and has no effect on the critical velocity.

Large Deflection of Various Functionally Graded Beam Using Shooting Method

2011 ◽  
Vol 110-116 ◽  
pp. 4705-4711 ◽  
Author(s):  
Ali Soleimani
Keyword(s):  
Exact Solution ◽  
Elastic Modulus ◽  
Loading Condition ◽  
Shooting Method ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Arbitrary Loading

The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

Numerical Study of Large Defection of Functionally Graded Beam with Geometry Nonlinearity

2011 ◽  
Vol 403-408 ◽  
pp. 4226-4230
Author(s):  
A. Soleimani ◽  
M. Saadatfar
Keyword(s):  
Elastic Modulus ◽  
Shooting Method ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Numerical Study ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Arbitrary Loading ◽  
Geometry Nonlinearity

The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results of shooting method are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

scholarly journals Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons

2021 ◽  
Vol 6 (6) ◽  
pp. 83
Author(s):  
Angelo Aloisio
Keyword(s):  
Elastic Modulus ◽  
Structural Reliability ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
Experimental Testing ◽  
Hybrid Approach ◽  
Reliable Estimate ◽  
Axial Deformation ◽  
Dynamic Identification ◽  
Concrete Girders

The estimate of internal prestressing in concrete beams is essential for the assessment of their structural reliability. Many scholars have tackled multiple and diverse methods to estimate the measurable effects of prestressing. Among them, many experimented with dynamics-based techniques; however, these clash with the theoretical independence of the natural frequencies of the forces of internally prestressed beams. This paper examines the feasibility of a hybrid approach based on dynamic identification and the knowledge of the elastic modulus. Specifically, the author considered the effect of the axial deformation on the beam length and the weight per unit of volume. It is questioned whether the uncertainties related to the estimate of the elastic modulus and the first natural frequency yield reasonable estimates of the internal prestressing. The experimental testing of a set of full-scale concrete girders with known design prestressing supports a discussion about its practicability. The author found that the uncertainty in estimating the natural frequencies and elastic modulus significantly undermines a reliable estimate of the prestressing state.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

scholarly journals Stochastic Natural Vibration Analyses of Free-Form Shells

2019 ◽  
Vol 9 (15) ◽  
pp. 3168
Author(s):  
Bingbing San ◽  
Yunlong Ma ◽  
Zhi Xiao ◽  
Dongming Feng ◽  
Liwei Yin
Keyword(s):  
Elastic Modulus ◽  
Shape Optimization ◽  
Shell Thickness ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Free Form ◽  
Probability Models ◽  
Geometric Imperfection ◽  
Natural Vibration Characteristics

This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.

scholarly journals Dynamics of axially functionally graded conical pipes conveying fluid

2021 ◽  
Vol 37 ◽  
pp. 318-326
Author(s):  
Yuzhen Zhao ◽  
Dike Hu ◽  
Song Wu ◽  
Xinjun Long ◽  
Yongshou Liu
Keyword(s):  
Natural Frequency ◽  
Critical Velocity ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Reduction Factor ◽  
Functionally Graded ◽  
Function Type ◽  
Pipes Conveying Fluid ◽  
Volume Fraction Function ◽  
Conveying Fluid

Abstract In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.

On stability of parallel flow of an incompressible fluid of variable density and viscosity

1962 ◽  
Vol 58 (4) ◽  
pp. 646-661 ◽  
Author(s):  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Water Waves ◽  
Salt Water ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Stability Equation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Vertical Variations ◽  
The Stability

ABSTRACTSome aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.

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