On thermo-mechanical vibration analysis of multi-scale hybrid composite beams

2018 ◽  
Vol 25 (4) ◽  
pp. 933-945 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Dabbagh
Keyword(s):  
Hybrid Composite ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Beam Theory ◽  
Composite Beams ◽  
Effect Of Temperature ◽  
Correction Coefficient ◽  
Beam Model ◽  
Multi Scale ◽  
Vibrational Characteristics

This article is primarily organized to analyze the thermo-elastic vibrational characteristics of multi-scale hybrid composite beams according to a refined beam model. In this novel type of composites, multi-scale reinforcing elements, carbon fiber (CF) and carbon nanotube (CNT) in particular, are presumed to be dispersed in an initial resin. The homogenization process is carried out employing a mixture of the Halpin–Tsai model and the rule of mixture. The effect of temperature and its gradient on the mechanical properties of CNTs and epoxy resin is rendered to present a more reliable thermal analysis. On the other hand, a refined trigonometric shear deformable beam theory is extended to derive the kinematic relations of the beam needless of any external shear correction coefficient. On the basis of Hamilton's principle, the partial differential equations of motion are developed. Thereafter, the natural frequencies are achieved by the means of Galerkin's method for both simply supported and fully clamped edge conditions. Then, the validity of the presented model is shown by comparing these results with those of previously published researches. Finally, effects of different parameters on the natural frequency of composite beams are rendered in the framework of some numerical case studies. It can be found that multi-scale hybrid composite beams can satisfy higher frequencies once compared with each of the CF- or CNT-reinforced composite beams.

Micro Cantilever Beam Theory for Transverse Dynamics Using a Continuum Mechanics Model

2011 ◽  
Vol 415-417 ◽  
pp. 760-763
Author(s):  
Cheng Li ◽  
Wei Guo Huang ◽  
Lin Quan Yao
Keyword(s):  
Scale Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Beam Model ◽  
Cantilever Beams ◽  
Mechanics Model ◽  
Axial Tension ◽  
Vibrational Characteristics ◽  
Micro Cantilever

The vibrational characteristics of cantilever beams with initial axial tension were studied using a nonlocal continuum Euler-Bernoulli beam model. Small size effects are essential to nanotechnology and it can not be ignored in micro or nano scale. Nonlocal elasticity theory has been proved to work well in nanomechanics and it is considered into the governing equation which can be transformed into a fourth-order ordinary differential equation together with a dispersion relation. Boundary conditions are applied so as to determine the analytical solutions of vibrational mode shape and transverse deformation through a numerical method. Relations between natural frequency and the small scale parameter are obtained, including the fundamental and the second order frequencies. It is found that both the small scale parameter and dimensionless initial axial tension play remarkable roles in dynamic behaviors of micro cantilever beams and their effects are analyzed and discussed in detail.

scholarly journals Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren Yongsheng ◽  
Du Chenggang ◽  
Shi Yuyan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation ◽  
Forced Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Composite Beams ◽  
Vibration Behavior ◽  
Shear Deformable

The nonlinear free and forced vibration of the composite beams embedded with shape memory alloy (SMA) fibers are investigated based on first-order shear deformation beam theory and the von Kármán type nonlinear strain-displacement equation. A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. The equations of motion are derived by using Hamilton’s principle. The approximate solution is obtained for vibration analysis of the composite beams based on the Galerkin approach. The parametric study is carried out to display the effect of the actuation temperature, the volume fraction, the initial strain of SMA fibers, and the length-to-thickness ratio. The shear deformation is shown to have a significant contribution to nonlinear vibration behavior of the composite beams with SMA fibers.

Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

2005 ◽  
Vol 11 (6) ◽  
pp. 829-848 ◽  
Author(s):  
Stefan Berczyński ◽  
Tomasz Wróblewski
Keyword(s):  
Dynamic Behavior ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Composite Beams ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Beam Model ◽  
Euler Beam ◽  
Flexural Vibrations

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

2016 ◽  
Vol 16 (07) ◽  
pp. 1550032 ◽  
Author(s):  
M. R. Ebrahimi ◽  
A. Moeinfar ◽  
M. Shakeri
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parametric Studies ◽  
The One ◽  
Nonlinear Equations Of Motion

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

scholarly journals Vibration Analysis of Inclined Laminated Composite Beams under Moving Distributed Masses

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
E. Bahmyari ◽  
S. R. Mohebpour ◽  
P. Malekzadeh
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Incline Angle ◽  
Centrifugal Forces ◽  
Coriolis And Centrifugal Forces ◽  
Laminated Composite Beams

The dynamic response of laminated composite beams subjected to distributed moving masses is investigated using the finite element method (FEM) based on the both first-order shear deformation theory (FSDT) and the classical beam theory (CLT). Six and ten degrees of freedom beam elements are used to discretize the CLT and FSDT equations of motion, respectively. The resulting spatially discretized beam governing equations including the effect of inertial, Coriolis, and centrifugal forces due to moving distributed mass are evaluated in time domain by applying Newmark’s scheme. The presented approach is first validated by studying its convergence behavior and comparing the results with those of existing solutions in the literature. Then, the effect of incline angle, mass, and velocity of moving body, layer orientation, load length, and inertial, Coriolis, and centrifugal forces due to the moving distributed mass and friction force between the beam and the moving distributed mass on the dynamic behavior of inclined laminated composite beams are investigated.

Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

2012 ◽  
Vol 28 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A. A. Khdeir ◽  
E. Darraj ◽  
O. J. Aldraihem
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
Beam Model ◽  
Laminated Beams ◽  
State Space Approach ◽  
Laminated Beam ◽  
Beam Surface

ABSTRACTAnalytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

scholarly journals Homogenization and Equivalent Beam Model for Fiber-Reinforced Tubular Profiles

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2069
Author(s):  
Daniel Gnoli ◽  
Sajjad Babamohammadi ◽  
Nicholas Fantuzzi
Keyword(s):  
Finite Element ◽  
Hollow Cylinder ◽  
Cross Sections ◽  
Laminated Composite ◽  
Beam Theory ◽  
Material Design ◽  
Composite Beams ◽  
Beam Model ◽  
2D And 3D ◽  
Euler Bernoulli Beam

The current work presents a study on hollow cylinder composite beams, since hollow cylinder cross-sections are one of the principal geometry in many engineering fields. In particular, the present study considers the use of these profiles for scaffold design in offshore engineering. Composite beams cannot be treated as isotropic ones due to couplings mainly present among traction, torsion, bending and shear coefficients. This research aims to present a simple approach to study composite beams as they behave like isotropic ones by removing most complexities related to composite material design (e.g., avoid the use of 2D and 3D finite element modeling). The work aims to obtain the stiffness matrix of the equivalent beam through an analytical approach which is valid for most of the laminated composite configurations present in engineering applications. The 3D Euler–Bernoulli beam theory is considered for obtaining the correspondent isotropic elastic coefficients. The outcomes show that negligible errors occur for some equivalent composite configurations by allowing designers to continue using commercial finite element codes that implement the classical isotropic beam model.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

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