• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.79-92
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• 2015

In this study, free vibration analyses of symmetric laminated cantilever and simply supported damaged composite beams are investigated by using finite element method (FEM). Free vibration responses of damaged beams are examined using Euler Bernoulli beam and classical lamination theories. A computer code is developed by using MATLAB software to determine the natural frequencies of a damaged beam. The local damage zone is assumed to be on the surface lamina of the beam by broken fibers after impact. The damaged zone is modeled as a unidirectional discontinuous lamina with $0^{\circ}$ orientations in this study. Fiber volume fraction ($v_f$), fiber aspect ratio ($L_f/d_f$), damage length ($L_D$) and its location (${\lambda}/L$), fiber orientation and stacking sequence parameters effects on natural frequencies are investigated. These parameters are affected the natural frequency values significantly.

• Smart Structures and Systems
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• v.25 no.6
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• pp.669-678
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• 2020

This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.581-599
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• 2014

In this paper the overall dynamic response of simple railway bridges subjected to high-speed trains is investigated numerically based on the mechanical models of simply supported single-span and continuous two-span Bernoulli-Euler beams. Each axle of the train, which is composed of rail cars and passenger cars, is considered as moving concentrated load. Distance, magnitude, and maximum speed of the moving loads are adjusted to real high-speed trains and to load models according to Eurocode 1. Non-dimensional characteristic parameters of the train-bridge interaction system are identified. These parameters permit a spectral representation of the dynamic peak response. Response spectra assist the practicing engineers in evaluating the expected dynamic peak response in the design process of railway bridges without performing time-consuming time history analyses.

• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.207-223
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• 2019

Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.295-309
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• 2023

The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

• Steel and Composite Structures
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• v.47 no.6
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• Advances in nano research
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• v.8 no.3
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• pp.245-254
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• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• Coupled systems mechanics
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• v.4 no.4
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• pp.337-364
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• 2015

In this paper we present methodology for parameters identification of constitutive model which is able to present behavior of a connection between two members in a structure. Such a constitutive model for frame connections can be cast in the most general form of the Timoshenko beam, which can present three failure modes. The first failure mode pertains to the bending in connection, which is defined as coupled plasticity-damage model with nonlinear softening. The second failure mode is seeking to capture the shearing of connection, which is defined as plasticity with linear hardening and nonlinear softening. The third failure mode pertains to the diffuse failure in the members; excluding it leads to linear elastic constitutive law. Theoretical formulation of this Timoshenko beam model and its finite element implementation are presented in the second section. The parameter identification procedure that will allow us to define eighteen unknown parameters is given in Section 3. The proposed methodology splits identification in three phases, with all details presented in Section 4 through three different examples. We also present the real experimental results. The conclusions are stated in the last section of the paper.

• Advances in aircraft and spacecraft science
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• v.10 no.5
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• pp.419-437
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• 2023

This paper presents the study of the effects of rigid-body motion simultaneously with the presence of the effects of temporal variation due to the existence of morphing speed on the aeroelastic stability of the two-stage telescopic wings, and hence this is the main novelty of this study. To this aim, Euler-Bernoulli beam theory is used to model the bending-torsional dynamics of the wing. The aerodynamic loads on the wing in an incompressible flow regime are determined by using Peters' unsteady aerodynamic model. The governing aeroelastic equations are discretized employing a finite element method based on the beam-rod model. The effects of rigid-body motion on the length-based stability of the wing are determined by checking the eigenvalues of system. The obtained results are compared with those available in the literature, and a good agreement is observed. Furthermore, the effects of different parameters of rigid-body such as the mass, radius of gyration, fuselage center of gravity distance from wing elastic axis on the aeroelastic stability are discussed. It is found that some parameters can cause unpredictable changes in the critical length and frequency. Also, paying attention to the fuselage parameters and how they affect stability is very important and will play a significant role in the design.