• Advances in nano research
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• v.10 no.1
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• pp.15-24
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• 2021

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1287-1294
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory Both the divergence and flutter critical loads are calculated from the load-frequency corves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the subtangential parameter, mass ratio and spring parameter.

• Structural Monitoring and Maintenance
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• v.3 no.4
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• pp.349-375
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• 2016

The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.283-294
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• 2020

In general, the study of a high-rise building's behaviour when subjected to a horizontal load (wind or earthquake) is carried out through numerical modelling with finite elements method. This paper proposes a new, original approach based on the use of a multi-beams model. By redistributing bending and axial stiffness of horizontal elements (beams and slabs) along vertical elements, it becomes possible to produce a system of differential equations able to represent the structural behaviour of the whole building. In this paper this approach is applied to the study of bending behaviour in a 37-storey building (Torre Pontina, Latina, Italy) with a regular reinforced concrete structure. The load considered is the wind, estimated in accordance with Italian national technical rules and regulations. To simplify the explanation of the approach, the wind load was considered uniform on the height of building with a value equal to the average value of the wind load distribution. The system of differential equations' is assessed numerically, using Matlab, and compared with the obtainable solution from a finite elements model along with the obtainable solutions via classical Euler-Bernoulli beam theory. The comparison carried out demonstrates, in the case study examined, an excellent approximation of structural behaviour.

• Wind and Structures
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• v.25 no.5
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• pp.459-474
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• 2017

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.

• Smart Structures and Systems
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• v.16 no.6
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• pp.1107-1132
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• 2015

A damage detection algorithm based on neuro fuzzy hybrid system is presented in this study for location and severity predictions of cracks in beam-like structures. A combination of eigenfrequencies and rotation deviation curves are utilized as input to the soft computing technique. Both single and multiple damage cases are considered. Theoretical expressions leading to modal properties of damaged beam elements are provided. The beam formulation is based on Euler-Bernoulli theory. The cracked section of beam is simulated employing discrete spring model whose compliance is computed from stress intensity factors of fracture mechanics. A hybrid neuro fuzzy technique is utilized to solve the inverse problem of crack identification. Two different neuro fuzzy systems including grid partitioning (GP) and subtractive clustering (SC) are investigated for the highlighted problem. Several error metrics are utilized for evaluating the accuracy of the hybrid algorithms. The study is the first in terms of 1) using the two models of neuro fuzzy systems in crack detection and 2) considering multiple damages in beam elements employing the fused neuro fuzzy procedures. At the end of the study, the developed hybrid models are tested by utilizing the noise-contaminated data. Considering the robustness of the models, they can be employed as damage identification algorithms in health monitoring of beam-like structures.

• Advances in nano research
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• v.8 no.3
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• pp.255-264
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• 2020

Buckling and post-buckling cases are often occurred in aorta artery because it affected by higher pressure. Also, its stability has a vital importance to humans and animals. The loss of stability in arteries may lead to arterial tortuosity and kinking. In this paper, post-buckling analysis of aorta artery is investigated under axial compression loads on the basis of Euler-Bernoulli beam theory by using finite element method. It is known that post-buckling problems are geometrically nonlinear problems. In the geometrically nonlinear model, the Von Karman nonlinear kinematic relationship is employed. Two types of support conditions for the aorta artery are considered. The considered non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The aorta artery is modeled as a cylindrical tube with different average diameters. In the numerical results, the effects of the geometry parameters of aorta artery on the post-buckling case are investigated in detail. Nonlinear deflections and critical buckling loads are obtained and discussed on the post-buckling case.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.832-835
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• 2005

The free vibration of tapered piles embedded in soil is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equations for the free vibrations of such members are solved numerically. The square tapered piles with one free and the other hinged end with rotational spring are applied in numerical examples. The lowest two natural frequencies are obtained over a range of non-dimensional system parameters: the rotational spring parameter, the embedded ratio, the foundation parameter, the width ratio of the contact area and the section ratio.

• Proceedings of the Acoustical Society of Korea Conference
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• autumn
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• pp.221-224
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• 2004

A theoretical model has been studied to describe the sound radiation analysis for structure vibration noise of vehicle tires under the action of random moving line forces. When a tire is analyzed, it had been modeled as curved beams with distributed springs and dash pots that represent the radial , tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The curved beam material and elastic foundation are assumed to be lossless Bernoulli-Euler beam theory including a tension force, damping coefficient and stiffness of foundation will be employed. The expression for sound power is integrated numerically and the results examined as a function of Mach number, wave-number ratio and stiffness factor. The experimental investigation for structure vibration noise of vehicle tire under the action of random moving line forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radiation are measured. Results strongly suggest that operation condition in the tire material properties and design factors of the tire govern the sound power and sound radiation characteristics.