• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.611-620
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• 2017

A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

• Steel and Composite Structures
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• v.43 no.1
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• pp.1-17
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• 2022

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

• Investigative Magnetic Resonance Imaging
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• v.4 no.1
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• pp.20-26
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• 2000

Gradient moment nulling techniques require the introduction of an additional gradient on each axis for each order of motion correction to be applied. The additional gradients introduce new constraints on the sequence design and increase the demands on the gradient system. The purpose of this paper is to demonstrate techniques for optimization of gradient echo gradient moment nulling sequences within the constraints of the gradient hardware. Flow compensated pulse sequences were designed and implemented on a clinical magnetic resonance imaging system. The design of the gradient moment nulling sequences requires the solution of a linear system of equations. A Mathematica package was developed that interactively solves the gradient moment nulling problem. The package allows the physicist to specify the desired order of motion compensation and the duration of the gradients in the sequence with different gradient envelopes. The gradient echo sequences with first, second, and third order motion compensation were implemented with minimum echo time. The sequences were optimized to take full advantage of the capabilities of the gradient hardware. The sequences were used to generate images of phantoms and human brains. The optimized sequences were found to have better motion compensation than comparable standard sequences.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Steel and Composite Structures
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• v.24 no.2
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• pp.151-176
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• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• Steel and Composite Structures
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• v.18 no.2
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• pp.409-423
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• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.97-112
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• 2019

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.

• Advances in concrete construction
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• v.15 no.2
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• pp.137-147
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• 2023

Dynamic analysis of a shear deformable shell is investigated with accounting thickness stretching using Hamilton's principle. Through this method, the total transverse is composed into bending, shearing and stretching portions, in which the third part is responsible for deformation along the transverse direction. After computation of the strain, kinetic and external energies, the governing motion equations are derived using Hamilton's principle. A comparative study is presented before presentation of full numerical results for confirmation of the formulation and methodology. The results are presented with and without thickness stretching to show importance of the proposed theory in comparison with previous theories without thickness stretching.

• Advances in nano research
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• v.4 no.3
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• pp.229-249
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• 2016

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Steel and Composite Structures
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• v.39 no.1
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• pp.1-20
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• 2021

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1 + z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1 + z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.