• Steel and Composite Structures
• /
• 제19권2호
• /
• pp.369-384
• /
• 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.

• Advances in nano research
• /
• 제7권4호
• /
• pp.249-263
• /
• 2019

In the current paper, an exact solution method is carried out for analyzing the thermo-mechanical vibration of curved FG nano-beams subjected to uniform thermal environmental conditions, by considering porosity distribution via nonlocal strain gradient beam theory for the first time. Nonlocal strain gradient elasticity theory is adopted to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field is considered. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Material properties of curved porous FG nanobeam are assumed to be temperature-dependent and are supposed to vary through the thickness direction of beam which modeled via modified power-law rule. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG nano-structures. The governing equations and related boundary condition of curved porous FG nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loading. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, porosity volume fractions, thermal effect, gradient index, opening angle and aspect ratio on the natural frequency of curved FG porous nanobeam are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Steel and Composite Structures
• /
• 제49권5호
• /
• pp.487-502
• /
• 2023

In the realm of nanotechnology, the nonlocal strain gradient theory takes center stage as it scrutinizes the behavior of spinning cantilever nanobeams and nanotubes, pivotal components supporting various mechanical movements in sport structures. The dynamics of these structures have sparked debates within the scientific community, with some contending that nonlocal cantilever models fail to predict dynamic softening, while others propose that they can indeed exhibit stiffness softening characteristics. To address these disparities, this paper investigates the dynamic response of a nonlocal cantilever cylindrical beam under the influence of external discontinuous dynamic loads. The study employs four distinct models: the Euler-Bernoulli beam model, Timoshenko beam model, higher-order beam model, and a novel higher-order tube model. These models account for the effects of functionally graded materials (FGMs) in the radial tube direction, giving rise to nanotubes with varying properties. The Hamilton principle is employed to formulate the governing differential equations and precise boundary conditions. These equations are subsequently solved using the generalized differential quadrature element technique (GDQEM). This research not only advances our understanding of the dynamic behavior of nanotubes but also reveals the intriguing phenomena of both hardening and softening in the nonlocal parameter within cantilever nanostructures. Moreover, the findings hold promise for practical applications, including drug delivery, where the controlled vibrations of nanotubes can enhance the precision and efficiency of medication transport within the human body. By exploring the multifaceted characteristics of nanotubes, this study not only contributes to the design and manufacturing of rotating nanostructures but also offers insights into their potential role in revolutionizing drug delivery systems.

• Advances in nano research
• /
• 제14권3호
• /
• pp.211-224
• /
• 2023

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

• Steel and Composite Structures
• /
• 제4권5호
• /
• pp.403-418
• /
• 2004

Lateral sway is most likely to control the design of semi-rigid steel frames where the frame arrangements do not include any form of bracing. This paper investigates the sway behaviour of semi-rigid regular steel frames i.e., frames having the same arrangement of beam and column sections at all levels, and hence proposes some design charts for the prediction of sway that eliminate the need for doing any numerical modelling. Schueller's equation has also been modified to incorporate connection flexibility in addition to its original rigid frame considerations. All the proposed methods have been validated using results obtained from numerical analysis.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2007년도 추계학술대회논문집
• /
• pp.708-713
• /
• 2007

Finite element model updating has been performed using an optimization technique in the paper. The objective function consists of natural frequencies, modal assurance criterion values, and bandwidths of modes, which are obtained from finite element analysis and experiment. Young's modulus and damping coefficient of the material are selected as design variables whose values are modified to make the objective function as small as possible. To consider the loading effect of an accelerometer, its mass and moment of inertia are added to design variables. This model updating method has been applied to a cantilever beam, and experimental data are measured by modal test.

• Computers and Concrete
• /
• 제6권5호
• /
• pp.377-390
• /
• 2009

In this paper an improved one-dimensional frame element for modelling of reinforced concrete beams and columns subjected to impact is presented. The model is developed in the framework of a flexibility fibre element formulation that ignores the shear effect at material level. However, a simple shear cap is introduced at section level to take account of possible shear failure. The effect of strain rate at the fibre level is taken into account by using the dynamic increase factor (DIF) concept for steel and concrete. The capability of the formulation for estimating the element response history is demonstrated by some numerical examples and it is shown that the developed 1D element has the potential to be used for dynamic analysis of large framed structures subjected to impact of air blast and rigid objects.

• Structural Engineering and Mechanics
• /
• 제66권4호
• /
• pp.543-555
• /
• 2018

Fiber Reinforced Polymer (FRP), which has a high strength to weight ratio, are now regularly used for strengthening of deficient reinforced concrete (RC) structures. While various researches have been conducted on FRP strengthening, an area that still requires attention is predicting the debonding failure load of prestressed FRP strengthened RC beams. Application of prestressing increases the capacity and reduces the premature failure of the beams largely, though not entirely. Few analytical methods are available to predict the failure loads under flexure failure. With this paucity, this research proposes a method for predicting debonding failure induced by intermediate crack (IC) for prestressed FRP-strengthened beams. The method consists of a numerical study on beams retrofitted with prestressed FRP in the tension side of the beam. The method applies modified Branson moment-curvature analysis together with the global energy balance approach in combination with fracture mechanics criteria to predict failure load for complicated IC-induced failure. The numerically simulated results were compared with published experimental data and the average of theoretical to experimental debonding failure load is found to be 0.93 with a standard deviation of 0.09.

• 한국소음진동공학회논문집
• /
• 제22권11호
• /
• pp.1128-1136
• /
• 2012

This paper analyzes the vibration characteristics of an optical pickup actuator, which has six wire-suspensions and is used in optical disc drives(ODDs). The vibration characteristics of the actuator is mathematically described by analyzing its beam configuration and motion condition confined to lateral and longitudinal directions of the beams. The accuracy of the vibration characteristics is proved by comparing mode frequencies with a finite element analysis. Finally, it is shown that mode frequencies and shapes can be modified by changing design parameters in mathematical expressions.

• 한국분말재료학회지
• /
• 제2권1호
• /
• pp.19-28
• /
• 1995

Powder forging is a combined technology of powder metallurgy and precision hot forging. Recently, the technology is developing rapidly because of its economic merits, especially in automotive part manufacturing. In the present study, the finite element technique was developed to predict density variation during P/M forging and the technique was applied to analysis of forging of a P/M connecting rod. Although deformation mode of the connecting rod was quite complex, several sections were selected and analyzed under an assumption of asymmetric or plane strain deformation. It was found that some modifications were necessary on the cross section of the beam portion. Therefore, the cross section was modified repeatedly until a satisfactory result of the analysis was obtained. On the other hand, no modifications were necessary in the ring and the pin portions. It is anticipated that the developed technique can be used to optimize preform design and manufacturing processes in P/M forging, which are highly critical to produce successful products in practice.