Sinusoidal Beam Research Articles

Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams

In this article, the wave dispersion analysis of heterogeneous functionally graded (FG) nanosize beams is undertaken in the framework of a nonlocal strain gradient higher-order beam theory. Shear deformation effects are completely included free from any additional shear correction coefficient by the means of a refined sinusoidal beam theorem. Furthermore, the small scale effects are covered based on the nonlocal strain gradient elasticity theory. This is proven that the aforementioned theory is powerful enough to guesstimate the behavior of the nanostructures better than formerly presented ones. In fact, both stiffness-softening and -hardening characteristics of nanosize elements are coupled together in this theory. On the other hand, the equivalent material properties are achieved utilizing the rule of mixture. The motion equations are derived extending the dynamic version of the principle of virtual work. Thereafter, the size-dependent partial differential equations of the problem are solved based on an exponential solution function to reach the circular wave frequency. Next, some graphical examples are presented to investigate the influences of various parameters on the wave propagation behaviors of FG nanobeams.

In-plane mechanics of a novel cellular structure for multiple morphing applications

Cellular structures are potential candidates as underlying supports for flexible skins due to their outstanding characteristics such as light weight, zero Poisson’s ratio and low effective moduli. This paper develops a novel zero Poisson’s ratio cellular structure composed of semi-periodic sinusoidal beams with light weight, low in-plane moduli and high strain capability. The equivalent in-plane elastic and shear moduli of the structure are studied through a combination of theoretical and finite element analysis. Then the maximum global strains are investigated to show the morphing capability of the structure. Results show that the in-plane moduli of the cellular structures are several orders of magnitude lower than the raw material. The global strains of the cellular structures could be over 10 times greater than the raw material. The results also demonstrate the potential of the proposed structure for uniaxial, shear or hybrid in-plane morphing.

Numerical study of the effect of the oscillation frequency in buttonhole welding

A three-dimensional transient simulation was conducted with comprehensive models of the laser welding process with a combination of wire feeding and one-dimensional sinusoidal beam oscillation. Both a realistic filler wire feeding and simultaneous melting by oscillating laser beam were considered. The buttonhole formation, which was shown in the simulations, was affected by the shape of the molten filler wire, e.g. the length and angle. The buttonholes formed at higher oscillation frequencies and became clearer with increasing oscillation frequency. The so-called chopping frequency of the wire, found in the frequency domain through Fourier analysis, became more dominant with increasing oscillation frequency. The wire chopping process seems to affect the number of multiple reflections, the power absorption, and the buttonhole behavior.

A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory

In this research, we analyze size-dependent bending and vibration of microbeams made of porous metal foams. The porous microbeam model is developed based on the sinusoidal beam theory and the modified strain gradient theory. Hamilton’s principle is employed to obtain the governing equations and boundary conditions of the porous microbeam. Analytical solutions are presented for deflections and natural frequencies of the porous microbeam by using Navier’s method. The influences of the porosity distribution, the porosity coefficient, the slenderness ratio, and the microbeam thickness are clarified on the static bending and free vibration of porous microbeams. These findings can be applied to the design of metal foam microstructures in engineering.

A new finite element formulation for free vibrations of planar curved beams

ABSTRACTThis study aims to derive a new finite element formulation for in-plane free vibrations of curved beams with arbitrary curvature, and cross-section variation. The stiffness matrix presented in this study are obtained from the exact solution of the static problem, considering the effects of axial extension, shear deformation. Using the exact solution for point loads, a consistent mass matrix is obtained, considering the effect of rotatory inertia. Numerous examples, related to the free vibrations of planar curved beams are solved to validate the presented approach. It is proved that presented formulation does not suffer from any locking phenomena. Circular beams with varying cross-section are investigated by assembling uniform elements. Parabolic, elliptic, and sinusoidal beams are examined by both using variable curvature elements, and assembling circular beam elements. This new formulation is thought to be an effective tool in structural analysis of curved beams.

Reduction of pores by means of laser beam oscillation during remote welding of AlMgSi

The influence of a spatial beam oscillation on the dynamics of the capillary and the mechanism leading to an increased or reduced generation of process pores was investigated for deep penetration laser beam welding of the aluminum alloy AlMgSi. Welding with a feed rate of 4 m/min and a welding depth of 4 mm was examined with sinusoidal (longitudinal and lateral) and circular beam oscillation patterns at frequencies of 100 Hz and 200 Hz. The welding processes were analyzed by means of online X-ray imaging with a frame rate of 2 kHz, which provides the temporal and spatial resolution required to resolve the dynamics of the capillary. With conventional rectilinear welding, the weld seams are prone to the formation of process pores. By applying a circular beam oscillation, the weld seams were found to be virtually free from porosity. The mechanism leading to a reduced occurrence of process pores differed for the two investigated beam oscillation frequencies. At an oscillation frequency of 100 Hz bubbles are regularly formed in the melt pool but immediately removed at the subsequent pass of the laser beam by degassing into the vapor capillary. At 200 Hz the formation of process pores is completely avoided from the first. For a sinusoidal beam oscillation in longitudinal direction, the bubbles formed in the weld pool were found to be further inflated at each pass of the laser beam.

Erratum to: Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

The article “Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes”, written by R. KOLAHCHI and A. M. MONIRI BIDGOLI, was originally published Online First without open access. After publication in Volume 37, Issue 2, Page 265–274, the authors decided to opt for Open Choice and to make the article an open access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2018 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The original article has been corrected.

Laser edge forming to increase the bending radius in hemming

Hemming can be used, for example, to join dissimilar materials which cannot be welded by conventional laser or arc based processes. A critical value in hemming is the ratio of outer sheet bending radius and outer sheet thickness because cracks can occur in outer sheets with low ductility due to a small bending radius. In this study, a novel approach is introduced for increasing the bending radius by laser based edge forming. The laser beam melts the edge of the inner sheet prior to the hemming process. In laser edge forming, the edge thickness increases due to the surface tension of the melt. The edge cross-section has typically a nearly circular shape after solidification. Two laser beam irradiation strategies were investigated. In case of the first strategy, a defocused laser beam was applied. The second strategy combined a focused laser beam resulting in the formation of a vapor capillary (keyhole) with sinusoidal beam oscillation transversal to the sheet edge. The results show that the position of the cylindrical edge cross-section according to the sheet plane could be affected by the applied irradiation strategy. The needed laser power was significantly lower when using a focused laser beam due to the deep penetration effect. The potential of the laser edge forming technique for crack-free hemming processes was demonstrated with 1 mm thick aluminum alloy sheets by carrying out stripe tests.

Dynamic behaviors of phase transforming cellular structures

In this work, the dynamic behaviors of phase transforming cellular structures (PTCS) consisted of sinusoidal beam with bi-stable configurations are studied. A nonlinear spring-bead model is developed, where the mechanical properties of the sinusoidal beam are described by a nonlinear spring and the mass is concentrated at the bead. Therefore, the PTCS are modeled as a chain of nonlinear spring-bead. Based on the nonlinear spring-bead model, the quasi-static and dynamic behaviors of PTCS are theoretically and numerically studied, which shows abundant dynamic behaviors depending on the loading rate and damping coefficient. For a 2-layered PTCS, there are four deformation patterns, that is the snap through deformation of the sinusoidal beams for relatively small loading rate and damping coefficient, the uniform deformation for relatively large damping coefficient, and the pulse deformation of the springs near bi-stable configurations for relatively large loading rate and small damping coefficient. While, for the multilayer PTCS, their dynamic behaviors are much more complicated due to the combined deformation of the multiple sinusoidal beams. However, the similar snap through and pulse deformation of the sinusoidal beams are also observed, respectively. To our knowledge, this work is the first time to systematically study the dynamic behaviors of PTCS.

A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation

Microstructure-dependent buckling behavior of single-walled carbon nanotubes (SWCNTs) surrounded by a two-parameter elastic foundation is investigated. The governing equations and corresponding boundary conditions in buckling are achieved by implementing minimum total potential energy principle via modified strain gradient theory and several beam theories. The resulting equations are analytically solved by employing Navier’s solution procedure for simply supported boundary conditions. A detailed parametric study is performed to indicate effects of diameter-to-length scale parameter ratio, diameter-to-length ratio, shear deformation, shear correction factor and foundation parameters on buckling loads of SWCNTs. Numerical results reveal that the classical buckling loads evaluated by all shear deformation beam theories agree well with each other while a discrepancy occurs between the size-dependent buckling loads of parabolic beam theory (PBT), sinusoidal beam theory (SBT) and Timoshenko beam theory with proposed shear correction factor (TBT∗), and those of Timoshenko beam theory (TBT).

Utilization of laser beam oscillation to enhance the process efficiency for deep-penetration welding in aluminum

Laser beam remote welding is an established process in modern production plants. For instance, remote welding is used as a fast joining technology with rather large structural welds in car body manufacturing. Besides the advantages, such as noncontact machining and low process times, laser beam processing is also characterized by a low efficiency in contrast to other joining technologies. Therefore, this research has drawn attention to the improvement of the process efficiency for laser beam welding of the aluminum alloy AlMgSi1. The experiments were performed using a high power diode laser with a beam converter. The used scanning unit allowed a lateral beam oscillation perpendicular to the feed direction. Thereby, a new process was developed on the basis of high frequent beam oscillation. Hence, the sinusoidal beam oscillation enabled a defined heat input, whereas the laser beam was accelerated and the molten pool was widened. As a consequence, the process design leads to a significant preheating of the process zone, which contributes to a reduction in the deep-penetration welding threshold. Accordingly, low laser power is necessary to generate comparably large molten pools by means of laser beam oscillation. Correlating the amount of molten material with the deposited laser power, the results clearly show an increased process efficiency for the deep-penetration welding regime.

Lattice Metamaterials with Mechanically Tunable Poisson’s Ratio for Vibration Control

Advances in additive manufacturing will enable the fabrication of metamaterials with ever more complex architectures, to realize unusual and superior physical properties. The authors design and build lattices of sinusoidal beams, yielding a class of metamaterials with unusual, extreme mechanical behavior: Poisson's ratio for the system switches from negative to positive upon large deformation (the nonlinear regime). Potential applications include energy absorption, tunable acoustics, vibration control, responsive devices, soft robotics, and stretchable electronics.

All-optical sampling and magnification based on XPM-induced focusing

We theoretically and experimentally investigate the design of an all-optical magnification and sampling function free from any active gain medium or additional amplified spontaneous noise emission. The proposed technique is based on the co-propagation of an arbitrary shaped signal together with an orthogonally polarized intense fast sinusoidal beating within a normally dispersive optical fiber. This process allows us to experimentally demonstrate a 40-GHz sampling operation as well as an 8-dB magnification of an arbitrary shaped nanosecond signal around 1550 nm in a 5-km long optical fiber. The experimental observations are in good agreement with numerical and theoretical analysis.

A firefly algorithm for optimum design of new-generation beams

ABSTRACTThis research addresses the minimum weight design of new-generation steel beams with sinusoidal openings using a metaheuristic search technique, namely the firefly method. The proposed algorithm is also used to compare the optimum design results of sinusoidal web-expanded beams with steel castellated and cellular beams. Optimum design problems of all beams are formulated according to the design limitations stipulated by the Steel Construction Institute. The design methods adopted in these publications are consistent with BS 5950 specifications. The formulation of the design problem considering the above-mentioned limitations turns out to be a discrete programming problem. The design algorithms based on the technique select the optimum universal beam sections, dimensional properties of sinusoidal, hexagonal and circular holes, and the total number of openings along the beam as design variables. Furthermore, this selection is also carried out such that the behavioural limitations are satisfied. Numerical examples are presented, where the suggested algorithm is implemented to achieve the minimum weight design of these beams subjected to loading combinations.

Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory

This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.

Size-dependent behaviour of functionally graded microbeams using various shear deformation theories based on the modified couple stress theory

This study investigates the mechanical behaviours of functionally graded (FG) microbeams based on the modified couple stress theory. The material properties of these beams are varied through beam’s depth and calculated by using classical rule of mixture and Mori–Tanaka scheme. The displacement fields are presented by using a unified framework which covers various theories including classical beam theory, first-order beam theory, third-order beam theory, sinusoidal beam theory, and quasi-3D beam theories. The governing equations of bending, vibration and buckling problems are derived using the Hamilton’s principle and then solved by using Navier solutions with simply-supported boundary conditions. A number of numerical examples are conducted to show the validity and accuracy of the proposed approaches. Effects of Poisson’s ratio, material length scale parameter, power-law index, estimation methods of material properties and slenderness ratio on deflections, stresses, natural frequencies and critical buckling loads of FG microbeams are examined.

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

In this study, a model for dynamic instability of embedded single-walled carbon nanotubes (SWCNTs) is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory (SSDBT). The modified couple stress theory (MCST) is considered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton’s principle. The differential quadrature method (DQM) in conjunction with the Bolotin method is used in order to calculate the dynamic instability region (DIR) of SWCNTs. The effects of different parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The results depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system (NEMS) and micro-electro-mechanical system (MEMS).

Investigation of innovative steel runway beam in industrial building

The design of a runway beam for overhead cranes is of great importance when constructing steel structures, as is the lateral-torsional buckling (LTB) value obtained for I-beam sections. Therefore, engineers must always consider the optimal design of these beams under overhead cranes loads. In this study, runway beams of three overhead crane groups were analyzed for LTB, and a sinusoidal runway beam body was developed. These runway beams with different sinusoidal angles were analyzed by using the finite element method (ABAQUS) and compared to each other and other runway IPE-IPN beam sections; furthermore, all models were compared with the Canadian Institute of Steel Construction standard. As a result, a new method was proposed for developing sinusoidal runway beams for overhead cranes. The sinusoidal runway beam has lower weight than runway IPE-IPN beam sections. Ultimately, a sinusoidal beam body was developed practically with a scale of 1:1.

Experimental investigation of sinus beams with end-plate connections

Using high-strength steel with reduced weight in buildings and industry is important because, as the weight of the buildings is reduced, the behavior of steel in various situations becomes important. In this study, moment–rotation curves of sinusoidal beams were investigated using fixed end-plate connections. Use of a new sinusoidal beam model is proposed. Results were compared with experiments performed not only with IPE profile but also with similar manufactured profile. In the result, weight was reduced for sinusoidal 70° beams, showing improvements in terms of moment resistance.

Improved method on image detection at low light level using a sinusoidal-shaped-function signal

This study proposes an improved method which employs the shaped-function technology and Discrete Fourier Series Transform (DFST)-based algorithm to improve the subjective impression at low light level. A sinusoidal wave light signal which is generated in the low frequency range plays the role of a shaped-function signal. The basic procedure of the proposed method is that an LED with a time-varying (sinusoidal) beam is used to illuminate the image sensor evenly. Then, a DFST-based algorithm is employed to remove the sinusoidal wave signal from the captured images for restoring the low-light-level image signal with a low gray resolution. The main purpose of this method was to improve gray-level resolution and signal-to-noise ratio of the acquired image and process the image data in real time by sliding the window. The derivation processes and experiments verify that the improved method not only can reveal a better result than the algorithms we have proposed before, but also have a better performance on the imaging speed.