• Smart Structures and Systems
• /
• v.25 no.4
• /
• pp.501-514
• /
• 2020

This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS.

• Steel and Composite Structures
• /
• v.35 no.4
• /
• pp.555-566
• /
• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Steel and Composite Structures
• /
• v.31 no.5
• /
• pp.489-502
• /
• 2019

This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

• Structural Engineering and Mechanics
• /
• v.44 no.6
• /
• pp.735-751
• /
• 2012

Although being one of the most popular strengthening techniques in reinforced concrete beams, the use of steel plates bonded to the soffit raises problems of ductility. This study aims at investigating the influence of the use of perforated steel plates instead of solid steel plates on the ductility of reinforced concrete beams. A total of nine reinforced concrete beams were tested. In addition to an unplated beam, eight beams with perforated steel plates of two different thicknesses (3 mm and 6 mm) were subjected to monotonic loading. Effect of bonding the plates to the beams with anchor bolts and with additional side plates bonded to the sides of the beam with and without anchors is also investigated. The use of bolts in addition to epoxy was found to greatly contribute to the ductility and energy absorption capacity of the beams, particularly in specimens with thick plates (6 mm) and the use side plates in addition to the bottom plate was found to be ineffective in increasing the ductility of a concrete beam unless the side plates are attached to the beam with anchors bolts. The thickness of the plate was found to have little effect on the bending rigidity of the beam.

• Structural Engineering and Mechanics
• /
• v.76 no.6
• /
• pp.765-779
• /
• 2020

This article presents a nonclassical size dependent model based on the modified couple stress theory to study and analyze the bending behavior of perforated microbeams under different loading patterns. Modified equivalent material and geometrical parameters for perforated beam are presented. The modified couple stress theory with one material length scale parameter is adopted to incorporate the microstructure effect into the governing equations of perforated beam structure. The governing equilibrium equations of the perforated Timoshenko as well as the perforated Euler Bernoulli are developed based on the potential energy minimization principle. The Poisson's effect is included in the governing equilibrium equations. Regular square perforation configuration is considered. Based on Fourier series expansion, closed forms for the bending deflection and the rotational displacements are obtained for simply supported perforated microbeams. The proposed methodology is validated and compared with the available results in the literature and an excellent agreement is detected. Numerical results demonstrated the applicability of the proposed methodology to investigate the bending behavior of regularly squared perforated beams incorporating microstructure effect under different excitation patterns. The obtained results are significantly important for the design and production of perforated microbeam structures.

• Steel and Composite Structures
• /
• v.38 no.5
• /
• pp.583-597
• /
• 2021

This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson's effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

• Steel and Composite Structures
• /
• v.32 no.5
• /
• pp.643-655
• /
• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1998.04a
• /
• pp.135-140
• /
• 1998

The buckling of the perforated web of a simply supported Η-section beam subjected to uniformly distributed load is examined by means of the finite element method. With buckling analysis results, the effect of this hole on the load carrying capacity of the beam with dimensions L/h = 11 and 13 ( L = span length h = web depth) is investigated. The parameters whose variation have been considered are hole size and location. It can be generally concluded that the buckling of the perforated web of an H-section beam is not affected seriously by the location of the perforation.

• Steel and Composite Structures
• /
• v.49 no.6
• /
• pp.667-684
• /
• 2023

In the context of finite element method, a computational simulation is presented to study and analyze the dynamic behavior of regularly perforated functionally graded rotating beam for the first time. To investigate the effect of perforation configurations, both regular circular and squared perforation patterns are studied. To explore impacts of graded material distributions, both axial and transverse gradation profiles are considered. The material characteristics of graded materials are assumed to be smoothly and continuously varied through the axial or the thickness direction according the nonlinear power gradation law. A computational finite elements procedure is presented. The accuracy of the numerical procedure is verified and compared. Resonant frequencies, axial displacements as well as internal stress distributions throughout the perforated graded rotating cantilever beam are studied. Effects of material distributions, perforation patterns, as well as the rotating beam speed are investigated. Obtained results proved that the graded material distribution has remarkable effects on the dynamic performance. Additionally, circular perforation pattern produces more softening effect compared with squared perforation configuration thus larger values of axial displacements and maximum principal stresses are detected. Moreover, squared perforation provides smaller values of nondimensional frequency parameters at most of vibration modes compared with circular pattern.

• Journal of Dental Rehabilitation and Applied Science
• /
• v.20 no.1
• /
• pp.43-50
• /
• 2004

This study was performed to measure the retentive force of dental impression tray according to retention form. The 9 resin beams($30{\times}60{\times}2.5mm$) were made of visible light-curing tray resin according to the surface texture, the size of hole and the number of rim. The resin block was fabricated in width 50mm, length 30mm, heght 40mm to maintain an even hydrocolloid impression material. The retentive force between the resin beam and hydrocolloid impression material was measured by Universal Testing Machine(Zwick Z020, Zwick Co., Germany). The results obtained in this study were as follows : 1. The retentive force of the resin beam with bilateral 4 rims, 2mm holes(9group) was highest(9.18kg), and the polishing resin beam(2group) was worst(4.85kg). 2. There was no significant difference between the polished the resin beam(2group) and the contrast resin beam(1group). 3. The retentive force of the rimmed resin beam was higher than the perforated resin beam. 4. The retentive force of the 2mm perforated resin beam(4group) was higher than the 3mm perforated resin beam(3group). 5. As increasing the number of rim increased the retentive force.