Effect Of Beam Thickness Research Articles

Size-dependent vibration of laminated functionally graded curved beams covered with piezoelectric layers

The nonlocal piezoelectric theory and first-order shear deformation theory are combined to study the nano-scale effect on the free vibration of a laminated functionally graded curved nano-beam covered with piezoelectric layers. The first-order shear deformation theory is introduced to consider the shear deformation and rotary inertia effects resulting from the torsional and flexural deformations. The effective elastic properties of the elastic nano-layers are estimated by using the Cox model. The governing equations are derived by employing Hamilton’s principle, and the efficient differential quadrature method is used to solve the discretized equations. Through numerical examples, it is found that the effects of beam thickness, volume fraction of fibers, curve parameter and boundary conditions on the natural frequencies are quite related to the nonlocal coefficient of curved beam. The vibration characters of curved nano-beam are discussed in detail.

Elastic interaction between nonlinear solitary waves in granular chains and composite beams: Experiments and modelling

We study the elastic interaction between strongly nonlinear solitary waves in lightly pre-compressed granular chains and laminated composite beams using experimental, analytical and numerical approaches. Experiments were conducted using a vertical array of 21 steel beads contacting a simply-supported composite beam at mid-span. A striker bead was dropped from a given height to initiate the propagation of a single solitary wave in the granular chain, whose interaction with the beam resulted in the propagation of multiple reflected solitary waves. The developed apparatus allowed measuring the delays and amplitudes of the reflected waves, and the obtained measurements were found in good agreement with numerical predictions based on a previously developed discrete element (DE) model. The numerical model was further simplified to derive a closed-form analytical solution for the delay of the primary reflected wave whose predictions showed no discernible differences to those obtained from the DE model. Experiments and predictions were performed on beams made of carbon fiber/epoxy and glass fiber/epoxy laminates, and the effects of beam thickness, width and flexural modulus on the characteristics of the reflected solitary waves were studied. We tested composite beams with thickness-to-length ratio in the range of 0.015 < H/L < 0.06 and found that the delays and amplitudes of the reflected nonlinear pulses are highly sensitive to the flexural modulus of the composite beam, concluding that the developed non-destructive technique is capable of measuring basic elastic properties of engineering composites, offering a reliable, time-efficient and cost-sensitive alternative to existing destructive and non-destructive test methods.

Investigation of the Effect of Electron Beam Quality on a 0.68-THz Second Harmonic Gyrotron

The lack of high-power terahertz sources is a major impediment to the development of terahertz science and technology. The gyrotron has great potential to generate high-power terahertz radiation, and so attracts extensive attention. In order to alleviate the problems of limited power capacity and wall loading, the high-order modes are often chosen to be the operating modes. Due to the dense spectrum of the modes, it will cause intense mode competition, which is harmful for the stable operation of a gyrotron. Currently, a 0.68-THz second harmonic gyrotron is under development in the Terahertz Research Center of University of Electronic Science and Technology (UESTC). The experiment shows that the measured output power is 2.75 kW with the efficiency of 9.05%. In order to determine whether the operating mode is the desired mode TE−15,2, the calculation of the starting current should be more accurate. In this article, we generalize the existing linear theory for the starting current, considering the effects of beam thickness and velocity spread. The starting currents of the operating mode and its competing modes are calculated using our designed gyrotron. We find out that the velocity spread and the beam thickness have significant influence on the starting current. The calculations also show that the desired mode TE−15,2 can be triggered first at the operating point. Besides, the measured output power from the experiment is much lower than that of the simulation result. Therefore, the effects of the velocity spread and beam thickness on beam–wave interactions are also analyzed; our results show that the efficiency is sensitive to the beam quality.

Theory of terahertz Smith-Purcell radiation from a cylindrical grating

An analysis of an annular electron beam propagating along a cylindrical grating with external magnetic field Bo is presented. The grating comprises a dielectric in its slots. The dispersion relation of the modes is derived. The results demonstrate that the dielectric shifts the frequencies of the system modes to smaller values. The growth rates of the modes which are in phase with the beam are also considered. It is found that the decline in the growth rate is brought about by the dielectric. In addition, increasing the thickness of the dielectric and decreasing the height of the slots cause it to rise. The effect of beam thickness on growth rate is considered too. This is shown to increase and then fall as beam thickness increases. These results show that utilizing cylindrical grating loaded with dielectric has a promising effect on developing new kinds of compact high-efficient THz free-electron lasers based on Smith–Purcell radiation.&#x0D; Edited by: A. B. Márquez

Correlation of CLPT and FSDT Responses in CNT/Polymer Composite Beams Under Deflection and Buckling

The principal intention of this research paper is to compare the Classical Laminate Plate Theory (CLPT) and First-order Shear Deformation Theory (FSDT) based on the buckling and deflection performance of Carbon Nanotube (CNT) Reinforced Polymer Composite beams. A symmetric, eight layered, and simply supported nanocomposite beam is taken for the comparison of CLPT and FSDT. The Mori-Tanaka micro-mechanical approach is used for the computation of elastic constants as a function of volume fraction of CNT reinforcement for the CNT/Polymer composite material. The elastic constants obtained are extensively utilized to discover the critical buckling loads and deflections by using CLPT and FSDT. The variations are presented in graphical form for the buckling and deflection of beams for various stacking sequences and CNT volume fractions. The effect of shear deformation is studied in both deflection and buckling of nanocomposite beams. The effect of beam thickness on the bending loads and buckling loads in both the theories is also studied from the results.

Nonlinear free vibration of an Euler-Bernoulli composite beam undergoing finite strain subjected to different boundary conditions

In this paper, the free vibration of an orthotropic beam undergoing finite strain are studied. The second Piola-Kirchhoff stress tensor and Green-Lagrange strain tensor according to finite strain assumption were used to obtain Euler-Bernoulli beam governing equations. The Galerkin method and Generalized Differential Quadrature method were employed for solving the governing equations and boundary condition. The effect of beam thickness and different boundary conditions were considered in finite strain formulation of the beam equations. Natural frequencies of different composite materials are obtained and compared. The results revealed that by increasing the beams thickness, the difference between maximum vibration amplitude increased between von Karman and finite strain formulations. Also, in a beam with simply- simply supports, differences between linear and non linear mode shapes was remarkable.

Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8) finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8) finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

Linear theory of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam

A three-dimensional model of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam for the beam-wave interaction is proposed. Based on this model, the hybrid-mode dispersion equation is derived with the Borgnis potential function by using the field-matching method. Its approximate solution is obtained under the assumption of a dilute electron beam. By using the Ansoft high frequency structural simulator (HFSS) code, the electromagnetic field distribution in the interaction structure is given. Through numerical calculations, the effects of beam thickness, beam and dielectric-layer gap distance, beam voltage, and current density on the resonant growth rate are analysed in detail.

Energy Harvesting Devices Using Macro-fiber Composite Materials

This study addresses the experimental validation of a design methodology for an energy harvesting device utilizing macro-fiber composite (MFC) materials. The energy harvesting device is composed of a cantilever beam with MFC elements, a tip mass, a rectifier, and an electrical resistance. A theoretical model of the energy harvesting device was developed for the estimation of generated power, voltage, and current under sinusoidal base excitation at its first natural frequency, and its performance verified via experiment. A parametric study was performed to gain insight into methods to maximize generated power and current based on perturbations to beam thickness, length, width, and density. Performance characteristics of the energy harvesting device utilizing two types of MFC patches (d31- and d33-types) were experimentally evaluated under different acceleration levels. In addition, the effects of beam thickness, natural frequency, and electrical resistance were experimentally investigated.

Dispersion and gain investigation of a cerenkov grating amplifier

The sheet electron beam propagation over a rectangular deep groove grating is investigated and the interaction between surface harmonic waves, which are evanescent above the grating surface, with a dilute sheet electron beam is analyzed. It is assumed that a strong axial magnetic field is applied to constrain the motion of electrons along the waveguide axis. Under these conditions, a complex dispersion equation is derived and analyzed by using Taylor expansion. This expansion results in an analytical formulation for the gain. Using the derived analytical formulation of the gain, the effects of beam thickness, beam-grating gap, and characteristics of grating on gain is investigated.

Discrete element analysis of dynamic response of Timoshenko beams under moving mass

In this paper, dynamic response of Timoshenko beams under moving mass is analyzed using a numerical method called discrete element technique (DET). In DET, continuous flexible beam elements are replaced by a system of rigid bars and flexible joints. We present a DET model of Timoshenko beams under moving mass. The results of our DET model are compared with the solutions obtained by PAFEC (programs for automatic finite element calculations) for Euler–Bernoulli beams and finite difference method for Timoshenko beams. The effects of beam thickness and moving mass velocity on dynamic response of beams under moving mass are numerically studied.

Effect of beam thickness in a Cherenkov laser

The effect of beam thickness in a two-dimensional Cherenkov laser is investigated on the basis of the fluid model for the electron beam. In the analysis, the transverse variation of the drift velocity for the electron beam is taken into account. The numerical simulation shows that there exists an optimum beam thickness for an efficient use of the electron beam in the Cherenkov laser.

Some Effects of Beam Thickness on Photon Migration in a Turbid Medium

Abstract We analyse the effects of extended rather than point optodes on several properties of photon migration in a turbid medium with internal absorption in a diffusion model suggested by a number of biomedical applications. The parameters considered include the surface flux of photons re-emitted back through the surface as a function of distance from the centre of the injecting optode, the surface intensity profile as a function of time for optodes separated by a fixed distance, and the distribution of the maximum depth reached by a photon, conditional on its being re-emitted through the interface at a variable distance from the injection point. Our major result is that the effects of extended optodes are much more significant when internal absorption is high.

Effect of energy spread and gyromotion on efficiency of a Smith-Purcell FEL

Abstract The start-oscillation current, gain and energy spread requirement for operation of a Smith-Purcell free-electron laser oscillator are determined. The effects of beam thickness, energy spread and gyromotion on the efficiency are discussed.