Sharif Digital Repository

This paper deals with the dynamic analysis of Euler-Bernoulli beams at the resonant condition. The governing partial differential equation of the problem is converted into an ordinary differential equation by applying the well-known Fourier transform. The solution develops a Green's function method which involves establishing the Green's function of the problem, applying the pertinent boundary conditions of the beam. Due to the special conditions of the resonant situation, a significant obstacle arises during the derivation of the Green's function. In order to overcome this hurdle, however, the Fredholm Alternative Theorem is employed; and it is shown that the modified Green's function of... 

Experimental and theoretical results of a two-stage beam shaping system based on a flexible plastic fiber-bundle and a prism duct are described in this study. An imaging technique is used to investigate the divergence effect on the output beam images and intensity profiles. Photograph pictures of the output beam at different axial distances are taken by a digital camera and the image data is converted into a response curve and presented in this study. According to the experimental results, the propagation in the free space transforms a square beam with a hat-top intensity distribution into a rectangular beam with a conical intensity distribution. For theoretical investigations, using VOB... 

In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration... 

Using a physical optics based near-field method, we have proposed a hierarchy procedure for the design of dual polarized doubly curved reflectors. Using equivalent magnetic and electric currents at the aperture of the feed antenna and employing free space dyadic Green's functions, an optimization was performed for the design of a fan beam shaped reflector, needless of any far-field approximation. The designed antenna has been fabricated and measured. The measurement data proves the effectiveness of method and shows a good agreement with simulated results  

In this work, some vibrational response parameters of strain gradient based micro-spinning Rayleigh beams with mass eccentricity distribution are investigated within infinitesimal deformation conditions. Governing equations of motion are derived utilizing the Hamilton’s principle. The gyroscopic effects and rotary inertia are both included in the formulation. By applying the Galerkin method, analytical expressions for natural frequencies of the micro beam in forward and backward whirl motions are obtained. In addition, an expression for the vibrational amplitude of the micro-beam due to mass eccentricity distribution is determined. Some numerical results are presented to study the effect of... 

In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam... 

In this paper, the pump depletion and cross-focusing effects on the generation of twisted terahertz radiation are investigated. Based on the beating of two Laguerre-Gaussian lasers in a radial plasma channel, a twisted terahertz radiation can be produced. In the presence of pump depletion, the lasers power is consumed. So, the ponderomotive force nonlinearity decreases and the output terahertz field approaches to a saturation value. Under competition between the diffraction and nonlinearity effects, the amplitude of laser beam width oscillation grows. When the incident laser beams have non-similar topological charge numbers, the normalized generated terahertz amplitude is low and the pump... 

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are... 

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the non-uniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution... 

Laminated composite beams with variable thickness are being widely used in many engineering applications. To enhance the dynamic behavior of structures subject to random loading, tapered laminated beams incorporated with magnetorheological (MR) fluids (MR-tapered beam) are proposed. A finite element model has been developed for random vibration analysis of MR-tapered beam based on layerwise displacement theory. The effects of thickness ratios of tapered beam, magnetic fields, statistical properties, correlation and autocorrelation on dynamic behaviors of structures have been investigated. The proposed structural element significantly enhances the dynamic response of MR-tapered beam under... 

Tapered piezoelectric beams, because of their more efficiency to generate power, are required to be analyzed by simple models. In this paper, single degree of freedom (SDOF) relations are used to model transvers vibration of an exponentially tapered piezoelectric beam. For this purpose, first, response of the damped cantilevered Euler–Bernoulli beam with base excitation is obtained. Then, lumped parameters of the beam are extracted in order to calculate the SDOF model response. Comparing the Euler-Bernoulli beam model with the SDOF model shows that the lumped parameter model is not accurate enough to predict the beam’s response. Therefore, a tapering parameter dependent correction factor is... 

In this paper, we present a Gaussian to tophat beam shaper (GTBS) based on an all-dielectric metasurface lens for sub terahertz (sub-THz) applications. In order to calculate the required phase profile of the GTBS, we use an analytical procedure based on the geometrical transformation technique. The calculated phase profile is then realized by a silicon (Si) metasurface lens consisting of rectangular-shaped pillars of subwavelength dimensions. Because of large solution domain relative to the operation wavelength, we combined the beam envelope and the finite element methods to simulate the structure with a high precision. By designing an anti-reflection metasurface made up of periodically... 

In this paper, a new approach is used to obtain the nonlinear mode for a flexible cantilever beam. The dependency of resonance of the beam on the exciting force amplitude is observed experimentally and theoretically. In this regard, the end response of a cantilever beam under the base excitation is measured for various force amplitudes. Then, by using the nonlinear normal modes, the reduced-order governing equation is obtained. The discrete model obtained according to identification of nonlinear terms can predict the frequency response of the beam and jump phenomenon properly. Comparison between experimental data and theoretical outputs show acceptable agreement. © 2020 Faculty of... 

Laminated composite beams with variable thickness are being widely used in many engineering applications. To enhance the dynamic behavior of structures subject to random loading, tapered laminated beams incorporated with magnetorheological (MR) fluids (MR-tapered beam) are proposed. A finite element model has been developed for random vibration analysis of MR-tapered beam based on layerwise displacement theory. The effects of thickness ratios of tapered beam, magnetic fields, statistical properties, correlation and autocorrelation on dynamic behaviors of structures have been investigated. The proposed structural element significantly enhances the dynamic response of MR-tapered beam under... 

Shear connectors are essential elements in the design of steel-concrete composite systems. These connectors are utilized to prevent the occurrence of potential slips at the interface of steel and concrete. The two types of shear connectors which have been recently employed in construction projects are C- and L-shaped connectors. In the current study, the behavior of C and L-shaped angle shear connectors is investigated experimentally. For this purpose, eight push-out tests were composed and subjected to monotonic loading. The load-slip curves and failure modes have been determined. Also, the shear strength of the connectors has been compared with previously developed relationships. Two... 

In this paper, a thorough investigation of response of a composite Timoshenko simply-supported beam with actuating layers, under the motion of a partially distributed mass is studied and a control system based on the feedback of beam's deflection velocity is applied to alleviate and suppress the vibration of the beam in either case when the mass is still traveling on the beam or departed the beam. The actuating layers are made up of Terfenol-D smart material which are sensitive to magnetic field (magnetostrictive materials) and this trait makes them very suitable to be used for vibration control. They introduce damping to the system through which the energy of system dissipates. The response... 

This paper deals with the possibilities of cancellation of unwanted signals by steering nulls of the pattern in the direction of arrival of signal while keeping the main beam to the desired direction. New iterative adaptive digital beam forming technique is presented here to enhance the conventional effectiveness of beam forming in common commercial application. Simulation and measurement results confirm that this algorithm can achieve effective Co-Channel Interference (CCI) suppression, while increasing the strength of the desired signal  

In this contribution, we have investigated the effects of magnetoelastic loads on free vibration characteristics of the magnetorheological-based sandwich beam. The considered sandwich beam consists of a magnetorheological core with elastic top and base layers. For these means, the structural governing equations are derived using the Hamilton principle and solved by the finite element method. The results are validated in comparison with the existing results in the literature. The effects of variation in the parameters such as magnetic field intensity and the thickness of the core and top layers on the deviation of the first natural frequency and the corresponding loss factor are studied as... 

The transverse free vibration of a class of variable-cross-section beams is investigated using the Wentzel, Kramers, Brillouin (WKB) approximation. Here the governing equation of motion of the Euler-Bernoulli beam including axial force distribution is utilized to obtain a singular differential equation in terms of the natural frequency of vibration and a WKB expansion series is applied to find the solution. Based on this formulation, a closed form solution is obtained for determination of natural vibration mode shapes and the corresponding frequencies. The first four terms of this asymptotic solution are simplified for homogenous beams to give a compact third-order WKB approximation. Next,... 

A new 'universal' structural joint with multiple applications was devised. Its application as a 'beam-to-column joint' was already investigated experimentally, and proven to be promising. The results were reported in previous OMAE conferences and elsewhere. Another fruitful application conceived for this joint is in the context of joining (diagonal) braces to the frame members of a structure. In particular, in chevron (inverted V) bracing systems, where the dominating exchanged forces between the combined diagonal braces and the horizontal brace (beam) are 'shear,' the use of the devised joint as a joining member can substantially improve the overall behaviour of the structure under dynamic...