Amin Barari

Non-linear vibration of Euler-Bernoulli beams

In this paper, variational iteration (VIM) and parametrized perturbation (PPM) methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions.

Calibration of Failure Criteria for Bucket Foundations on Drained Sand under General Loading

A new concept with respect to offshore wind turbines, the bucket foundation, is known in the oil and gas industry, although the load conditions for wind turbines are significantly different. An extensive number of loading tests with small-scale bucket foundations subjected to combined loading were carried out in the geotechnical laboratory at Aalborg University in Aalborg, Denmark. Tests were performed on buckets of various sizes, embedment ratios, and load paths on saturated dense Aalborg University Sand No. 1. The experimental results were used to evaluate the behavior of the bucket foundations in accordance with the macromodel approach. An expression to describe the combined capacity of bucket foundations was developed by calibrating the failure criteria for bucket foundations.

Application of He's energy balance method to Duffing-harmonic oscillators

In this article, Hes energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems.

Dynamic Response of Inextensible Beams by Improved Energy Balance Method

An improved Hes energy balance method (EBM) for solving non-linear oscillatory differential equation using a new trial function is presented. The problem considered represents the governing equations of the non-linear, large-amplitude free vibrations of a slender cantilever beam with a rotationally flexible root and carrying a lumped mass at an intermediate position along its span. Based on the simple EBM, the variational integral of the non-linear conservative system is established, and the Fourier series expansion is employed to address the governing algebraic equations. An alternate procedure for a particular value of the initial condition is then used to estimate the constants. This semi-analytical representation gives excellent approximations to the exact solutions for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the simple EBM. Two illustrative examples are considered in order to elucidate the methods described, and to reveal the improvements made by the modified method.

Approximate analysis of two-mass-spring systems and buckling of a column

Max-Min Approach (MMA) is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system. After finding maximal and minimal solution thresholds of a nonlinear problem, an approximate solution of the nonlinear equation can be easily achieved using He Chengtians interpolation. Numerical results indicate the effectiveness of the proposed method both in respect of the whole range of involved parameters as well as the excellent agreement with the approximate frequencies and periodic solutions with the exact ones. It is predicted that MMA can be found widely applicable in engineering.

Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method

Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.

Vibrational analysis of curved single-walled carbon nanotube on a Pasternak elastic foundation

Continuum mechanics and an elastic beam model were employed in the nonlinear force vibrational analysis of an embedded, curved, single-walled carbon nanotube. The analysis considered the effects of the curvature or waviness and midplane stretching of the nanotube on the nonlinear frequency. By utilizing Hes Energy Balance Method (HEBM), the relationships of the nonlinear amplitude and frequency were expressed for a curved, single-walled carbon nanotube. The amplitude frequency response curves of the nonlinear free vibration were obtained for a curved, single-walled carbon nanotube embedded in a Pasternak elastic foundation. Finally, the influence of the amplitude of the waviness, midplane stretching nonlinearity, shear foundation modulus, surrounding elastic medium, radius, and length of the curved carbon nanotube on the amplitude frequency response characteristics are discussed. As a result, the combination effects of waviness and stretching nonlinearity on the nonlinear frequency of the curved SWCNT with a small outer radius were larger than the straight one.

Adaptive plasticity model for bucket foundations

AbstractBased on experimental investigations, the literature proposes different methods for modeling the behavior and capacity of foundations subjected to combined loading. Generally, two methods are used to predict the behavior of foundations: traditional approaches and hardening plasticity solutions. The first method is only capable of determining the capacity of the foundations and not the prepeak behavior. Thus, a new strain-hardening criterion is developed by calibrating failure criteria by employing data from small-scale tests on bucket foundations subjected to static loads. The shape of the yield, potential, and failure surfaces are found to be dependent on the embedment ratio (i.e., ratio of skirt length to the diameter) and load path. For the models tested, associated flow is observed to be plausible in the radial planes, whereas nonassociated flow is observed in the planes along the V-axis.

An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.