This paper examines the solution of a damped beam equation whose damping characteristics are well-defined by the fractional derivative (FD). Homotopy Analysis Method (HAM) is applied for calculating the dynamic response (DR). Unit step and unit impulse functions are deliberated for this analysis. Acquired results are illustrated to show the movement of the beam under various sets of parameters ...

In this work, the dynamic response of Euler–Bernoulli beams four different boundary conditions with fractional order internal damping under a traversing moving load is investigated. The assumed to be values constant velocity. A proposed approach obtain closed-form solution problem based on Green’s functions combined decomposition technique in Laplace transform domain introduced. Several cases a...

We present some models of viscoelastic systems with long-memory behaviour; we then provide both thorough mathematical analysis and numerical simulations of these models by means of so-called diiusive representations. The models under consideration are the basic harmonic oscillator with fractional damping, the generalized Lokshin model of waves, and also the boundary feedback control of the Eule...

This paper proposes the design of Fractional Order (FO) Butterworth filter in complex w-plane (w=sPqP; q being any real number) considering the presence of under-damped, hyper-damped, ultra-damped poles. This is the first attempt to design such fractional Butterworth filters in complex w-plane instead of complex s-plane, as conventionally done for integer order filters. Firstly, the concept of ...

First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the po...

We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with frictionally string by conditions. show that for this structure, the dissipation produced frictional part is strong enough to produce exponential decay of solution no matter how small its size. For stability in damped-damped-damped situation we use energy method. undamped-damped...

the dynamic response of the railway under accelerated moving load using dynamic green function is presented in this paper. for this purpose, an exact and direct modeling technique is introduced for the railway modeling as the damped euler-bernoulli beam on the partial winkler foundation with arbitrary boundary conditions subjected to the moving load. the effects of the elastic coefficient of wi...