Abstract
In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.
Highlights
Moving beams are broadly explored in various engineering industries, such as telescopic robotic manipulators, band-saw blades, crane hoist cables, high-speed magnetic tapes, and thread lines in the textile industry
It is worth noting that the governing equation of the system reduces to that of axially functionally graded (AFG) moving EB beam by setting β = 0
The stability of the AFG moving Rayleigh beams is profoundly affected by the sign of imaginary and real parts of the natural frequency
Summary
Moving beams are broadly explored in various engineering industries, such as telescopic robotic manipulators, band-saw blades, crane hoist cables, high-speed magnetic tapes, and thread lines in the textile industry. Dehrouyeh-Semnani et al [19] carried out a numerical investigation on the vibration characteristics of axially moving microbeams based on the Timoshenko beam theory Their numerical results obtained the size-dependent frequencies and critical velocities of the system for clamped-clamped and supported boundary conditions. With the aid of modulating materials properties, engineers improved the mechanical behavior of the moving systems [24,25,26] In this sense, employing the multiple scales method, the nonlinear forced vibration of axially moving sandwich viscoelastic beams was studied by Li et al [27]. They obtained the dynamic response and instability boundaries of the considered beam for various values of the core layer thickness and initial tension.
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