Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

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.

Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

“…In this paper, the Galerkin technique used to solve the vibration equations of a cracked graded Rayleigh beam. The general form of Galerkin technique is given as [31]:…”

“…Raising the regression index of material property causes the drop in natural frequencies, while natural frequencies rise in the case of an increase in axial velocity as manifest in the results. A. Shariati et al [31], the vibration equation of the viscoelastic moving graded beam in which properties change axially based on exponential law distribution was derived according to Euler and Rayleigh models. The vibration equations were resolved by the Galerkin approach.…”

“…The differential equation of the second-order can be reduced to the differential equation of the first order, as [31]…”

Aeroelastic Optimization of the High Aspect Ratio Wing with Aileron

“…This influence has direct effect on wing performances and therefore is considered as one of the challenging problems. The aeromechanical design instructions can be revealed from the study on positioning and instability of the ailerons [20] at the trailing edge of different wings which were conducted by researchers via the Finite volume method [21,22]. Dixon and Mei expanded the use of the applicable design methods for composite panels as they are considered common materials in aerospace industry.…”

Vibration Localization and Anti-Localization of Nonlinear Multi-Support Beams with Support Periodicity Defect

“…Numerous studies have reported characteristic frequencies [1][2][3][4], modal localization and buckling [5][6][7][8][9][10][11][12][13][14], quasi-periodic distribution parameter effects [15][16][17][18] and application [19][20][21][22][23][24][25][26][27] based on transfer matrix method, spatial (Bloch) harmonic expansion method, (Floquet-Bloch and Galerkin) double expansion method and finite element method, etc. Waves and vibration in beams with non-uniform distribution parameters have also been pursued using a fundamental solution, semianalysis and finite element methods [28][29][30][31][32][33][34]. Perturbation and multiple scale methods were applied for weakly periodic parameter cases [35,36].…”