The Response of a Prestressed Beam-type Structure subjected to Partially Distributed Load Moving at Non-Uniform Velocities

The transverse vibration of a prismatic Rayleigh beam resting on bi-parametric Vlasov foundation and continuously acted upon by partially distributed masses moving at varying velocities is investigated. For the solution of the fourth order partial differential equation with singular and variable coefficients, use is made of the technique based on the Generalized Finite Fourier Integral Transform, Struble’s asymptotic technique and the use of Fresnel sine and cosine identities. Numerical results in plotted curves are presented. The results show that the response amplitude of the beam traversed by a distributed load moving with variable velocity decrease with an increase in the value of foundation modulus, Other structural parameters such as axial force, rotatory inertia and shear modulus are also found to reduce the displacement response of the beam as their values are increased in the dynamical system. The results also show that the critical speed for the system traversed by a moving distributed force is found to be greater than that traversed by moving mass. This confirms that the inertia effect of the moving distributed load must be considered for accurate and safe assessment of the response to moving distributed load of elastic structural members.

Sliding Frictional Contact of Functionally Graded Magneto-Electro-Elastic Materials Under a Conducting Flat Punch

This paper presents the two-dimensional sliding frictional contact between a rigid perfectly conducting flat punch and a functionally graded magneto-electro-elastic material (FGMEEM) layered half-plane. The electric potential and magnetic potential of the punch are assumed to be constant within the contact region. The magneto-electro-elastic (MEE) material properties of the FGMEEM layer vary as an exponential function along the thickness direction, and the Coulomb type friction is adopted within the contact region. By using the Fourier integral transform technique, the problem is reduced to coupled Cauchy singular integral equations of the first and second kinds for the unknown surface contact pressure, electric charge, and magnetic induction. An iterative method is developed to solve the coupled equations numerically and obtain the surface MEE fields. Then, the interior MEE fields are also obtained according to the surface MEE fields. Numerical results indicate that the gradient index and friction coefficient affect both the surface and interior MEE fields significantly.

Mode I Crack Problem for a Functionally Graded Orthotropic COATING-Substrate Structure

In this paper, the Fourier integral transform-singular integral equation method is presented for the Mode I crack problem of the functionally graded orthotropic coating-substrate structure. The elastic property of the material is assumed vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. Numerical examples are presented to illustrate the effects of the crack length, the material nonhomogeneity and the thickness of coating on the stress intensity factors.

Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part II: Implementation, Validation, and Numerical Results

In part I of the present article the formulation for a dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full-space has been presented. The solution is obtained within the frame of a double Fourier integral transform. These inverse integral transforms must be evaluated numerically. In the present paper, the technique to evaluate numerically the inverse double Fourier integrals is described. The procedure is validated, and a number of original displacement results for the stationary loading case are reported.

Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

A dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full space is presented. The solution is obtained within the frame of a double Fourier integral transform. Closed-form solutions for general loadings within the full space are furnished in the transformed wave number domain. Expressions for three boundary value problems, associated to a normal and two tangential rectangular loadings in the original physical space, are given in terms of a double inverse Fourier integral. These inverse integral transforms must be evaluated numerically. In the second part of the present paper a strategy to evaluate these integrals is described, the procedure validated and a number of original results are reported.