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Abstract: An analytical approach is employed to investigate the transient and steady-state stresses in an isotropic, homogeneous half-space subjected to moving concentrated loads with subsonic speeds. Applying the Stokes–Helmholtz resolution to the Navier’s equation of motion for the half-space results in a system of wavetype partial differential equations. Based on the new moving coordinate system, a modified system of partial differential equations is obtained. Applying a concurrent two-sided and one-sided Laplace transformation, this system is modified to a system of ordinary differential equations, the solutions of which are obtained with respect to boundary conditions. The transformed transient stresses can be inverted by the Cagniard–de Hoop method. Special properties of Laplace transformation yield the steady-state stresses through an analytical approach. Numerical examples are presented to illustrate the methodology. Final results revealed the importance of considering the stresses related to the initial stages of the loading. [Copyright &y& Elsevier]

Abstract: A three-dimensional semi-analytic analysis based on the linear elasticity theory is offered to study the transient vibration characteristics of an arbitrarily thick, simply supported, functionally graded (FGM) rectangular plate, resting on a linear Winkler–Pasternak viscoelastic foundation, and subjected to general distributed driving forces of arbitrary temporal and spatial variations. The problem solution is obtained by adopting a laminate model in conjunction with the powerful state space solution technique involving a global transfer matrix and Durbin’s numerical Laplace inversion algorithm. Numerical calculations are carried out for the transient displacement and stress responses of aluminum-zirconia FGM square plates of selected thickness parameters and compositional gradients, resting on “soft” or “stiff” elastic foundations, under the action of moving transverse forces as well as uniformly distributed blast loads. Also, the response curves for the FGM plates are compared with those of equivalent bilaminate plates containing comparable total volume fractions of constituent materials. It is observed that the material gradient variation is substantially more influential on the dynamic stress concentrations induced across the plate thickness than on the displacement response of the inhomogeneous plates. In particular, the displacement response of the equivalent bilaminate plates can provide an accurate estimate for prediction of the dynamic response of the corresponding FGM plates, especially for thick plates resting on a stiff foundation. Limiting cases are considered and good agreements with the data available in the literature as well as with the computations made by using a commercial finite element package are obtained. [Copyright &y& Elsevier]

Abstract: A mathematical model, the formulation of which is premised on the higher-order modified couple stress theory, is presented for the free vibration analysis of a circular doubly-symmetric spinning micro beam embedded in an elastic medium. Based on the higher-order constitutive model, the extended Hamilton''s principle is applied to the size-dependent energy expressions to arrive at the coupled elastodynamics governing equations of the micro beam in two orthogonal planes. The spectral element method (SEM) is then used for detailed frequency analyzes of the micro beam in the presence of the material length scale, Poisson''s ratio and an elastic medium of the Winkler-type. The accuracy of the SEM predictions is numerically ascertained by contrasting with exact solutions of the classical model. Numerical results from the frequency analyzes reveal the doubling of the forward critical speed of the spinning micro beam under a range of the size effect. Parametric studies through an applied statistical tool of Pareto charts demonstrate the existence of interaction effects under nonlinear variations of the material length scale, the Poisson''s ratio, the elastic foundation stiffness and the spinning rate. [Copyright &y& Elsevier]

I present analytical time-domain expressions for the Green's functions, which represent the transient stress response of an infinite, homogeneous and isotropic medium to a constant slip rate on a triangular fault that continues perpetually after the slip onset. The solution can be utilized in the formulation of boundary element methods, which discretize a fault plane of any arbitrary geometry into an assembly of small triangular elements and assume the slip rate to be piecewise constant within each discrete element. [ABSTRACT FROM AUTHOR]