M. Attar

Dynamic response of cracked Timoshenko beams on elastic foundations under moving harmonic loads

A thorough understanding of the dynamic behavior of one-dimensional structural members such as beams plays a crucial role in specialized disciplines including ocean, bridge and railway engineering. The vibratory response of an in-service beam-like component may deviate from that expected from the intact structure when defects are present. In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of the subgrade are considered. The effects of transverse open cracks are modeled by massless rotational springs with a linear moment-rotation constitutive law to account for the local flexibility induced by the damage. Based on the transfer matrix method, the defective structure is treated as an assembly of sub-beams to derive the eigenvalue solution of the system. The time response is then obtained by utilizing identical generalized coordinates for lateral and rotational displacement components when applying the modal expansion technique. The use of general elastic end constraints allows us to recover all possible boundary conditions. Numerical examples are also provided to demonstrate the robustness and accuracy of the proposed method, and also to investigate the influence of important parameters on the dynamic behavior of the damaged structure.

Dynamics of a micro scale Timoshenko beam subjected to a moving micro particle based on the modified couple stress theory

In this study, the free and forced vibration analysis of a micro scale Timoshenko beam resting on a Pasternak elastic foundation and subjected to a moving micro particle is presented. Based on the modified couple stress theory and employing Hamilton’s principle, the governing equations along with the boundary conditions are derived. A semi-analytical solution is obtained for the free vibration of the problem by expressing the dynamic lateral displacement and cross-section rotation in terms of the series of Legendre polynomials and extremizing the objective functional of the problem with respect to the unknown displacements and Lagrange multipliers. Correspondingly, the computed eigenvalue information of the system is utilized in the modal expansion technique to obtain the transient dynamic response. For comparison purposes, the free vibration frequencies of the micro beam and the dynamic deflections using the classical Timoshenko beam theory are compared with previously published studies and very good agreements have been observed. Furthermore, more numerical examples for natural frequencies and dynamic deflection of the beam are presented and the effects of some parameters, such as the material length scale parameter, the velocity of micro particle, the Pasternak elastic foundation parameters, shear deformation effects and boundary conditions are examined.

Lattice Finite Strain Theory for Non-hydrostatically Compressed Materials

The purpose of this paper is to describe the nonlinear behaviour of geomaterials within the principles of thermodynamics. The main components of this contribution are (1) a new method to estimate the properties of minerals subjected to the non-hydrostatic compression in diamond anvil cell using the finite strain theory is introduced and (2) a proper measure of deformation that applies to a wide range of minerals is identified. This research work shows that the logarithmic (Hencky) strain produces a good agreement with experiments for a wide range of materials.