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Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation.

a b s t r a c tA traveling mass due to its mass inertia has significant effects on the dynamic response of the structures. According to recent developments in structural materials and constructional technologies, the structures are likely to be affected by sudden changes of masses and substructure elements, in which the inertia effect of a moving mass is not negligible. The transverse inertia effects have been a topic of interest in bridge dynamics, design of railway tracks, guide way systems and other engineering applications such as modern high-speed precision machinery process. In this study an analytical-numerical method is presented which can be used to determine the dynamic response of beams carrying a moving mass, with various boundary conditions. It has been shown that the Coriolis acceleration, associated with the moving mass as it traverses along the vibrating beam shall be considered as well. Influences regarding the speed of the moving mass on the dynamic response of beams with various boundary conditions were also investigated. Results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC's.

Summary Studies on corrugated steel shear walls (CSSWs) generally indicate noticeable increase of energy absorption, as well as increasing shear buckling capacity of corrugated plates being more likely rather than the flat plates. In this paper, the effect of variation in the angle of trapezoidal plate on the behavior of CSSWs has extensively been investigated. Three specimens of CSSW with 1 story and single bay in half scale are tested under cyclic load. The observations of experiment do indicate that stress concentration has been increased in the corner of subpanels, by increasing of the corrugation angle. Development of the tensile field and wall yield and damage depends on the geometry of the plate. By increasing the corrugation angle, the stiffness and energy dissipation decrease; in addition, large loss of strength takes place. Comparing the numerical and experimental results indicates that for a closer look at behavior of trapezoidal CSSWs, fracture mechanics, fatigue, and damping of materials should be considered by numerical analysis.