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Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.

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An analytical solution is performed using stress function approach for multi-layered filament-wound composite cylinders subjected to combined internal pressure and thermal loading. It is assumed that there is a liquid or gas of various temperatures in the cylinders. The effects of the wind angle variation through the radial section of the cylinders are also investigated. Thus, the layers are oriented symmetrically and antisymmetrically for (0°/90°), (30°/-30°), (45°/-45°) and (60°/-60°) orientations. A computer program is developed to conduct stress and deformation analyses of composite cylinder with different winding angle. All the integration constants are found from the radial stress and displacement in the normal direction of layers.