In the present study, an analytical closed form solution for free vibration response of hybrid composite plate reinforced with shape memory alloy (SMA) fibers is derived. Recovery stresses generated during martensitic phase transformation are obtained based on onedimensional Brinson's model. The mechanical properties of plate are assumed to be temperature dependent. Based on the first-order shear deformation theory (FSDT) the governing equations are obtained via Hamilton's principle. Ritz method is used to obtain the fundamental natural frequency of the plate for different temperatures. A detailed parametric analysis shows the strong influence of the volume fraction, pre-strain, orientation and location of SMA fibers as well as the aspect ratio of the plate on the fundamental natural frequency and the onset of the thermal buckling.

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In the present study, the response of a flexible string with large amplitude transverse vibration is studied utilizing amplitude-frequency formulation, improved amplitude-frequency formulation and max-min approach. In order to verify the accuracy of these approaches, obtained results are compared with other methods such as variational approach method, variational iteration method, coupling Newton's method with the harmonic balance method and Hamiltonian approach. It has been found that for this problem, while amplitude-frequency formulation and max-min approach give the same results, improved amplitude frequency formulation is not an appropriate choice.Keywords nonlinear vibration, string, amplitude-frequency formulation, improved amplitude-frequency formulation and max-min approach.

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