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Every mechanical structure exhibit natural mode of vibrations. Beams with variable cross-section and material properties are frequently used in aeronautical, mechanical, civil engineering .Given the elastic and inertia characteristics of the structures, mode of vibration can be computed, the study being known as modal analysis. Sandwich beams offer designers a number of advantages, such as the high strength to weight ratio, flexibility, high bending and buckling resistances.Sandwich materials are frequently used wherever high strength and low weight are important criteria.(Maha M. A. Lashin e tal, 2015) In the present study a sandwich beam of size 10 mm X 10 mm cross-section with a length of 1 meter is considered. Analysis is done for different combinations of material and randomly varying the type of material across the depth of the cross-section of the beam. The response is calculated in terms of natural frequency. Using Monte-Carlo simulation design matrix was generated. Response surface methodology was applied in the present study using Design expert software for modeling and analysis of response parameter in order to obtain the natural frequency of the beam. A multiple regression analysis was carried out to obtain coefficients and the equations that can be used to predict the responses viz natural frequency. The sandwich beam which gave maximum frequency is Carbon-Aluminium-Carbon. The maximum frequency for the first mode was found out to be 41.22 Hz. Further, optimisation is carried and the best possiblecombination in order to get the maximum frequencyis found out.

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