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This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

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The investigation to analyze a sandwich beam's dynamic stabilitywith asymmetric configuration, tapered along the thickness and width, and influenced by an alive axial load with temperature gradient is executed for several boundary conditions employing computational method. Use of Hamilton’s principle results in the equations of motion and related boundary conditions. Hill’s equations are achieved using non-dimensionalized equations of motion with the Galerkin’s method. Then, the influence ofseveral parameterson the dynamic stability for different boundary conditions are attained by applying Saito-Otomi conditions. The impact of differentparameters on the regions of instabilities observed and is showcased in a sequence of graphs using the appropriate MAT LAB program.

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