Golden Equations for Dynamic Characteristics of Beam-Spring Systems

In damage detection of civil, mechanical, aerospace, nuclear, bio-mechanic, and offshore engineering, dynamic characteristics of beam-spring structures (BSS) play an important role. Recently, a new and innovative method for the free vibration of cracked bars is proposed. The method is extended for the free vibration of BSS. By introducing a new and innovative conjugate beam through defining a new variable, a single ordinary differential equation, golden equation, is obtained. The solution for the golden governing equation (GGE) is the same as that for an intact beam and so great simplicity and generality is obtained. Using the GGE, both closed form and numerical solutions are obtained. Through applying the work to specific examples and comparison of the results with the others, the accuracy, efficiency and robustness of the work is verified.

Keywords:

Beam-Spring System , Dynamic Characteristics , crack , Ranjbaran Transformation , Stiffness Reduction Method , Golden Equation , Golden Derivative