TY - JOUR ID - 240646 TI - Golden Equations for Dynamic Characteristics of Beam-Spring Systems JO - Journal of Seismology and Earthquake Engineering JA - JSEE LA - en SN - 1735-1669 AU - Ranjbaran, Abdolrasoul AU - Ranjbaran, Mohammad AD - Shiraz University Y1 - 2012 PY - 2012 VL - 14 IS - 3 SP - 219 EP - 225 KW - Beam-Spring System KW - Dynamic Characteristics KW - crack KW - Ranjbaran Transformation KW - Stiffness Reduction Method KW - Golden Equation KW - Golden Derivative DO - N2 - 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. UR - http://www.jsee.ir/article_240646.html L1 - http://www.jsee.ir/article_240646_f2922b7d2f342c34614462272aa5d816.pdf ER -