Vibration analysis for stability of singular non-self-adjoint beam-columns using stochastic FEM

Mechanical properties of modern engineering materials such as fibre reinforced laminated composites, possess a stochastic variation over mass products. The response characteristics become stochastic as a result and so a probabilistic approach should be deployed for vibration testing, vibration analysis and design. In this context, existing works deal only with the self-adjoint mechanical systems. However, a vast majority of machinery and structural systems, such as the rotor-bearing systems, active control systems and fluid flowing pipes, are non-self-adjoint systems. A stochastic analysis methodology based on the Finite Element Method, that has many computational advantages and is more accurate, is developed in the present paper for such non-self-adjoint systems. Since applications in both design and testing are the objectives of the present work, the complex case of the so-called singular non-self-adjoint systems that arises in the vibration testing of mechanical systems is considered. In the formulation, the virtual work done by the forces that make the mechanical system is considered. In the formulation, the virtual work done by the forces that make the mechanical system non-self-adjoint, is determined considering the virtual displacements to be the variations of the actual displacements. An eigenvalue shifting scheme that is appropriate to the stochastic analysis is developed and deployed. The probabilistic quantification of vibration frequencies and critical loads is then performed based on the sensitivity gradients. (C) 1998 Elsevier Science Ltd. All rights reserved.