Article

# On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 4, 1113 Sofia, Bulgaria

Journal of Sound and Vibration (Impact Factor: 1.61). 01/2008; 311:1431-1437. DOI: 10.1016/j.jsv.2007.10.005 -
##### Article: Integral equation formulation and flutter analysis of damped non-conservative Timoshenko beams.

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**ABSTRACT:**This paper presents a mathematical modeling and a numerical methodological approach based on integral equation formulation and radial basis functions (RBF) for the dynamic behaviour damped Timoshenko beams under follower forces. Using the fundamental solution of the main operator and the RBF, the governing non-self-adjoint partial differential equation is transformed into an integral equation. Based on the harmonic assumption and internal concatenation points an eigenvalue problem is obtained and numerically solved. The flutter analysis, complex modes and the frequency load responses are investigated for beams under various subtangential follower loads, aspect ratios, internal and viscous damping.Mathematical and Computer Modelling. 01/2011; 53:234-248. - [Show abstract] [Hide abstract]

**ABSTRACT:**In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.Applied Mathematical Modelling 11/2011; 35(10):4796-4815. · 2.16 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The dynamic stability of cracked beams under the axial and follower force is studied. The governing equation and the closed form solution for the dynamic stability interaction diagram are derived. Innovative and simple algebraic equations for the interaction diagram are proposed. Thanks to these equations for construction of a diagram only the coordinates of the key points on the load and frequency axes is needed. Through extensive numerical experiments the accuracy, efficiency and robustness of the work is verified.Scientia Iranica 04/2013; 20(1):57-64. · 0.54 Impact Factor

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