Mechanical Engineering Commons^™

Transcendental Eigenvalue Problems Associated With Vibration, Buckling And Control, Jayaram Subramanian

LSU Master's Theses

The static and dynamic analysis of structures requires us to obtain solutions of their espective governing differential equations subject to appropriate boundary conditions. The dynamic analysis of non-uniform continuous structures is of primary interest, as most traditional methods take the help of discrete models to analyze them. Well established discrete model methods lead to an algebraic eigenvalue problem, the characteristic equation associated with which is a polynomial. The spectral characteristics of a continuous system nevertheless are represented by transcendental functions and cannot be approximated by polynomials efficiently. Hence finite dimensional discrete models are not capable of predicting the response of …