Shueei Muh Lin

Dynamic Analysis of Nonuniform Beams With Time-Dependent Elastic Boundary Conditions

The dynamic response of a nonuniform beam with time-dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained nonuniform beams given by Lee and Kuo. The time-dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third-order degree, instead of the fifth-order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.

Free vibration of a rotating non-uniform beam with arbitrary pretwist, an elastically restrained root and a tip mass

Abstract The governing differential equations for the coupled bending–bending vibration of a rotating beam with a tip mass, arbitrary pretwist, an elastically restrained root, and rotating at a constant angular velocity, are derived by using Hamiltons principle. The frequency equation of the system is derived and expressed in terms of the transition matrix of the transformed vector characteristic governing equation. The influence of the tip mass, the rotary inertia of the tip mass, the rotating speed, the geometric parameter of the cross-section of the beam, the setting angle, and the pretwist parameters on the natural frequencies are investigated. The difference between the effects of the setting angle on the natural frequencies of pretwisted and unpretwisted beams is revealed.

Analysis of rotating nonuniform pretwisted beams with an elastically restrained root and a tip mass

Abstract Using Hamiltons principle derives the governing differential equations for the coupled bending–bending vibration of a rotating pretwisted beam with an elastically restrained root and a tip mass, subjected to the external transverse forces and rotating at a constant angular velocity. Using the mode expansion method derives the closed-form solutions of the dynamic and static systems. The orthogonal condition for the eigenfunctions of the system with elastic boundary conditions is discovered. The self-adjointness of the system is proved. Moreover, the Green functions of the system are obtained. The symmetric properties of the Green functions are revealed. The frequency response on the steady response of the beam is also investigated.

Closed-form solutions for dynamic analysis of extensional circular Timoshenko beams with general elastic boundary conditions

Abstract Closed-form solutions for dynamic analysis of extensional circular Timoshenko beams with general elastic boundary conditions are derived. Taking the Laplace transform and some procedures, the system composed of three coupled governing differential equations and six coupled boundary conditions is uncoupled and reduced to a single equation in terms of the angle of rotation due to bending. The explicit relations between the inward radial displacement, the tangential displacement and the angle of rotation due to bending are revealed. Six exact normalized fundamental solutions of the uncoupled governing differential equation are obtained by the Frobenius method. The exact transformed general solution of the uncoupled system is expressed in terms of the six fundamental solutions, using the generalized Green function given by Lin. The systems based on the Rayleigh and Bernoulli–Euler beam theories can be obtained by taking the corresponding limiting procedures. Without the Laplace transform, the exact solutions for the steady and free vibrations of the general system are obtained. The effects of the spring constants, the opening angle, the rotary inertia and the shear deformation on the natural frequencies are investigated.

Modified Method of Semi-Analytical Transition Matrix on the Analysis of a Coupled Vibration System.

The coupled bending-extensional in-plane vibration of a rotating curved beam is considered. The dynamic system is governed by two coupled differential equations and six boundary conditions. The conventional method of transition matrix is usually used to solve the system composed of one nth order differential equation and n boundary conditions. In this study, the system of a rotating curved beam is different from that of the conventional one. The modified method of a semi-analytical transition matrix is developed to study this system. Finally, several physical observations about the rotating curved beam are manifested.