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An exact vibration-rotation kinetic energy operator for polyatomic molecules has been obtained. Using this Hamiltonian for sequentially bonded tetra-atomic molecules, all rovibrational terms have been derived with internal coordinates as the vibrational variables. The present approach is greatly simplified with less algebra compared with conventional methods. Also, simple and explicit expressions for the vibration-rotation coupling terms in internal coordinates are presented  

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass.... 

In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration... 

The transverse free vibration of a class of variable-cross-section beams is investigated using the Wentzel, Kramers, Brillouin (WKB) approximation. Here the governing equation of motion of the Euler-Bernoulli beam including axial force distribution is utilized to obtain a singular differential equation in terms of the natural frequency of vibration and a WKB expansion series is applied to find the solution. Based on this formulation, a closed form solution is obtained for determination of natural vibration mode shapes and the corresponding frequencies. The first four terms of this asymptotic solution are simplified for homogenous beams to give a compact third-order WKB approximation. Next,...