By utilizing the Hamilton principle and the consistent linearization of the fully nonlinear beam theory, two coupled governing differential equations for a rotating inclined beam are derived. Both the extensional deformation and the Coriolis force effect are considered. It is shown that the vibration system can be considered as the superposition of a static subsystem and a dynamic subsystem. The method of Frobenius is used to establish the exact series solutions of the system. Several frequency relations that provide general qualitative relations between the natural frequencies and the physical parameters are revealed without numerical analysis. Finally, numerical results are given to illustrate the general qualitative relations and the influence of the physical parameters on the natural frequencies of the dynamic system.

Based on the generalized differential quadrature (GDQ) method, this paper presents, for the first instance, the free-vibration behavior of a rotating thin truncated open conical shell panel. The present governing equations of free vibration include the effects of initial hoop tension and the centrifugal and Coriolis accelerations due to rotation. Frequency characteristics are obtained to study in detail the influence of panel parameters and boundary conditions on the frequency characteristics. Further, qualitative differences between the vibration characteristics of rotating conical panels and that of rotating full conical shells are investigated. To ensure the accuracy of the present results using the GDQ method, comparisons and verifications are made for the special case of a stationary panel.

It is well known that the in-plane stress and displacement distributions in a stationary annular disk under stationary edge tractions can be obtained through the use of Airy stress function in the classical theory of linear elasticity. By using Lame’s potentials, this paper extends these solutions to the case of a spinning disk under stationary edge tractions. It is also demonstrated that the problem of stationary disk-spinning load differs from the problem of spinning disk-stationary load not only by the centrifugal effect, but also by additional terms arising from the Coriolis effect. Numerical simulations show that the amplitudes of the stress and displacement fields grow unboundedly as the rotational speed of the disk approaches the critical speeds. As the rotational speed approaches zero, on the other hand, the in-plane stresses and displacements are shown, both numerically and analytically, to recover the classical solutions derived through the Airy stress function.

Without considering the Coriolis force, the governing differential equations for the pure bending vibrations of a rotating nonuniform Timoshenko beam are derived. The two coupled differential equations are reduced into two complete fourth-order differential equations with variable coefficients in the flexural displacement and in the angle of rotation due to bending, respectively. The explicit relation between the flexural displacement and the angle of rotation due to bending is established. The frequency equations of the beam with a general elastically restrained root are derived and expressed in terms of the four normalized fundamental solutions of the associated governing differential equations. Consequently, if the geometric and material properties of the beam are in polynomial forms, then the exact solution for the problem can be obtained. Finally, the limiting cases are examined. The influence of the coupling effect of the rotating speed and the mass moment of inertia, the setting angle, the rotating speed and taper ratio on the natural frequencies, and the phenomenon of divergence instability (tension buckling) are investigated.

An exact solution of oscillatory Ekman boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and other at rest, is obtained. The effect of coriolis force on the resultant velocities and shear stresses for steady and unsteady flow has been studied.

The dynamic response of a single-degree-of-freedom structure attached to the interior of a rigid ring that is rotating with constant angular velocity is investigated. It is assumed that the deformations of the structure from the undeformed configuration are small, and that the structure exhibits linear elastic material behavior. Both undamped and viscously damped structures are considered. Inclusion of all of the essential dynamic features of the problem (notably Coriolis effects) results in a nonlinear differential equation governing the response of the attached structure. Numerical and analytical studies are performed on the nonlinear governing equation to determine the response and stability of the structure.

A general theory is presented to account for the out-of-plane motion of uniformly curved tubes containing flowing fluid. The systems are grouped as conservative and nonconservative according to the support conditions. A general solution for the natural frequency is obtained and numerical results are presented. The effects of the flow velocity and Coriolis force on the natural frequency are discussed. It is shown that when the flow velocity exceeds a certain value, the tube becomes subject to the buckling-type instability for conservative cases and the fluttering-type instability for nonconservative cases. In the subcritical range of flow velocity, the conservative system performs free oscillations, while the nonconservative system performs damped oscillations.

The free oscillations of a fluid in a rotating, axially symmetric container are investigated under the assumption that the equilibrium motion of the fluid be a rigid-body rotation. Gravitational forces are neglected. The resulting boundary-value problem leads to an elliptic or hyperbolic partial differential equation, depending on the frequency/angular velocity ratio. The problem is solved for a cylindrical container and discussed exhaustively. Due to the Coriolis force, there exist modes with the radial velocity component vanishing inside the fluid (“nodal cylinders”), besides the usual nodes in axial and azimuthal direction. The oscillations in the neighborhood of critical container dimensions are analyzed. Numerical results are presented in graphs.