Qiao Ni

Application of the differential transformation method to vibration analysis of pipes conveying fluid

Abstract In this paper, a relatively new semi-analytical method, called differential transformation method (DTM), is generalized to analyze the free vibration problem of pipes conveying fluid with several typical boundary conditions. The natural frequencies and critical flow velocities are obtained using DTM. The results are compared with those predicted by the differential quadrature method (DQM) and with other results reported in the literature. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of pipes conveying fluid.

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth-order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.

MODELING AND DYNAMICS ANALYSIS OF SHELLS OF REVOLUTION BY PARTIALLY ACTIVE CONSTRAINED LAYER DAMPING TREATMENT

A new model for a smart shell of revolution treated with active constrained layer damping (ACLD) is developed, and the damping effects of the ACLD treatment are discussed. The motion and electric analytical formulation of the piezoelectric constrained layer are presented first. Based on the authors’ recent research on shells of revolution treated with passive constrained layer damping (PCLD), the integrated first-order differential matrix equation of a shell of revolution partially treated with ring ACLD blocks is derived in the frequency domain. By virtue of the extended homogeneous capacity precision integration technology, a stable and simple numerical method is further proposed to solve the above equation. Then, the vibration responses of an ACLD shell of revolution are measured by using the present model and method. The results show that the control performance of the ACLD treatment is complicated and frequency-dependent. In a certain frequency range, the ACLD treatment can achieve better damping characteristics compared with the conventional PCLD treatment.

Transfer matrix method for analyzing vibration and damping characteristics of rotational shell with passive constrained layer damping treatment

The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory. Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer. A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology. The numerical results show that present method is accurate and effective.

Nonlinear Vibration of A Loosely Supported Curved Pipe Conveying Pulsating Fluid under Principal Parametric Resonance

In this paper, the nonlinear dynamics of a curved pipe is investigated in the case of principal parametric resonance due to pulsating flow and impact with loose supports. The coupled in-plane and out-of-plane governing equations with the consideration of von Karman geometric nonlinearity are presented and discretized via the differential quadrature method (DQM). The nonlinear dynamic responses are calculated numerically to demonstrate the influence of pulsating frequency. Finally, the impact is taken into consideration. The influence of clearance on fretting-wear damage, such as normal work rate, contact ratio and impact force level, is demonstrated.