Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics

Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid

Nonlinear energy sink with inerter

The free thermal vibration of functionally graded material (FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise (UTR), nonlinear temperature rise (NLTR), and linear temperature rise (LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the strain-displacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover, the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

https://link.springer.com/content/pdf/10.1007%2Fs10483-018-2388-6.pdf

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

In this paper, a detailed review on the dynamics of axially moving systems is presented. Over the past 60 years, vibration control of axially moving systems has attracted considerable attention owing to the board applications including continuous material processing, roll-to-roll systems, flexible electronics, etc. Depending on the system’s flexibility and geometric parameters, axially moving systems can be categorized into four models: String, beam, belt, and plate models. We first derive a total of 33 partial differential equation (PDE) models for axially moving systems appearing in various fields. The methods to approximate the PDEs to ordinary differential equations (ODEs) are discussed; then, approximated ODE models are summarized. Also, the techniques (analytical, numerical) to solve both the PDE and ODE models are presented. The dynamic analyses including the divergence and flutter instabilities, bifurcation, and chaos are outlined. Lastly, future research directions to enhance the technologies in this field are also proposed. Considering that a continuous manufacturing process of composite and layered materials is more demanding recently, this paper will provide a guideline to select a proper mathematical model and to analyze the dynamics of the process in advance.

/pdf/dynamic-models-of-axially-moving-systems-a-review-3tble75glj.pdf

Dynamic models of axially moving systems: A review

Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid

Nonlinear frequencies and forced responses of pipes conveying fluid via a coupled Timoshenko model

Parametric resonances of Timoshenko pipes conveying pulsating high-speed fluids

Super-critical transporting continua are often discussed in the context of an Euler beam model. Here Timoshenko beam theory is applied to study free vibration of high-speed transporting continua. Therefore, effects of rotary inertia and shear deformation on transverse vibration of super-critical transporting beams are discovered for the first time. The Galerkin method is applied to solve natural frequencies with the simply supported boundary conditions. Meanwhile, the weighted residual method (WRM) is employed to deal with the fixed ends. The natural frequencies of super-critical continua are verified by using the discrete Fourier transform (DFT). In the super-critical regime, the straight configuration of the beam loses its stability. The buckling configurations, due to the nonlinear stiffness, are deduced from the nonlinear static equilibrium equation. Furthermore, the governing equation for the transverse vibration of the super-critical transporting Timoshenko beam is derived based on the buckling shape. Time histories are calculated by using the finite difference method (FDM). Furthermore, natural frequencies of nonlinear free vibration are determined by using the DFT. In addition, the effect of nonlinear stiffness on the natural frequencies is discovered. On the other hand, a partially linearized equation is deduced by regarding buckling configurations and its spatial derivatives as constant coefficients. Then, natural frequencies are extracted by using the Galerkin method. The two different approaches are compared. Numerical results show that the rotary inertia and the shear deformation significantly affect vibration characteristics of the super-critical transporting beam for some configurations. Moreover, comparisons with an Euler-Bernoulli beam model reveal that the fundamental frequency of the Timoshenko beam is higher when the speed is slightly greater than the critical value.

Xia Tan

Papers

Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid

Nonlinear frequencies and forced responses of pipes conveying fluid via a coupled Timoshenko model

Parametric resonances of Timoshenko pipes conveying pulsating high-speed fluids

Natural frequencies of a super-critical transporting Timoshenko beam

Primary and super-harmonic resonances of Timoshenko pipes conveying high-speed fluid