Bio: Yi Li is an academic researcher from Shanghai University. The author has contributed to research in topics: Inertia & Cantilever. The author has an hindex of 2, co-authored 2 publications receiving 23 citations.
TL;DR: In this article, a viscoelastic beam supported by vertical springs is proposed with nonrotatable left boundary and freely rotatable right end, and the steady-state responses of the beam excited by a distributed harmonic force are obtained by an approximate analytical method and a numerical approach.
Abstract: Under the conditions of horizontal placement and only considering geometric nonlinearity, depending on the boundary constraints, primary resonances of an elastic beam exhibit either hardening or softening nonlinear behavior. In this paper, the conversion of softening nonlinear characteristics to hardening characteristics is studied by using the multi-scale perturbation method. Therefore, in a local sense, the condition is established for the resonance of the elastic beam exhibits only linear characteristics by finding the balance between asymmetric elastic support and geometric nonlinearity. A viscoelastic beam supported by vertical springs is proposed with nonrotatable left boundary and freely rotatable right end. In order to truncate the continuous system, natural frequencies and modes of the proposed asymmetric beam are analyzed. The steady-state responses of the beam excited by a distributed harmonic force are, respectively, obtained by an approximate analytical method and a numerical approach. Under the condition that the beam is placed horizontally, the transition from the cantilever state to the clamped–pinned state is demonstrated by constructing different asymmetry support conditions. The resonance peak of the first-order primary resonance is used to demonstrate the transition from softening nonlinear characteristics to the hardening characteristics. This research shows that the transformation from softening characteristics to hardening characteristics caused by asymmetric elastic support and geometric nonlinearity exists only in the first-order mode resonance.
TL;DR: In this article, the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime are investigated, and two kinds of boundary conditions are also compared.
Abstract: The most important issue in the vibration study of an engineering system is dynamics modeling. Axially moving continua is often discussed without the inertia produced by the rotation of the continua section. The main goal of this paper is to discover the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime. Specifically, an integro-partial-differential nonlinear equation is modeled for the transverse vibration of the moving beam based on the generalized Hamilton principle. Then the effects of rotary inertia on the natural frequencies, the critical speed, post-buckling vibration frequencies are presented. Two kinds of boundary conditions are also compared. In super-critical speed range, the straight configuration of the axially moving beam loses its stability. The buckling configurations are derived from the corresponding nonlinear static equilibrium equation. Then the natural frequencies of the post-buckling vibration of the super-critical moving beam are calculated by using local linearization theory. By comparing the critical speed and the vibration frequencies in the sub-critical and super-critical regime, the effects of the inertia moment due to beam section rotation are investigated. Several interesting phenomena are disclosed. For examples, without rotary inertia, the study overestimates the stability of the axially moving beam. Moreover, the relative differences between the super-critical fundamental frequencies of the two theories may increase with an increasing beam length.
TL;DR: In this article, a step function and a porosity volume fraction are introduced to describe the porosities in functionally graded material (FGM) sandwich cylindrical shells with porosity on an elastic substrate.
Abstract: The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.
TL;DR: The present work provides a comprehensive review on the recent advances in nonlinear vibration energy harvesting and vibration suppression technologies and in particular, the latest developments in multifunctional hybrid technologies are proposed.
Abstract: Limited by the structure, the high-efficiency vibration energy harvesting and vibration suppression have always been a theoretical bottleneck and technical challenge in this field. The nonlinear design of the new vibration structure is an indispensable link in the development of vibration energy harvesting and vibration suppression technologies. Nonlinear technologies not only have the potential to improve the efficiency of the energy harvesters by increasing the useful frequency bandwidth and output power but also have the potential to improve the efficiency of vibration suppressors by reducing the transmission rate and transfer energy. Nonlinear vibration energy harvesting and vibration suppression technologies have been salient topics in the literature and have attracted widespread attention from researchers. The present work provides a comprehensive review on the recent advances in nonlinear vibration energy harvesting and vibration suppression technologies. In particular, the latest developments in multifunctional hybrid technologies are proposed. Various key aspects to improve the performance of nonlinear vibration energy harvesting and vibration suppression systems are discussed, including implementations and configuration designs, nonlinear dynamics mechanisms, various optimizations, multifunctional hybrid, application prospects, and future outlooks.
TL;DR: In this article, an inertial nonlinear energy sink (NES) is proposed for the elimination of multimode resonance of composite plates by an inerter to reduce the weight of the attached device.
Abstract: Bending vibration of the elastic structure has many resonance modes. Especially, the composite plate structure has many low frequency modes. Therefore, devices capable of achieving wide-band vibration suppression are required. Multimode resonances elimination of composite plates by an inertial nonlinear energy sink (NES) is proposed for the first time. Different with the traditional NES, the mass of the absorber in the present work is replaced by an inerter to reduce the weight of the attached device. The response of the plate is investigated by the Galerkin discretization together with the harmonic balance method (HBM). The gravity effect of the mass of the traditional NES is presented. It shows the benefits of the inertial NES without affecting the resonant frequency of the primary system. By comparing the resonance with and without the NES, the proposed device is certified that it has good efficiency in vibration eliminating for both low-order and high-order resonance. It finds that the mass of the inertial NES, which can achieve the effective suppression effect, is relatively tiny. The parameter effect of the NES is discussed fully to achieve the optimum design. Optimal parameters on the resonance response of different modes are not identical. This paper will provide a good reference for vibration elimination of multimode resonance of plates.
TL;DR: This paper will provide a guideline to select a proper mathematical model and to analyze the dynamics of the process in advance and future research directions to enhance the technologies in this field are proposed.
Abstract: 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.
TL;DR: In this paper, a dynamic stiffness matrices for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundary conditions are discussed for the first time, where the beam is supported by torsional springs and vertical springs at both ends.
Abstract: Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.