On the multi-mode behavior of vibrating rods attached to nonlinear springs

Santo, Douglas Roca; Mencik, Jean‐Mathieu; Gonçalves, Paulo José Paupitz

doi:10.1007/s11071-020-05647-x

Cited by 13 publications

(7 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the increasing demand for nonlinear vibration control, scholars have attempted to utilize nonlinear principles to design various nonlinear supports 14 – 17 Engineers then installed these supports into elastic structures to assess the feasibility of controlling vibrations using nonlinear supports. Santo et al 18 constructed a vibration prediction model for a vibrating rod with nonlinear springs and studied its multimodal behavior. Hao et al 19 designed a nonlinear vibration isolator and incorporated it into a flexible plate.…”

Section: Introductionmentioning

confidence: 99%

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

Zhao,

Cui

2024

Sci Rep

View full text Add to dashboard Cite

In engineering, shafting systems are typically subjected to longitudinal vibration excitations, which may result in unwanted vibration. To study the control of longitudinal vibration in shafting systems, they can be simplified to rod structures. Currently, engineers have attempted to apply the nonlinear principle to design nonlinear supports to control the vibration of flexible structures. However, the flexible structures referenced in the literature are usually composed of a single component, which limits the application of nonlinear supports to more complex structures. To explore the potential application of nonlinear supports in marine engineering, this work introduces a longitudinal vibration prediction model for a double-rod system equipped with longitudinal nonlinear supports. The generalized Hamilton principle is used to derive the governing equations for the double-rod system with longitudinal nonlinear supports. The longitudinal vibration responses of the double-rod system are numerically solved using the Galerkin truncation method. The numerical results confirm that a 1-term truncation number guarantees the stability of the longitudinal vibration prediction model. Under certain conditions, the longitudinal vibration responses are significantly affected by longitudinal nonlinear supports. It is recommended to install longitudinal nonlinear supports on both Rod 1 and Rod 2 simultaneously to suppress vibration in the first two main resonance orders. With reasonable excitations, the vibration state and magnitudes of the double-rod system can be effectively controlled by adjusting the longitudinal nonlinear supports. Complex longitudinal vibration responses are more readily induced by altering the parameters of the longitudinal nonlinear support installed on Rod 1. Choosing appropriate parameters for the nonlinear supports on Rod 1 and Rod 2 positively contributes to the reduction of vibration in the double-rod system.

show abstract

Section: Introductionmentioning

confidence: 99%

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

Zhao,

Cui

2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Recently, complex rod models can include nonlinearity and/or graded material. For instance, Santo et al 20 investigated the harmonic response of vibrating homogeneous rods with nonlinear elastic boundary conditions. In this study, we investigate the mode shapes as well as the energy distribution of functionally graded (position-dependent stiffness) elastic rods with elastic and viscous boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Lelkes,

Bak,

Kalmár-Nagy

2024

Sci Rep

View full text Add to dashboard Cite

Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted.

show abstract

“…Due to the characteristics of sub-wavelength sizes and dynamic equivalent parameters being different from those of traditional material structures, the metamaterial structures have a very broad application prospect in the fields of vibration reduction, sound absorption and wave direction control [ 11 , 12 , 13 ]. Researchers have designed many kinds of metamaterial structures such as rods [ 14 , 15 ], beams [ 16 , 17 , 18 ] and plates [ 19 , 20 , 21 ] which are composed of periodically distributed local resonators. A metamaterial plate is a two-dimensional periodic structure, which is mostly composed of continuous plates and periodic components such as holes and cylinders.…”

Section: Introductionmentioning

confidence: 99%

A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates

Linzhongyang

et al. 2023

Materials

View full text Add to dashboard Cite

In this study, elastic metamaterial sandwich plates with axially deformed Timoshenko beam cores, considering both the out-of-plane and in-plane deformations of the face plates, are designed and the vibration band-gap properties are explored. The beam cores act as local resonators that can bear axial force, bending moment and shearing force. The finite element method (FEM) and the spectral element method (SEM) are combined to create the finite/spectral element hybrid method (FE-SEHM) for establishing the dynamic model and calculating the frequency response functions (FRFs) of the elastic metamaterial sandwich plate with axially deformed beam cores. It is observed that the metamaterial sandwich plate possesses both the axial and transverse vibration band-gaps of the beams, and the two kinds of band-gaps are independent. Compared with the metamaterial sandwich plates with rod cores, those with axially deformed beam cores have more extensive application ranges for vibration reduction.

show abstract

On the multi-mode behavior of vibrating rods attached to nonlinear springs

Cited by 13 publications

References 25 publications

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates

Contact Info

Product

Resources

About