Using nonlinear springs to reduce the whirling of a rotating shaft

Carrella, A.; Friswell, Michael I.; Зотов, А. Н.; Ewins, D. J.; Tichonov, A.

doi:10.1016/j.ymssp.2009.03.006

Cited by 54 publications

(28 citation statements)

References 15 publications

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“…Assumption There exist a polynomial function

c (y) \geq 0

and constants

- 1 / n < τ_{1} \leq 0

and

τ_{2} \geq 0

such that

| φ_{i} (η, v, t) | \leq c (y) ([], {falsefalse}_{\sum}^{j = 1} ((), | η_{j} |^{\frac{1 + i τ_{1}}{1 + (j - 1) τ_{1}}} + | η_{j} |^{\frac{1 + i τ_{2}}{1 + (j - 1) τ_{2}}})), i = 1, \dots, n .

Remark We emphasize that the aforementioned assumption is more general than those in because it not only includes both low‐order and high‐order terms but also takes polynomial‐type output‐dependent incremental rate into account. The physical interpretation of c ( y ) can be found in some mechanical control systems, in which elastic loads or springs may exhibit the polynomial‐type nonlinearity; see, for instance, and .…”

Section: Preliminariesmentioning

confidence: 99%

Robust output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities

Lin

2015

Int. J. Robust. Nonlinear Control

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SUMMARYIn this paper, we consider the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are assumed to be bounded by both low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate. Instead of the previously proposed dual observer, based on the homogeneous domination approach, a new reduced-order observer is constructed, which greatly simplifies the closed-loop controller and is able to cover a more general class of nonlinear systems. Copyright

show abstract

“…Assumption There exist a polynomial function

c (y) \geq 0

and constants

- 1 / n < τ_{1} \leq 0

and

τ_{2} \geq 0

such that

| φ_{i} (η, v, t) | \leq c (y) ([], {falsefalse}_{\sum}^{j = 1} ((), | η_{j} |^{\frac{1 + i τ_{1}}{1 + (j - 1) τ_{1}}} + | η_{j} |^{\frac{1 + i τ_{2}}{1 + (j - 1) τ_{2}}})), i = 1, \dots, n .

Section: Preliminariesmentioning

confidence: 99%

Robust output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities

Lin

2015

Int. J. Robust. Nonlinear Control

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show abstract

“…For various vibration isolation purposes, quasi-zero-stiffness (QZS) vibration isolation systems for one direction vibration have been extensively studied to improve working environments and provide a better background for aerospace devices and precision instruments [16][17][18][19][20][21][22][23][24]. In order to induce the adjustable stiffness property with sufficient loading capacity, a structure with springs, called scissor-like structure (SLS), is proposed.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Dynamics of a MDOF Isolation System

Song

Sun

2017

Applied Sciences

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This study analyzes the modeling and dynamics of a novel passive multi-degree-of-freedom (MDOF) vibration isolation platform which can achieve a significant isolation effect. Symmetrical scissor-like structures (SLSs) are utilized in the proposed MDOF isolation platform as the supporting and isolation elastic components. Based on the mathematical modeling and theoretical analysis of the MDOF vibration isolation system with SLSs, the effects of structural parameters and joint friction on the stiffness and damping properties are investigated. It is shown that due to geometric relations within the SLSs, the natural frequencies can be reduced via adjusting structural parameters of the SLS for different direction vibration isolation. Theoretical and experimental results show that the SLS isolation platform can achieve much better loading capacity and vibration isolation performance simultaneously by only using linear passive components because of the MDOF adjustable stiffness property. Therefore, with low cost and energy consumption, the proposed novel isolation platform can improve the vibration suppression in various engineering practices.

show abstract

“…For various vibration isolation purposes, Quasi-zero-stiffness (QZS) vibration isolation systems for one direction vibration have been extensively studied to improve working environment and provide better background for aerospace devices and precision instruments [12][13][14][15][16][17][18][19][20]. In order to induce adjustable stiffness property with sufficient loading capacity, a structure with springs called Scissor-Like structure (SLS) is proposed.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Dynamics of a MDOF Isolation System

Song¹,

Sun²

2017

Preprint

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This study analyzes the modeling and dynamics of a novel passive in Multi-Degree-of-Freedom (MDOF) vibration isolation platform which can achieve significant isolation effect. Symmetrical Scissor-Like structures (SLSs) are utilized in the proposed MDOF isolation platform as the supporting and isolation elastic components. Based on the mathematical modeling and theoretical analysis of the MDOF vibration isolation system with SLSs, the effect of structural parameter and joint friction on stiffness and damping properties is investigated. It is shown that due to geometric relations within the SLSs, the natural frequencies can be reduced via adjusting structural parameters of the SLS for different direction vibration isolation. Theoretical and experimental results show that the SLS isolation platform can achieve much better loading capacity and vibration isolation performance simultaneously by only using linear passive components because of the MDOF adjustable stiffness property. Therefore, with low costing and energy consumption, the proposed novel isolation platform can provide the improvement of vibration suppression in various engineering practices.

show abstract

Using nonlinear springs to reduce the whirling of a rotating shaft

Cited by 54 publications

References 15 publications

Robust output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities

Robust output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities

Modeling and Dynamics of a MDOF Isolation System

Modeling and Dynamics of a MDOF Isolation System

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