Stability conditions for non-conservative dynamical systems

Krätzig, Wilfried B.; Li, Long-yuan; Nawrotzki, Peter

doi:10.1007/bf00372684

Cited by 13 publications

(6 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where = − ( − ) is the Lagrangian function, and q is the general displacement vector. Substituting Eqs (1)-(4), (8), (10), (16) into (17), the governing equation for the dynamic instability analysis of a castellated beam is obtained as follows (Kratzig and Nawrotzki, 1991;Li, 1991;Patel et al, 2006) […”

Section: Governing Equations For Dynamic Instability Analysis Of Castmentioning

confidence: 99%

Dynamic instability of castellated beams subjected to transverse periodic loading

Elaiwi¹,

Kim²,

Li³

2019

CJSMEC

View full text Add to dashboard Cite

In this study, an analytical solution is developed for the investigation of free vibration, static buckling and dynamic instability of castellated beams subjected to transverse periodic loading. Bolotin’s method is used to perform the dynamic instability analysis. By assuming the instability modes, the mass, stiffness, and geometric stiffness matrices are derived using the kinetic energy, strain energy and potential of applied loads. Analytical equations for determining the free vibration frequency, critical buckling moment, and excitation frequency of castellated beams are derived. In addition, the influences of the flange width of the castellated beam and the static part of the applied load on the variation of dynamic instability zones are discussed.

show abstract

Section: Governing Equations For Dynamic Instability Analysis Of Castmentioning

confidence: 99%

Dynamic instability of castellated beams subjected to transverse periodic loading

Elaiwi¹,

Kim²,

Li³

2019

CJSMEC

View full text Add to dashboard Cite

show abstract

“…The dynamic instability regions of the structure described by Eq. (8) can be determined by examining periodic solutions with the periods of T=2 and 2T=4 [36,[39][40][41]. The solution with the period of 2T is of particular importance, representing the primary instability region of the structure, which can be expressed using the form of trigonometric series given by Eq.…”

Section: Governing Equations For Dynamic Instability Analysis Of Chanmentioning

confidence: 99%

Dynamic instability of channel-section beams under periodic loading

Zhu

Qian

2018

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

This paper presents an analytical investigation on the free vibration, static buckling and dynamic instability of channel-section beams when subjected to periodic loading. The analysis is carried out by using Bolotin's method. By assuming the instability modes, the kinetic energy and strain energy of the beam and the loss of the potential of the applied load are evaluated, from which the mass, stiffness and geometric stiffness matrices of the system are derived. These matrices are then used to carry out the analyses of free vibration, static buckling and dynamic instability of the beams. Theoretical formulae are derived for the free vibration frequency, critical buckling moment, and excitation frequency of the beam. The effects of the lateral restraint applied to the flange, the section size of the beam and the static part of the applied load on the variation of dynamic instability zones are also discussed.

show abstract

“…The governing equation for the dynamic instability analysis of a structure can be expressed as follows [28][29][30],  is the loading factor. Assume that the externally applied load is periodic, in which case the loading factor can be divided into two parts as expressed in Eq.…”

Section: Governing Equation For Dynamic Instability Analysismentioning

confidence: 99%

“…The dynamic instability regions of the structure described by Eq. (1) can be determined by periodic solutions with the periods of T=2/ and 2T=4/ [28][29][30]. The solution with the period of 2T is of particular importance, representing the primary instability region of the structure, which can be expressed using the form of trigonometric series given by Eq.…”

Section: Governing Equation For Dynamic Instability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Dynamic instability of laterally-restrained zed-purlin beams under uplift loading

Zhu

Qian

2017

International Journal of Mechanical Sciences

View full text Add to dashboard Cite

This paper presents an analytical investigation on the free vibration, static buckling and dynamic instability of laterally-restrained zed-section purlin beams when subjected to uplift wind loading. The analysis is carried out by using the classical principle of minimum potential energy. By assuming the instability modes, the kinetic energy and strain energy of the beam and the loss of the potential energy of the applied load are evaluated, from which the mass, stiffness and geometric stiffness matrices of the system are derived. These matrices are then used to carry out the analyses of free vibration, static buckling and dynamic instability of the beams. Theoretical formulae are derived for the free vibration frequency, critical buckling moment, and excitation frequency of the beam. The effects of the section size of the beam and the static part of the applied load on the change of dynamic instability zone are also discussed.

show abstract

Stability conditions for non-conservative dynamical systems

Cited by 13 publications

References 2 publications

Dynamic instability of castellated beams subjected to transverse periodic loading

Dynamic instability of castellated beams subjected to transverse periodic loading

Dynamic instability of channel-section beams under periodic loading

Dynamic instability of laterally-restrained zed-purlin beams under uplift loading

Contact Info

Product

Resources

About