Introduction to Finite Element Vibration Analysis

Petyt, M.

doi:10.1017/cbo9780511624292

Cited by 337 publications

(110 citation statements)

References 188 publications

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“…Here the derivatives of the dimensionless, global matrices K and M can be calculated explicitly from the element stiffness and mass matrices in [36]. If all the design variables are changed simultaneously, the linear increment is given by the scalar product…”

Section: Sensitivity Results For Simple Eigenfrequenciesmentioning

confidence: 99%

“…In Eq. (2b), K and M are symmetric positive definite global stiffness and mass matrices (with corresponding element matrices available in [36]) of the generalized structural eigenvalue problem for the vibrating beam structure. Thus, the J candidate eigenfrequencies ( J n > ) considered in the optimization problem will all be real and can be ordered as follows by magnitude:…”

Section: Camentioning

confidence: 99%

See 1 more Smart Citation

On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. A band-gap structure usually consists of a periodic distribution of elastic materials or segments, where the propagation of waves is impeded or This paper extends earlier optimum shape design results for transversely vibrating Bernoulli-Euler beams by determining new optimum band-gap beam structures for (i) different combinations of classical boundary conditions, (ii) much larger values of the orders n (n>1) and n-1 of adjacent upper and lower eigenfrequencies of maximized band-gaps, and (iii) different values of a minimum beam cross-sectional area constraint. In the present paper, instead of maximizing band-gaps between frequencies of propagating waves or forced vibrations excited by external time-harmonic loads, the closely relatedproblem of maximizing the gap between two adjacent eigenfrequencies ω n and ω n-1 of any given consecutive orders n (n>1) and n-1, is considered. This is justified by the fact that external time-harmonic dynamic loads cannot excite resonance with high vibration levels of standing waves, if the eigenfrequencies of the structure are moved outside the range of the external excitation frequencies by the optimization.Finally, the present study shows that if an infinite beam structure is constructed by repeated translation of an inner beam segment obtained by the aforementioned frequency gap optimization, then a band-gap of traveling waves in this infinite beam is found to correlate almost perfectly with the maximized frequency gap in the finite structure.

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Section: Sensitivity Results For Simple Eigenfrequenciesmentioning

confidence: 99%

Section: Camentioning

confidence: 99%

On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…(90) with the modal elastic energy error Eq. (89), two typical plane-strain solids will be analyzed: earth dam discretized by a regular mesh of TR6 elements [23], Fig. 9; and bridge pier discretized by a quasi-regular mesh of QU8 elements [24], Fig.…”

Section: Numerical Researchmentioning

confidence: 99%

An Error Indicator Based on a Wave Dispersion Analysis for the in-Plane Vibration Modes of Isotropic Elastic Solids Discretized by Energy-Orthogonal Finite Elements

Castro¹

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Bending terms are integrated exactly while shear terms are integrated with only one point of the Gauss quadrature. More details can be found in [24,26], e. g. As mentioned previously, the matrices (12), (13), and (14) were assembled into the global matrices M g , K g , and E g . As a result of the space-time integration of the right hand side of (11), the local vector of external force takes the following form …”

Section: Simplex Shaped Space-time Approachmentioning

confidence: 99%

Efficient numerical approach to unbounded systems subjected to a moving load

Dyniewicz

2014

Comput Mech

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The present paper solves numerically the problem of vibrations of infinite structures under a moving load. A velocity formulation of the space-time finite element method was applied. In the case of simplex shaped space-time finite elements, the 'steady state' dynamic behaviour of the system was obtained. A properly performed discretization allowed of propagating information in a given direction at a limited velocity. The solutions were obtained under the assumption that the deformation is quasi-stationary, i.e., stationary in the coordinate system that moves with the load. The unbounded Timoshenko beam subjected to a distributed moving load was used as a test example. The dynamical system is placed on an elastic foundation. The matrices describing an infinite dynamical system subjected to a moving load are derived and the stability of the numerical scheme is analysed. The numerical results are compared with the analytical solutions in the literature and the classical numerical method.

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Introduction to Finite Element Vibration Analysis

Cited by 337 publications

References 188 publications

On Optimum Design and Periodicity of Band-Gap Structures

On Optimum Design and Periodicity of Band-Gap Structures

An Error Indicator Based on a Wave Dispersion Analysis for the in-Plane Vibration Modes of Isotropic Elastic Solids Discretized by Energy-Orthogonal Finite Elements

Efficient numerical approach to unbounded systems subjected to a moving load

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