The Rayleigh–Ritz Method for Structural Analysis

Ilanko, Sinniah; Monterrubio, Luis E.; Mochida, Yusuke

doi:10.1002/9781118984444

Cited by 67 publications

(40 citation statements)

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“…The approximate results for all these 55 cases were given in Ref. 10. These were obtained using the Rayleigh-Ritz method and are highly accurate upper bounds.…”

Section: Numerical Resultsmentioning

confidence: 99%

Benchmark Vibration Frequencies of Square Thin Plates with all Possible Combinations of Classical Boundary Conditions

Deutsch

Tenenbaum

Eisenberger

2019

Int. J. Str. Stab. Dyn.

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In this work, a new method is used for the exact vibration analysis of plates with classical boundary conditions. Four classical edge conditions are included: Cclamped, S -Simply supported, Ffree, and Gguided. For square plates, all the possibilities add up to 55 cases. The solutions for the natural frequencies of the plates are found in this paper using static analysis. Starting from the equations of motion of an isotropic rectangular thin plate supported on Winkler elastic foundation, with a positive or negative value, the solution for the vibration frequencies of the plate is equivalent to¯nding the values of the negative elastic foundation that will yield in¯nite de°ection under a point load on the plate. The solution is composed of three parts, the sum of which satis¯es exactly both the¯eld equation and the boundary conditions. For zero force, the vibration frequencies are found up to the desired accuracy. Benchmark results of the¯rst six normalized natural frequencies, of isotropic square plates, for all possible 55 combinations of classical boundary conditions are given, many for the¯rst time.

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“…The approximate results for all these 55 cases were given in Ref. 10. These were obtained using the Rayleigh-Ritz method and are highly accurate upper bounds.…”

Section: Numerical Resultsmentioning

confidence: 99%

Benchmark Vibration Frequencies of Square Thin Plates with all Possible Combinations of Classical Boundary Conditions

Deutsch

Tenenbaum

Eisenberger

2019

Int. J. Str. Stab. Dyn.

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“…By attaching translational and rotational springs along the plate edges, any typical set of boundary conditions can be incorporated with the penalty method [25]. The strain energy due to attached springs along the plate edges, Ve is given by Eq.…”

Section: Methodsmentioning

confidence: 99%

Vibration Analysis of Cracked Structures as a Roving Body Passes a Crack Using the Rayleigh-Ritz Method

Ilanko¹,

Mochida

Rois³

2018

EPI-IJE

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The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.

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“…This solution technique requires the use of assumed shape functions for the displacement, and in this application Chebyshev Polynomials of the First Kind have been selected. The coupling between adjacent plates is handled by first solving the plate equations for each partition, and then joining together the partitions using the Courant's penalty method in the form of artificial springs [49].…”

Section: B Structural Modelmentioning

confidence: 99%

Numerically Efficient Three-Dimensional Fluid-Structure Interaction Analysis for Composite Camber Morphing Aerostructures

Rivero¹,

Cooper²,

Woods

2020

AIAA Scitech 2020 Forum

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This paper presents a newly developed three-dimensional Fluid-Structure Interaction (FSI) routine for the Fish Bone Active Camber (FishBAC) concept that couples a three-dimensional Lifting-Line theory analysis to a two-dimensional viscous corrected panel method (XFOIL) to create a viscous corrected three-dimensional wing aerodynamic solver. This aerodynamic model is then coupled to a previously developed multi-component Mindlin-Reissner plate model based composite analysis routine for the FishBAC morphing device. The methodology is explained, and predictions are validated against existing modeling tools. The FSI model developed in this paper shows good agreement when compared against other structural, aerodynamic and FSI tools. Additionally, results show the FishBAC's ability to improve aerodynamic performance at a wide range of operating conditions.

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The Rayleigh–Ritz Method for Structural Analysis

Cited by 67 publications

References 0 publications

Benchmark Vibration Frequencies of Square Thin Plates with all Possible Combinations of Classical Boundary Conditions

Benchmark Vibration Frequencies of Square Thin Plates with all Possible Combinations of Classical Boundary Conditions

Vibration Analysis of Cracked Structures as a Roving Body Passes a Crack Using the Rayleigh-Ritz Method

Numerically Efficient Three-Dimensional Fluid-Structure Interaction Analysis for Composite Camber Morphing Aerostructures

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