Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

Kim, Kookhyun; Kim, Byung-Hee; Choi, Tae-Muk; Cho, Dae‐Seung

doi:10.2478/ijnaoe-2013-0095

Cited by 20 publications

(37 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mathematical model for the vibration analysis of different plate systems based on the assumed mode method is already applied in [8], [16] and [21], and here its outline with some extensions is given. The Mindlin thick plate theory [2] which takes shear influence and rotary inertia into account is adopted in the model.…”

Section: Outline Of the Mathematical Formulationmentioning

confidence: 99%

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Cho

Vladimir

Choi³

2015

Polish Maritime Research

View full text Add to dashboard Cite

Thin and thick plates, plates with holes, stiffened panels and stiffened panels with holes are primary structural members in almost all fields of engineering : civil, mechanical, aerospace, naval, ocean etc. In this paper, a simple and efficient procedure for the free vibration analysis of such elements is presented. It is based on the assumed mode method and can handle different plate thickness, various shapes and sizes of holes, different framing sizes and types as well as different combinations of boundary conditions. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations. Mindlin theory is applied for a plate and Timoshenko beam theory for stiffeners. The applicability of the method in the design procedure is illustrated with several numerical examples obtained by the in-house developed code VAPS.Very good agreement with standard commercial finite element software is achieved.

show abstract

Section: Outline Of the Mathematical Formulationmentioning

confidence: 99%

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Cho

Vladimir

Choi³

2015

Polish Maritime Research

View full text Add to dashboard Cite

show abstract

“…It should be noted here that when using the assumed mode method, the orthogonal polynomials corresponding to the property of target model should be applied to achieve accurate analysis. For this purpose, the characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies the specified edge constraints are used, and their complete derivation is presented by Kim et al (2012). In addition, it should be mentioned that developed procedure is not fully physical consistent, since in the Rayleigh-Ritz method all assumed shape function should satisfy at least geometric boundary conditions (Szilard, 2004), which is not unconditionally the case in the presented procedure at the opening boundaries.…”

Section: Outline Of Assumed Mode Methodsmentioning

confidence: 99%

“…where [M] and [K] are the mass and the stiffness matrix, respectively, and their constitution is described in details in Kim et al (2012). If we assume harmonic vibrations, i.e.…”

Section: Outline Of Assumed Mode Methodsmentioning

confidence: 99%

“…and / S kGh D = for a rectangular plate of length a and breadth b , one can write for the strain and kinetic energy of rectangular plate without openings, V and T, respectively (Kim et al, 2012):…”

Section: Energy Of a Rectangular Plate Without Openingsmentioning

confidence: 99%

“…Recently, assumed mode method using characteristic orthogonal polynomials is applied to problem of free vibration of rectangular plates of arbitrary edge constraints (Chung et al, 1993;Kim et al, 2012). In this paper, assumed mode method is applied to natural vibration analysis of plates with openings of different shape and arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

Cho¹,

Vladimir²,

Choi³

2013

International Journal of Naval Architecture and Ocean Engineeri

View full text Add to dashboard Cite

Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular

show abstract

Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel

2021

Aerospace Science and Technology

View full text Add to dashboard Cite

Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

Cited by 20 publications

References 8 publications

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel

Contact Info

Product

Resources

About