BOTH STATIC DEFLECTION AND VIBRATION MODE OF UNIFORM BEAM CAN SERVE AS A BUCKLING MODE OF A NON-UNIFORM COLUMN

The inadequacy of beam vibration mode shapes when used in the Ritz method to obtain approximate solutions for flexural problems concerning plates involving free edges is demonstrated. A new set of functions, related to beam mode shapes, is postulated which allows considerably more accurate treatment of such plates. Several numerical examples concerning static deflection and free vibration of plates involving free edges are examined and serve to illustrate the applicability and accuracy of the new functions and to further demonstrate the inadequacy of the ordinary beam functions.

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Free Vibration of Thermally Buckled Composite Sandwich Plates

Journal of Vibration and Acoustics ◽

10.1115/1.2149388 ◽

2005 ◽

Vol 128 (1) ◽

pp. 1-7 ◽

Cited By ~ 42

Author(s):

Le-Chung Shiau ◽

Shih-Yao Kuo

Keyword(s):

Free Vibration ◽

Vibration Mode ◽

Free Vibration Analysis ◽

Sandwich Plates ◽

Vibration Modes ◽

Buckling Mode ◽

Composite Sandwich ◽

Plate Buckling ◽

Pattern Change ◽

Composite Sandwich Plates

A high precision triangular plate element is developed for the free vibration analysis of thermally buckled composite sandwich plates. Due to an uneven thermal expansion in the two principal material directions, the buckling mode of the plate may change from one pattern to another in the postbuckling region for certain fiber orientation and aspect ratio of the plate. Because of this buckle pattern change, the sequence of natural frequencies of the plate is also suddenly altered. By examining the buckling and free vibration modes of the plate, a clear picture of buckle pattern change and vibration mode shifting is presented. Numerical results show that if the shape of a free vibration mode is similar to the plate buckling mode then the natural frequency of that mode will drop to zero when the temperature reaches the buckling temperature.

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Tailoring vibration mode of a uniform beam by acoustic metamaterial synthesis

Active and Passive Smart Structures and Integrated Systems XII ◽

10.1117/12.2296781 ◽

2018 ◽

Author(s):

Jiong Tang ◽

Jiawen Xu ◽

Shilong Li

Keyword(s):

Vibration Mode ◽

Acoustic Metamaterial ◽

Uniform Beam

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Local vibration mode pairs for damage identification in axisymmetric tubular structures

Journal of Sound and Vibration ◽

10.1016/j.jsv.2020.115845 ◽

2020 ◽

pp. 115845

Author(s):

Obukho E. Esu ◽

Ying Wang ◽

Marios K. Chryssanthopoulos

Keyword(s):

Vibration Mode ◽

Damage Identification ◽

Tubular Structures ◽

Local Vibration

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Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽

10.3390/ma14030567 ◽

2021 ◽

Vol 14 (3) ◽

pp. 567

Author(s):

Łukasz Żmuda-Trzebiatowski ◽

Piotr Iwicki

Keyword(s):

Natural Frequencies ◽

Vibration Mode ◽

Mode Shapes ◽

Correlation Technique ◽

Limit Loads ◽

Linear Buckling ◽

Geometrical Imperfections ◽

Linear Problems ◽

Formed Channel ◽

Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

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Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2011-105 ◽

2012 ◽

Vol 13 (1) ◽

Cited By ~ 1

Author(s):

Jia-Bin Sun ◽

Xin-Sheng Xu ◽

Chee-Wah Lim

Keyword(s):

Hamiltonian System ◽

Critical Load ◽

Impact Load ◽

Dynamic Buckling ◽

Inertia Force ◽

Elastic Cylindrical Shell ◽

Symplectic Method ◽

Buckling Mode ◽

Axial Impact ◽

Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

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