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A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates.

Li R, Wang P, Tian Y, Wang B, Li G - Sci Rep (2015)

Bottom Line: A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates.The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation.The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates. The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation. The main advantage of the developed approach is its wide applicability since no trial solutions are needed in the analysis, which is completely different from the other methods. Numerical examples for both static bending and free vibration plates are presented to validate the developed analytic solutions and to offer new numerical results. The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

No MeSH data available.


Related in: MedlinePlus

Convergence of the normalized bending and free vibration solutions of a square thin plate with four corners point-supported.
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Related In: Results  -  Collection

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f4: Convergence of the normalized bending and free vibration solutions of a square thin plate with four corners point-supported.

Mentions: An important issue concerned in solving the above problems is the convergence of the solutions. To examine it, we investigate a square corner-supported plate. Figure 4 illustrates the normalized central bending deflection and fundamental frequency versus the series terms adopted in calculation. It is seen that both the bending and free vibration solutions converge rapidly since only dozens of terms are enough to furnish satisfactory convergence. Actually rapid convergence is found for most solutions. The maximum number of series terms is taken to be 100 to achieve the convergence of all current numerical results to the last digit of five significant figures.


A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates.

Li R, Wang P, Tian Y, Wang B, Li G - Sci Rep (2015)

Convergence of the normalized bending and free vibration solutions of a square thin plate with four corners point-supported.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4660308&req=5

f4: Convergence of the normalized bending and free vibration solutions of a square thin plate with four corners point-supported.
Mentions: An important issue concerned in solving the above problems is the convergence of the solutions. To examine it, we investigate a square corner-supported plate. Figure 4 illustrates the normalized central bending deflection and fundamental frequency versus the series terms adopted in calculation. It is seen that both the bending and free vibration solutions converge rapidly since only dozens of terms are enough to furnish satisfactory convergence. Actually rapid convergence is found for most solutions. The maximum number of series terms is taken to be 100 to achieve the convergence of all current numerical results to the last digit of five significant figures.

Bottom Line: A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates.The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation.The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates. The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation. The main advantage of the developed approach is its wide applicability since no trial solutions are needed in the analysis, which is completely different from the other methods. Numerical examples for both static bending and free vibration plates are presented to validate the developed analytic solutions and to offer new numerical results. The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

No MeSH data available.


Related in: MedlinePlus