An Improvement of the Myklestad Method for Flexural-Vibration Problems

1959 ◽  
Vol 26 (1) ◽  
pp. 46-50 ◽  
Author(s):  
S. MAHALINGAM
Keyword(s):  
Flexural Vibration ◽  
Vibration Problems

The Wave Method for Solving Flexural Vibration Problems

1954 ◽  
Vol 21 (1) ◽  
pp. 75-80
Author(s):  
R. P. N. Jones
Keyword(s):  
Normal Mode ◽  
Flexural Vibration ◽  
Initial Response ◽  
Time Base ◽  
Subsequent Response ◽  
Mode Solution ◽  
Vibration Problems ◽  
Wave Methods ◽  
Theoretical Results ◽  
Good Agreement

Abstract In this paper the use of normal mode and wave methods in problems of dynamic loading on beams is discussed, and the methods are applied to simple problems of uniform beams under a suddenly applied load. For these problems, mathematically exact results have been obtained, enabling a comparison to be made between the two types of solution. Experimental results for these problems also have been obtained, using an apparatus which releases the beam from a deflected position, and displays a record of the resultant response on an oscillograph screen, using a time base synchronized with the release of the beam. Good agreement is obtained between the experimental and theoretical results, and it is shown that the wave solution is useful for determining the initial response of the beam, while the subsequent response can be better obtained from the normal-mode solution.

Flexural vibration of Piezocomposite solid cylinders

2008 ◽  
Vol 3 (4) ◽  
pp. 27-32
Author(s):  
V.K. Nelson ◽  
◽  
Nehru Erode Santhanam ◽  
Keyword(s):  
Flexural Vibration

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

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