An approximate method for simultaneous modification of natural frequencies and buckling loads of thin rectangular isotropic plates

2009 ◽  
Vol 31 (1) ◽  
pp. 208-215 ◽  
Author(s):  
R. Mirzaeifar ◽  
S. Shahab ◽  
H. Bahai
Keyword(s):  
Approximate Method ◽  
Natural Frequencies ◽  
Buckling Loads ◽  
Isotropic Plates

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

scholarly journals Investigation of natural frequencies of axially loaded thin-walled columns

2018 ◽  
Vol 219 ◽  
pp. 02018
Author(s):  
Łukasz Żmuda-Trzebiatowski
Keyword(s):  
Applied Load ◽  
Natural Frequencies ◽  
Elastic Buckling ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Perfectly Plastic ◽  
Linear Buckling ◽  
Thin Walled ◽  
Elastic Perfectly Plastic ◽  
Flexural Torsional Buckling

The paper deals with correlation between natural frequencies of two steel thin-walled columns and the corresponding applied load. The structures are made of cold-formed lipped channel sections. The columns lengths were assumed to follow two buckling patterns – global flexural and flexural-torsional buckling. In the thicker structure two material models were considered – linearly-elastic and elastic-perfectly plastic. Numerical computations cover dynamic eigenvalue problem, linear buckling and geometrically (and materially) non-linear analysis. The correlation between squares of natural frequencies and the applied load is linear in both columns. The first natural frequencies drop to zero due to structural buckling. This method, called the Vibration Correlation Technique, allows to predict buckling loads on the basis of measured vibration frequencies of the structures. Plasticity does not affect the corresponding curves – the use of the presented technique is limited to the structures exhibiting elastic buckling behaviour.

Buckling of Bars of Variable Rigidity with Varying Axial Load

1963 ◽  
Vol 67 (635) ◽  
pp. 734-736
Author(s):  
K. T. Sundara Raja Iyengar ◽  
S. Anantharamu
Keyword(s):  
Numerical Methods ◽  
Approximate Method ◽  
Convenient Method ◽  
Axial Load ◽  
Difficult Problem ◽  
Variable Rigidity ◽  
Rigorous Solution ◽  
Approximate Methods ◽  
Buckling Loads ◽  
End Conditions

The Evaluation of buckling loads of columns presents a difficult problem whose rigorous solution may be very difficult particularly when the variation of moment of inertia or the axial load does not follow a simple law. Hence approximate methods such as the variational and numerical methods will have to be employed. An approximate method is suggested in this note which offers a convenient method for the calculation of buckling loads of bars with any type of end conditions.

Buckling Loads and Natural Frequencies of Drill Bits and Fluted Cutters

1984 ◽  
Vol 106 (3) ◽  
pp. 196-204 ◽  
Author(s):  
E. B. Magrab ◽  
D. E. Gilsinn
Keyword(s):  
Natural Frequencies ◽  
Twist Angle ◽  
Axial Loading ◽  
Basis Functions ◽  
Mode Shapes ◽  
Euler Beam ◽  
Buckling Loads ◽  
Drill Bits ◽  
Out Of Plane ◽  
Beam Type

The buckling loads, natural frequencies and mode shapes of twist-drill bits and certain fluted cutters under a variety of combinations of twist angle, cross-section geometry, and axial loading have been obtained. The drill bit is modelled as a twisted Euler beam under axial loading that is clamped at both ends. The governing system of differential equations is solved by the Galerkin procedure. Explicit forms for the basis functions used to generate the Galerkin coefficients are presented in general form in an appendix. They may be used for obtaining numerical results for that class of problems which use the Rayleigh-Ritz-Galerkin methods with beam-type functions as the basis functions. The representative set of modes obtained exhibit a complex out-of-plane twisting-type motion that suggests a possible explanation for the out-of-roundness of certain drilled holes.

Natural Frequencies and Critical Buckling Loads of Marine Risers

1988 ◽  
Vol 110 (1) ◽  
pp. 2-8 ◽  
Author(s):  
Y. C. Kim
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Simple Procedure ◽  
Variable Cross Section ◽  
Mode Shapes ◽  
Variable Cross ◽  
Bending Rigidity ◽  
Buckling Loads ◽  
Closed Form Solutions ◽  
Marine Risers

Natural frequencies, mode shapes and critical buckling loads of marine risers simply supported at both ends are given in closed form by using the WKB method. These solutions allow variable cross section, bending rigidity, tension and mass distribution along the riser length. Furthermore, a simple procedure to predict natural frequencies for other boundary conditions is described. Some special forms of these closed-form solutions are compared with existing solutions in the literature.

Fast Calculation of the Statistics of the Forced Response of Mistuned Bladed Disk Assemblies With Friction Contacts

2002 ◽  
Author(s):  
Walter Sextro ◽  
Lars Panning ◽  
Florian Go¨tting ◽  
Karl Popp
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Frequency Response ◽  
Approximate Method ◽  
Natural Frequencies ◽  
Computation Time ◽  
System Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Bladed Disk

In turbomachinery one major problem is still the calculation and the optimization of the spatial vibrations of mistuned bladed disk assemblies with friction contacts. Friction contacts are widely used to reduce dynamic stresses in turbine blades. Due to dry friction and the relative motion of the contact planes energy is dissipated. This effect results in a reduction of blade vibration amplitudes. In the case of a tuned bladed disk cyclic boundary conditions can be used for the calculation of the dynamic response. For a mistuned bladed disk the complete system has to be modeled and simulated. To reduce the computation time the so-called substructure method is applied. This method is based on the modal description of each substructure, especially disk and blades, combined with a reduction of the degrees of freedom, to describe the dynamics of each component. The spatial dynamical behavior of each component is considered and described by the mode shapes, natural frequencies and modal damping ratios. Using the Harmonic Balance Method the nonlinear friction forces can be linearized. From here it is possible to calculate the frequency response functions of a mistuned bladed disk assembly with friction contacts. In many cases Monte-Carlo simulations are used to find regions, where the system response is sensitive to parameter uncertainties like the natural frequencies of the blades. These simulations require a large computation time. Therefore, an approximate method is developed to calculate the envelopes of the frequency response functions for statistically varying natural frequencies of the blades. This method is based on a sensitivity analysis and the Weibull-distribution of the vibration amplitudes. From here, a measure for the strength of localization for mistuned cyclic systems is derived. Regions, where localization can occur with a high probability, can be calculated by this method. The mean value and the standard deviation of the vibration amplitudes are calculated by simulation and by the approximate method. The comparisons between the approximate method and the Monte-Carlo simulations show a good agreement. Therefore, applying this method leads to remarkable reduction of computation time and gives a quick insight into the system behavior. The approximate method can also be applied to systems, that include the elasticity of the disk and/or the coupling by shrouds or other friction devices.

Sign in / Sign up

Export Citation Format

Share Document