Modal analysis of Kelvin viscoelastic solids under arbitrary excitation: Circular plates under moving loads

1992 ◽  
Vol 91 (5) ◽  
pp. 2703-2707
Author(s):  
I. Y. Shen ◽  
C. D. Mote
Keyword(s):  
Modal Analysis ◽  
Circular Plates ◽  
Moving Loads ◽  
Viscoelastic Solids

scholarly journals METHODS FOR WHEEL PAIR DYNAMICS MODELING TAKING INTO ACCOUNT ELASTICITY

2019 ◽  
Vol 2019 (4) ◽  
pp. 40-51
Author(s):  
Геннадий Михеев ◽  
Gennadiy Miheev ◽  
Дмитрий Погорелов ◽  
Dmitriy Pogorelov ◽  
Александр Родиков ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Finite Element ◽  
Modal Analysis ◽  
Finite Element Models ◽  
Moving Loads ◽  
Dynamics Modeling ◽  
Wheel Pair ◽  
First Results ◽  
Wheel Profile ◽  
Universal Mechanism

The computer simulation of railway wheel pair (WP) dynamics taking into account elasticity allows analyzing WPs highfrequency oscillations and vibroaccelerations of crew part units connected with them, modeling strain gage wheel pairs, estimating the WP deformation impact upon force distributions in gears of locomotive drives, and also solving other ur-gent problems. In the paper there are offered two approaches to the analysis of the dynamics of elastic WPs within the limits of which their finite element models with the rotating and nonrotating grid are under consideration. The WP kinematics is presented as a sum of its motion as an absolute solid together with the jointed co-ordinates (C) and small elastic removals regarding co-ordinates given which are calculated on the basis of the results of WP modal analysis. A wheel profile kinematics is described taking into account unit elastic motions. There are presented algorithms for the calculation of generalized forces of moving loads in the wheelrail contact taking into account WP elasticity. Both approaches are realized in the “Universal mechanism” program. The first results of modeling confirming the correctness of the methods offered are shown.

scholarly journals Modal Analysis of Circular Symmetrical Plates by Means of Generalized Finite Difference Method

2019 ◽  
Vol 17 (3) ◽  
pp. 88-98
Author(s):  
A. E. Mansour
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Modal Analysis ◽  
Difference Method ◽  
Numerical Solutions ◽  
Analysis Procedure ◽  
Machine Design ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Classical Formulation

In this paper, a simplified modal analysis procedure of circular plates procedures (on polar domains) through generalized (modernized) finite difference method (abbreviated next as – FDM) is developed.Generally, circular plates are widely used for a plenty of modern civilian and industrial utilities, machine design and many other purposes. They form a spectrum of elements starting with trains’ bogies along with engine pistons, dampers and up to slabs and roofs over circular-shaped buildings, train stationsand other transportation facilities. Nowadays, FDM predominates the numerical solutions of partial differential equations (abbreviated next as – PDE) not less than the method of finite elements (abbreviated next as – FEM). This is wide-famous mathematical-discretization method that is economic to compute and simple to code, less regarding to computation tools in hands and how powerful/less powerful they are, since it bases on replacing each derivative by a difference algebraic quotient in a classical formulation. In a sense, a finite difference formulation offers a more direct approach to the numerical solution of the PDE especially in polar coordinates domain problems considering curvilinear dimensions that even FEM does not.The generalized approach of FDM considers many parameters less regarded by the classical one.  Consequently, the use of classical approach negatively affects the accuracy of calculation (convergence to the exact solution values) and the tendency of results, the thing been healed by the generalized approach.

scholarly journals Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Taehyun Kim ◽  
Ilwook Park ◽  
Usik Lee
Keyword(s):  
Modal Analysis ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Moving Loads ◽  
Analysis Method ◽  
Simply Supported

The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

scholarly journals Vibration analysis of irregular-shaped plates on simple supports

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210184
Author(s):  
Abhijit Ghosh ◽  
Anirvan DasGupta
Keyword(s):  
Boundary Conditions ◽  
Modal Analysis ◽  
Circular Plate ◽  
Solution Structure ◽  
Circular Plates ◽  
Perturbative Approach ◽  
Irregular Boundary ◽  
Generalized Fourier Series ◽  
Perturbative Solution ◽  
Smallness Parameter

In this work, we propose a general perturbative approach for modal analysis of irregular-shaped plates of uniform thickness with uniform boundary conditions. Given a plate of irregular boundary, first, a uniform circular plate of identical thickness and area, centred at the centroid, is determined. The irregular boundary is then treated as a perturbation with a suitable smallness parameter, and is expressed as a generalized Fourier series. The frequency parameter, shape function and boundary conditions are then perturbed in terms of the smallness parameter. The homogeneous zeroth-order equation corresponds to the circular plate, which is exactly solvable. We show that the inhomogeneous equations in the higher orders can also be solved exactly using a particular solution structure. We can then construct the exact perturbative solution up to any order. The proposed method is demonstrated through the modal analysis of simply supported super-circular plates. The results are validated using the numerical results obtained from ANSYS ® , which are an excellent match. Interestingly, the supposedly degenerate modes with an even number of nodal diameters of super-circular plates are found to split naturally.

scholarly journals Comparative study for modal analysis of circular plates with various cutouts and end conditions

2019 ◽  
Vol 29 ◽  
pp. 87-93 ◽  
Author(s):  
Vedanth Bhatnagar ◽  
Pavan Kishore Mamaduri ◽  
Sreenivasulu B
Keyword(s):  
Comparative Study ◽  
Modal Analysis ◽  
Circular Plates ◽  
End Conditions
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