Simple Models for Periodic Lattices

1991 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Optimal Solution ◽  
Mode Shapes ◽  
Design Stage ◽  
Continuum Models ◽  
Original Structure ◽  
Vibration Modes ◽  
Equivalent Properties

Abstract In many applications, the dynamic behavior of large periodic structures must be modeled accurately, thus requiring the determination of a significant number of natural frequencies and mode shapes. In order to perform that task most efficiently, a continuum modeling approach can be adopted. The discrete structure is then replaced by a continuum model which can be analyzed more efficiently. Therefore, at the design stage many analyses can be performed while searching for the optimal solution. Known structural models are usually used as continuum models, and several methods are available to determine the equivalent properties from the properties of the original structure. This task is usually cumbersome, and in addition, in certain cases, continuum models cannot represent all modes of deformation. In this article, a simple approach to develop continuum models without explicit reference to an existing structural theory is presented. Very accurate results are obtained, and all vibration modes can now be handled easily.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

1997 ◽  
Author(s):  
Mintae Kim ◽  
Joonho Moon ◽  
Jonathan A. Wickert
Keyword(s):  
Mode Shape ◽  
Natural Frequencies ◽  
Periodic Structures ◽  
Spatial Modulation ◽  
Vibration Modes ◽  
Algebraic Relation ◽  
Natural Frequencies And Modes ◽  
Axisymmetric Structure ◽  
Technical Interest ◽  
Model Features

Abstract When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.

An Extension of the Holzer Method for Redundant Drive Trains

1974 ◽  
Vol 96 (2) ◽  
pp. 697-698 ◽  
Author(s):  
M. S. Hundal
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
System Of Equations ◽  
Redundant System ◽  
Drive Trains ◽  
Redundant Drive

A method is described for the determination of natural frequencies and mode shapes of closed drive trains. It is an extension of the Holzer method to a redundant system. The “error” for a given value of frequency is computed by the solution of a tridiagonal system of equations.

Module-Based Static Structural Design of a Modular Reconfigurable Robot

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Richard Phillip Mohamed ◽  
Fengfeng (Jeff) Xi ◽  
Allan Daniel Finistauri
Keyword(s):  
Structural Design ◽  
Design Method ◽  
Optimal Solution ◽  
Local Deformation ◽  
Design Stage ◽  
Coordinate Frame ◽  
Reconfigurable Robots ◽  
Nonlinear Approach ◽  
Reconfigurable Robot

In this paper, the structural design of modular reconfigurable robots (MRRs) is studied. This problem is defined as the determination of proper module sizes according to the robot’s payload and end-effector deflection specifications. Because an MRR has multiple configurations, a simple design process is proposed in order to avoid performing the structural design stage at each configuration. The final structural design is only carried out at a single configuration that can guarantee the robot’s satisfactory performance for all remaining feasible configurations. It is shown that the module structural design stage can be performed at the local coordinate frame of each module. While the module local force requirement can be fully determined, the determination of the module local deformation requirement is redundant. Thus, there can exist multiple design solutions. To overcome this problem, a nonlinear approach using a genetic algorithm is used to search for an optimal solution. Finally, a design simulation is performed on an example MRR, and the results show the effectiveness of the proposed design method.

scholarly journals On the determination of natural frequencies and mode shapes of cable-stayed bridges

2001 ◽  
Vol 25 (12) ◽  
pp. 1099-1115 ◽  
Author(s):  
F.T.K. Au ◽  
Y.S. Cheng ◽  
Y.K. Cheung ◽  
D.Y. Zheng
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Cable Stayed Bridges

Structural Response of Pipeline Free Spans Based on Beam Theory

2002 ◽  
Author(s):  
Olav Fyrileiv ◽  
Kim Mo̸rk
Keyword(s):  
Natural Frequencies ◽  
Structural Response ◽  
Beam Theory ◽  
Vertical Vibration ◽  
Mode Shapes ◽  
Ocean Current ◽  
Vibration Modes ◽  
Wave Loading ◽  
Vortex Induced Vibrations ◽  
Subsea Pipelines

One of the main risk factors for subsea pipelines exposed on the seabed is fatigue failure of free spans due to ocean current or wave loading. This paper describes how the structural response of a free span, as input to the fatigue analyses, can be assessed in a simple and still accurate way by using improved beam theory formulations. In connection with the release of the DNV Recommended Practice, DNV-RP-F105 “Free Spanning Pipelines”, the simplified structural response quantities have been improved compared to previous codes. The boundary condition coefficients for the beam theory formulations have been updated based an effective span length concept. This concept is partly based on theoretical studies and partly on a large number of FE analyses. The updated expressions are general and fit all types of soil and pipe dimensions for lower lateral and vertical vibration modes. The present paper focus on estimation of simplified response quantities such as lower natural frequencies and associated mode shapes. Hydrodynamical aspects of Vortex Induced Vibrations (VIV) are outside the scope of this paper.

scholarly journals Direct Method for the Determination of Coefficients of Characteristic Equation of a MDOF System

2019 ◽  
Vol 15 (2) ◽  
pp. 26-31
Author(s):  
Mahesh Chandra Luintel
Keyword(s):  
Characteristic Equation ◽  
Natural Frequencies ◽  
Direct Method ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Vibratory System ◽  
Single Degree Of Freedom ◽  
Dynamic Matrix ◽  
Eigen Values

Dynamic response of any single degree of freedom (SDOF) vibratory system is studied by evaluating its natural frequencies whereas that of any multi degree of freedom (MDOF) vibratory system is studied by evaluating its natural frequencies and corresponding mode shapes. Efficient method to determine the natural frequencies and mode shape of a MDOF system is to determine its dynamic matrix and to calculate its eigen-values and eigen-vectors. As the number of degree of freedom (DOF) of the system increases, the size of the dynamic matrix increases and the use of a computer program or package become essential. Hence this paper proposes a new method to directly calculate the coefficients of characteristic equation of any degree of freedom system from which eigen-values and then natural frequencies can be determined.  

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