Investigation and Comparison of Possible Boundary Conditions and System Vibration Modes in Two-Link Flexible Manipulators

2001 ◽  
Author(s):  
Joono Cheong ◽  
Youngil Youm ◽  
Wan Kyun Chung
Keyword(s):  
Boundary Conditions ◽  
Mode Shapes ◽  
Natural Mode ◽  
Vibration Modes ◽  
Flexible Robot ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Robot Systems ◽  
Comparative Concept ◽  
System Vibration

Abstract In the slewing multi-link flexible robot systems, the natural frequencies and mode shapes have been determined using the assumed component mode method with clamped-joint condition, in which the system modes is reconstructed by the series of assumed modes of each link. This method, however, requires large number of assumed modes to accurately describe the system and even more, sometimes, the results are erroneous. The direct analytic solution of entire system vibration mode which is a comparative concept of assumed mode method can accurately account for the entire vibration with a few number of significant modes. This paper deals with system vibration modes of two-link flexible robot and their appropriate boundary conditions. There are four possible set of boundary conditions, that is, clamped-clamped, clamped-spring, spring-clamped, spring-spring, according to joint servo condition, and we compare mode shapes and modal frequencies of each case by numerical and experimental results. We also provide important characteristics of natural mode when imposed certain kind of boundary conditions.

scholarly journals Free Vibration Analysis of Piezoelectric Cylindrical Nanoshell: Nonlocal and Surface Elasticity Effects

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Surface Elasticity ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Assumed Mode Method ◽  
Mode Method

Vibration analysis of piezoelectric cylindrical nanoshell subjected to visco-Pasternak medium with arbitrary boundary conditions is investigated. In these analysis simultaneous effects of the nonlocal, surface elasticity and the different material scale parameter are considered. To this end, Eringen nonlocal theory and Gurtin–Murdoch surface/interface theory considering Donnell's shell theory are used. The governing equations and boundary conditions are derived using Hamilton’s principle and the assumed mode method combined with Euler–Lagrange method is used for discretizing the equations of motion. The viscoelastic nanoshell medium is modeled as Visco-Pasternak foundation. A variety of new vibration results including frequencies and mode shapes for piezoelectric cylindrical nano-shell with non-classical restraints as well as different material parameters are presented. The convergence, accuracy and reliability of the current formulation are validated by comparisons with existing experimental and numerical results. Also, the effects of nonlocality, surface energy, nanoshell radius, circumferential wavenumber, nanoshell damping coefficient, and foundation damping are accurately studied on frequencies and mode shapes of piezoelectric cylindrical nanoshell.

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Squeal Analysis of a Disc Brake Considering Damping between a Disc and a Pad Lining

2012 ◽  
Vol 157-158 ◽  
pp. 1000-1003
Author(s):  
Ke Wei Zhou ◽  
Cheol Kim ◽  
Min Ok Yun ◽  
Ju Young Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Element Model ◽  
Disc Brake ◽  
Vibration Modes ◽  
Assumed Mode Method ◽  
Frictional Damping ◽  
System Components ◽  
Mode Method ◽  
Assumed Mode

The improved equations of motion for a friction-engaged brake system have been newly derived on the basis of the assumed mode method and frictional damping. The equations of motion with a finite element model were constructed by a set of vibration modes found from FE modal analysis on all system components. Consequently, the modal information of system components are combined with equations of motion derived from the analytical model. Numerical analysis showed the mode which was unstable in an undamped case became stable in a damped case.

Sensitivity Analysis of a Flexible Marine Riser Using Sobol’s Method

2017 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Arastou Azimi ◽  
Robert G. Parker
Keyword(s):  
Sensitivity Analysis ◽  
Structural Parameters ◽  
Unit Length ◽  
Mode Shapes ◽  
External Diameter ◽  
Marine Riser ◽  
Assumed Mode Method ◽  
Flexible System ◽  
Mode Method ◽  
Sobol’S Method

In this research, sensitivity analysis of upper and lower end angles in addition to the midpoint displacement of the flexible marine riser with respect to structural parameters such as: uniform mass per unit length, external diameter and the tension of the riser are conducted. Harsh environmental circumstances of ocean flow in addition to exerted tension on top of risers may lead to irreparable damages, so it is important to have a parametric study of dynamic response before it is controlled. The “Sobol” method is applied here as a reliable statistical method to sensitivity analysis of a flexible system. Motion equation of the system is developed based on Hamilton’s principle. The riser is modeled as a distributed parameter system. Moreover, simulations are carried out based on Assumed Mode Method (AMM) to solve PDE of the riser through mode shapes and generalized coordinates. Finally, the results of sensitivity analysis are presented.

Analytical Model for Low-Frequency Transmission Loss Calculation of Zero-Prestressed Plates With Arbitrary Mass Loading

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
William T. Edwards ◽  
Chia-Ming Chang ◽  
Geoffrey McKnight ◽  
Steven R. Nutt
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Transmission Loss ◽  
Mass Density ◽  
Low Frequency ◽  
Sound Attenuation ◽  
Mode Shapes ◽  
Natural Mode ◽  
Rectangular Plates ◽  
Acoustic Metamaterials

As the importance of sound attenuation through weight-critical structures has grown and mass law based strategies have proven impractical, engineers have pursued alternative approaches for sound attenuation. Membrane-type acoustic metamaterials have demonstrated sound attenuation significantly higher than mass law predictions for narrow, tunable bandwidths. Similar phenomena can be achieved with plate-like structures. This paper presents an analytical model for the prediction of transmission loss through rectangular plates arbitrarily loaded with rigid masses, accommodating any combination of clamped and simply supported boundary conditions. Equations of motion are solved using a modal expansion approach, incorporating admissible eigenfunctions given by the natural mode shapes of single-span beams. The effective surface mass density is calculated and used to predict the transmission loss of low-frequency sound through the plate–mass structure. To validate the model, finite element results are compared against analytical predictions of modal behavior and shown to achieve agreement. The model is then used to explore the influence of various combinations of boundary conditions on the transmission loss properties of the structure, revealing that the symmetry of plate mounting conditions strongly affects transmission loss behavior and is a critical design parameter.

Complex Modal Analysis of a Non-Modally Damped Continuous Beam

2013 ◽  
Author(s):  
Xing Xing ◽  
Brian F. Feeny
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Separation Of Variables ◽  
Mode Shapes ◽  
Modal Assurance Criterion ◽  
Assumed Mode Method ◽  
State Variable ◽  
Mode Method ◽  
Cantilevered Beam ◽  
Assumed Mode

This work represents an investigation of the complex modes of continuous vibration systems with nonmodal damping. As an example, a cantilevered beam with damping at the free end is studied. Traditional separation of variables for this problem leads to a differential eigenvalue problem which requires a numerical solution. In this paper, assumed modes are applied to discretize the eigenvalue problem in state-variable form, to then obtain estimates of the frequencies and modes. The finite-element method (FEM) is also utilized to get the mass, stiffness, and damping matrices and further to solve a state-variable eigenproblem. A comparison between the assumed-mode and finite-element eigenvalues and modal vectors shows that the methods produce consistent results. The comparison of the modes was done visually and also by using the modal assurance criterion (MAC) on the modal vectors. The assumed-mode method is then used to study the effects of the damping coefficient on mode shapes and modal damping.

Mode Evolution of Asymmetric Rotors Assembled to Flexible Bearings and Housing

2009 ◽  
Author(s):  
Hyunchul Kim ◽  
I. Y. Shen
Keyword(s):  
Boundary Conditions ◽  
Vibration Mode ◽  
Fluid Dynamic ◽  
Modal Testing ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Fixed Boundary ◽  
Practical Applications ◽  
Asymmetric Rotor ◽  
Surface Integrals

This paper is to study how vibration modes of a stationary asymmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to the assembly, vibration modes of the rotor are classified as “balanced modes” and “unbalanced modes.” Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as “unbalanced modes.” In this paper, we first develop two mathematical criteria to identify balanced modes. For the first criteria, the rotor is subjected to fixed boundary conditions at the bearings prior to assembly. In this case, a vibration mode will be a balanced mode if the reactions at the fixed boundary vanish. For the second criterion, the rotor is subjected to free boundary conditions (including the bearing points) prior to assembly. In this case, a vibration mode will be a balanced mode if the bearing locations are nodal points of the vibration mode. These mathematical criteria are then applied to a rotor consisting of a rigid hub supporting a flexible structure, which appears in many practical applications. For balanced modes, the criteria lead to a conclusion that surface integrals of modal forces and moments at the flexible-rigid rotor interface will vanish. Moreover, these surface integrals can be conveniently calculated using finite element methods. To validate the mathematical criteria, modal testing was conducted on a disk with 4 pairs of brackets mounted on a rigid spindle, a ball-bearing spindle and a fluid-dynamic bearing spindle.

Free Vibration Analysis of Rectangular Plates With Multiple Rectangular Openings and Arbitrary Edge Constraints

2014 ◽  
Author(s):  
Dae-Seung Cho ◽  
Nikola Vladimir ◽  
Tae-Muk Choi
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Relevant Literature ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Ocean Engineering ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

Free vibration analysis of plates with openings represents an important issue in naval architecture and ocean engineering applications. Namely, they are often primary design members of complex structures and knowledge about their dynamic behavior becomes a prerogative for the proper structural design. This paper deals with application of assumed mode method to free vibration analysis of rectangular plates with multiple rectangular openings at arbitrary defined locations. Developed method can be applied to both thin and thick plates as well as to classical and non-classical edge constraints. In the assumed mode method natural frequencies and mode shapes of a corresponding plate are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations of motion. The developed procedure actually represents an extension of a method for the natural vibration analysis of rectangular plates without openings, which has been recently presented in the relevant literature. The effect of an opening is taken into account in a simple and intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with single and multiple rectangular openings with various thicknesses and different combinations of boundary conditions. Also, the influence of the rectangular opening area on the plate dynamic response is analyzed. The comparisons of the results with those obtained using the finite element method (FEM) is also provided, and very good agreement is achieved. Finally, related conclusions are drawn and recommendations for future investigations are presented.

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