scholarly journals Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link, Using Perturbation Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
N. S. Viliani ◽  
H. Zohoor ◽  
M. H. Kargarnovin
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Vibration Analysis ◽  
Compliant Mechanism ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Flexible Link ◽  
Assumed Mode Method ◽  
New Type ◽  
Assumed Mode

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed.

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.

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.

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.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

Mechanical Behavior of an Electrostatically Actuated Microplate

2003 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Finite Dimension ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Mode Shapes ◽  
Design Parameters ◽  
Electrostatically Actuated ◽  
Linear Eigenvalue Problem ◽  
Electrically Actuated

We present a nonlinear model of electrically actuated microplates. The model accounts for the nonlinearity in the electric forcing as well as mid-plane stretching of the plate. We use a Galerkin approximation to reduce the partial-differential equations of motion to a finite-dimension system of nonlinearly coupled second-order ordinary-differential equations. We find the deflection of the microplate under DC voltage and study the pull-in phenomenon. The natural frequencies and mode shapes are then obtained around the deflected position of the microplate by solving the linear eigenvalue problem. The effect of various design parameters on both the static response and the dynamic characteristics are studied.

Truncation errors of assumed shape modeling for flexible-link manipulators

2012 ◽  
Vol 226 (11) ◽  
pp. 2627-2644 ◽  
Author(s):  
Fatemeh Heidari ◽  
Mohammad Vakil ◽  
Reza Fotouhi ◽  
Peter N Nikiforuk
Keyword(s):  
Mode Shape ◽  
Dynamic Models ◽  
Transfer Functions ◽  
Degree Of Freedom ◽  
Flexible Manipulator ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Flexible Link ◽  
Dimensional Parameters ◽  
Assumed Mode

The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between approximate zeros and analytical zeros versus the number of mode shapes as well as all the physical parameters is performed. Moreover, guidelines are provided to select the numbers of mode shapes such that the approximate zeros become close to the analytical zeros. These guidelines can easily be used by control and modeling engineers, making them valuable for modeling and control of flexible robot manipulators.

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