Nonlinear Sensitivity Analysis of Twin Non-Symmetric Micro-Cantilever Beams

2017 ◽  
Author(s):  
M. Amin Changizi ◽  
Ion Stiharu ◽  
Peyman Hajheidari ◽  
Davut Erdem Sahin
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Dynamic Performance ◽  
High Sensitivity ◽  
Numerical Approach ◽  
Cantilever Beams ◽  
Micro Cantilever ◽  
Deflection Theory

In this paper, the dynamic performance of two parallel micro-cantilever beams is investigated and the results are presented. The dynamic response is of high interest in MEMS structures as it is related to the performance of the micro-devices. The micro-cantilever beams can be easily fabricated and yield high sensitivity to variations of physical quantities. In this work, the dynamic response of two parallel flexible cantilever beams subjected to a difference of potential is analyzed. This configuration was modeled as mass-damper spring systems with two degrees of freedom. Such a system can be used to measure the viscosity of liquids. This viscosity is related to damping between two masses representing the two beams in the discrete system model. The fabrication of two identical beams using MEMS fabrication processes may be difficult as the fabrication process may yield some variabilities. Thus, the two beams may be slightly different which will be reflected in their mass and stiffness. This condition was assumed in the proposed model. As the system is sensitive to the applied difference of potential such that the pull-in voltage represents a good indicator of the sensitivity performance. The dynamic analysis was carried out at potentials close to the pull-in value. Stability of the system was evaluated and the responses of the beams were calculated at a potential close to the pull-in voltage. The sensitivity of the system was calculated for different viscosities of liquid between two beams. It was found that an increase of the viscosity yields higher nonlinearity and consequently loose of accuracy while assuming linear stiffness for the beams. In this research, the stiffness of micro-cantilever beams was calculated from small deflection theory of beams. However, there are other methods that could be considered to evaluate the stiffness of the beams. One of this different methods was considered and the sensitivity of the modeled stiffness is discussed. Since the stiff nonlinear differential equations cannot be solved analytically, the numerical approach was exploited. In this work ISODE method from Maple software was used to solve the model described by the two differential equations.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

scholarly journals Dynamical analysis of a 2-degrees of freedom spatial pendulum

2018 ◽  
Vol 184 ◽  
pp. 01003 ◽  
Author(s):  
Stelian Alaci ◽  
Florina-Carmen Ciornei ◽  
Sorinel-Toderas Siretean ◽  
Mariana-Catalina Ciornei ◽  
Gabriel Andrei Ţibu
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dynamical Analysis ◽  
Analysis Software ◽  
Lagrange Equations ◽  
Moments Of Inertia ◽  
Dynamical Simulation ◽  
Principal Moments Of Inertia

A spatial pendulum with the vertical immobile axis and horizontal mobile axis is studied and the differential equations of motion are obtained applying the method of Lagrange equations. The equations of motion were obtained for the general case; the only simplifying hypothesis consists in neglecting the principal moments of inertia about the axes normal to the oscillation axes. The system of nonlinear differential equations was numerically integrated. The correctness of the obtained solutions was corroborated to the dynamical simulation of the motion via dynamical analysis software. The perfect concordance between the two solutions proves the rightness of the equations obtained.

PERIODIC SOLUTIONS OF FORCED OSCILLATORS WITH SEVERAL DEGREES OF FREEDOM

2002 ◽  
Vol 34 (3) ◽  
pp. 308-318 ◽  
Author(s):  
RAFAEL ORTEGA ◽  
LUIS A. SÁNCHEZ
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Forced Oscillators ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient ◽  
New Phenomena

Results of the Landesman–Lazer type provide necessary and sufficient conditions for the existence of periodic solutions of certain nonlinear differential equations with forcing. Typically, they deal with scalar problems. This paper presents a discussion of possible extensions to systems. The emphasis is placed on the new phenomena produced by the increase of the dimension.

scholarly journals ANALYSIS OF FORCED VIBRATIONS OF NONLINEAR PLATES IN A VISCOELASTIC MEDIUM UNDER THE CONDITIONS OF THE DIFFERENT COMBINATIONAL INTERNAL

2019 ◽  
Vol 15 (3) ◽  
pp. 131-148
Author(s):  
Marina Shitikova ◽  
Vladimir Kandu
Keyword(s):  
Comparative Analysis ◽  
Differential Equations ◽  
Dynamic Response ◽  
Fractional Derivative ◽  
Viscoelastic Medium ◽  
Nonlinear Differential Equations ◽  
Forced Vibrations ◽  
Numerical Calculations ◽  
Free And Forced Vibrations ◽  
Nonlinear Plate

In the present paper, the force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied. The motion of the plate is described by three coupled nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal combinational resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. A comparative analysis of numerical calculations for the cases of free and forced vibrations has been carried out.

Nonlinear Vibration Analysis of a Micro Beam Exposed to an External Flow

2011 ◽  
Author(s):  
Hashem Mazaheri ◽  
Ali Hosseinzadeh ◽  
Mohammad T. Ahmadian ◽  
Ahmad Barari
Keyword(s):  
Flow Velocity ◽  
Nonlinear Vibration ◽  
Vibration Frequency ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
High Sensitivity ◽  
Runge Kutta Method ◽  
Velocity Flow ◽  
Micro Cantilever ◽  
Good Agreement

In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity.

scholarly journals Bertolino-Baksa stability at nonlinear vibrations of motor vehicles

2017 ◽  
Vol 44 (2) ◽  
pp. 271-291 ◽  
Author(s):  
Ljudmila Kudrjavceva ◽  
Milan Micunovic ◽  
Danijela Miloradovic ◽  
Aleksandar Obradovic
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Motor Vehicles ◽  
Numerical Code ◽  
Parameter Method ◽  
Spatial Stability ◽  
Linear Vibrations ◽  
Linear Differential

Research of vehicle response to road roughness is particularly important when solving problems related to dynamic vehicle stability. In this paper, unevenness of roads is considered as the source of non-linear vibrations of motor vehicles. The vehicle is represented by an equivalent spatial model with seven degrees of freedom. In addition to solving the response by simulating it within a numerical code, quasi-linearization of nonlinear differential equations of motion is carried out. Solutions of quasi-linear differential equations of forced vibrations are determined using the small parameter method and are indispensable for the study of spatial stability of the vehicle. An optimal stabilization for a simplified two-dimensional model was performed. Spatial stability and internal resonance are considered briefly.

scholarly journals The interference galloping of two circular cylinders with equal diameters.

2007 ◽  
Vol 1 (1) ◽  
pp. 087-102
Author(s):  
Ewa Błazik-Borowa
Keyword(s):  
Differential Equations ◽  
Turbulence Intensity ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Numerical Analyses ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom

The paper deals with numerical analyses of interference galloping of two elasticcaly supported circular cylinders of equal diameters. The basis of the analyses is a quasi-steady model of this phenomenon. The model assumes that both cylinders participate in the process of interference galloping and they have two degrees of freedom. The movement of the cylinders is described as a set of four nonlinear differential equations. On the basis of numerical solutions of these equations the author evaluate the correctness of this quasi-steady model. Then they estimate the dependence of a critical reduced velocity on the Scruton number, turbulence intensity and arrangements of the cylinders.

scholarly journals On the transition from regular to chaotic behaviors in the two degrees of freedom dynamical system

2007 ◽  
Vol 29 (3) ◽  
pp. 353-374
Author(s):  
Nguyen Van Khang ◽  
Nguyen Hoang Duong
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Dynamical Behavior ◽  
Control Parameters ◽  
Lagrange Equations ◽  
Chaotic Motions ◽  
Two Degrees Of Freedom

The main objective of the present paper is to study the transition from periodic regular mot ion to chaos in a two degrees of freedom dynamical system by changing control parameters. The nonlinear differential equations governing motion of the system are derived from the Lagrange equations. By use of the Poincare map, the dynamical behavior is identified based on numerical solutions of the ordinary differential equations. The Lyapunov exponent and the frequency spectrum are calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the considered system.

scholarly journals A Numerical Approach Based on Taylor Polynomials for Solving a Class of Nonlinear Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
C. Guler ◽  
S. O. Kaya
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Numerical Approach ◽  
The Other ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Taylor Coefficients ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Taylor Polynomials

In this study, a matrix method based on Taylor polynomials and collocation points is presented for the approximate solution of a class of nonlinear differential equations, which have many applications in mathematics, physics and engineering. By means of matrix forms of the Taylor polynomials and their derivatives, the technique we have used reduces the solution of the nonlinear equation with mixed conditions to the solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with the unknown Taylor coefficients. On the other hand, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing results in literature.

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