Forced Vibration Analysis for Damped Periodic Systems With One Nonlinear Disorder

1998 ◽  
Vol 67 (1) ◽  
pp. 140-147 ◽  
Author(s):  
H. C. Chan ◽  
C. W. Cai ◽  
Y. K. Cheung
Keyword(s):  
Degrees Of Freedom ◽  
Order Approximation ◽  
Structural Parameters ◽  
Harmonic Excitation ◽  
Zero Order ◽  
Periodic Systems ◽  
Pass Band ◽  
Driving Frequency ◽  
Attenuation Constant ◽  
Forced Vibration Analysis

The steady-state responses of damped periodic systems with finite or infinite degrees-of-freedom and one nonlinear disorder to harmonic excitation are investigated by using the Lindstedt-Poincare method and the U-transformation technique. The perturbation solutions with zero-order and first-order approximations, which involve a parameter n, i.e., the total number of subsystems, as well as the other structural parameters, are derived. When n approaches infinity, the limiting solutions are applicable to the system with infinite number of subsystems. For the zero-order approximation, there is an attenuation constant which denotes the ratio of amplitudes between any two adjacent subsystems. The attenuation constant is derived in an explicit form and calculated for several values of the damping coefficient and the ratio of the driving frequency to the lower limit of the pass band. [S0021-8936(00)01101-6]

scholarly journals Response of Duffing's Oscillator to Harmonic Base Excitation and Significance of First Order Term

2020 ◽  
Vol 25 (3) ◽  
pp. 408-424
Author(s):  
K. Divya ◽  
K. Renji
Keyword(s):  
Fundamental Frequency ◽  
Order Approximation ◽  
Order Term ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Zero Order ◽  
Low Frequencies ◽  
First Order ◽  
Response Characteristics ◽  
First Order Approximation

Responses of systems with nonlinear stiffness subjected to base harmonic excitation are determined. An expression to estimate the amplitude in the fundamental frequency of oscillation is derived from first principles using Lindstedt's method. It is observed that the amplitude determined using the zero order approximation is in error at low frequencies. Therefore, an expression for the first order approximation of the amplitude of response at the fundamental frequency is derived. Zero order and first order approximation terms together form the response. Characteristics showing the variation of the amplitude with the excitation frequency for various nonlinear spring parameters are presented. The issue at low frequencies is resolved by the incorporation of the first order term. An expression for the phase difference and the expression of the asymptote where the responses converge are also derived.

scholarly journals The Hamiltonian Dynamics of The Two Gyrostats Problem

1999 ◽  
Vol 172 ◽  
pp. 303-312
Author(s):  
F. Mondejar ◽  
A. Vigueras
Keyword(s):  
Euler Equations ◽  
Degrees Of Freedom ◽  
Order Approximation ◽  
Hamiltonian Dynamics ◽  
Equations Of Motion ◽  
Reduction Process ◽  
Zero Order ◽  
Canonical Structure ◽  
Central Force Field ◽  
Zero Order Approximation

AbstractThe problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian and give explicit forms corresponding to non-canonical Poissson brackets. Finally, we study the case where one of the gyrostats has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable in the zero order approximation.

Simultaneous Determination of Several Elements by Spectrochemical Addition Method … (II) (Tabulation of Analytical Value)

1968 ◽  
Vol 22 (6) ◽  
pp. 749-752 ◽  
Author(s):  
Isoo Masuda ◽  
Tamon Inouye
Keyword(s):  
Simultaneous Determination ◽  
Order Approximation ◽  
Analytical Data ◽  
Zero Order ◽  
Dilution Factor ◽  
Improved Method ◽  
Addition Method ◽  
Zero Order Approximation ◽  
First Approximation

An improved method for the tabulation of analytical data, obtained by addition and successive dilution procedures for spectrochemical analysis, is presented. The author's previous work shows that the solution of the first approximation diverges at some dilution factor smaller than unity when the slope of the working curve of added series is greater than that of unadded series. By obtaining the distance between this position and the origin, and taking it as a correction factor for zero-order approximation, tabulation of the analytical value, in the case of β>α, is carried out. One parameter of the calculation is deleted by normalizing the spectral intensity; therefore, the tabulation can be simplified.

Numerical and Experimental Approaches to Investigate the Stability of a Motorcycle Vehicle

2006 ◽  
Author(s):  
Federico Cheli ◽  
Marco Bocciolone ◽  
Marco Pezzola ◽  
Elisabetta Leo
Keyword(s):  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Experimental Tests ◽  
Roll Angle ◽  
Longitudinal Motion ◽  
Reference Trajectory ◽  
Steering Angle ◽  
Steady State Condition ◽  
The Stability ◽  
Linearized Model

The study of motorcycle’s stability is an important task for the passenger’s safety. The range of frequencies involved for the handling stability is lower than 10 Hz. A numerical model was developed to access the stability of a motorcycle vehicle in this frequency range. The stability is analysed using a linearized model around the straight steady state condition. In this condition, the vehicle’s vertical and longitudinal motion are decoupled, hence the model has only four degrees of freedom (steering angle, yaw angle, roll angle and lateral translation), while longitudinal motion is imposed. The stability was studied increasing the longitudinal speed. The input of the model can be either a driver input manoeuvre (roll angle) or a transversal component of road input able to excite the vibration modes. The driver is introduced in the model as a steering torque that allows the vehicle to follow a reference trajectory. To validate the model, experimental tests were done. To excite the vehicle modes, the driver input was not taken into account considering both the danger for the driver and the repeatability of the manoeuvre. Two different vehicle configurations were tested: vehicle 1 is a motorcycle [7] and vehicle 2 is a scooter. Through the use of the validated model, a sensitivity analysis was done changing structural (for example normal trail, steering angle, mass) and non structural parameters (for example longitudinal speed).

Chaotic Amplitude Dynamics for Parametrically Excited Systems With Quadratic Nonlinearities

1995 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Order Approximation ◽  
Amplitude Equations ◽  
Analytical Technique ◽  
First Order ◽  
Numerical Studies ◽  
Quadratic Nonlinearities ◽  
First Order Approximation

Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.

scholarly journals Wavelet multi-resolution approximation of time-varying frame structure

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879559 ◽  
Author(s):  
Min Xiang ◽  
Feng Xiong ◽  
Yuanfeng Shi ◽  
Kaoshan Dai ◽  
Zhibin Ding
Keyword(s):  
Parameter Estimation ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Identification Problem ◽  
Frame Structure ◽  
Structural Parameter ◽  
Time Varying ◽  
Engineering Structures ◽  
Time Frequency ◽  
Non Parametric

Engineering structures usually exhibit time-varying behavior when subjected to strong excitation or due to material deterioration. This behavior is one of the key properties affecting the structural performance. Hence, reasonable description and timely tracking of time-varying characteristics of engineering structures are necessary for their safety assessment and life-cycle management. Due to its powerful ability of approximating functions in the time–frequency domain, wavelet multi-resolution approximation has been widely applied in the field of parameter estimation. Considering that the damage levels of beams and columns are usually different, identification of time-varying structural parameters of frame structure under seismic excitation using wavelet multi-resolution approximation is studied in this article. A time-varying dynamical model including both the translational and rotational degrees of freedom is established so as to estimate the stiffness coefficients of beams and columns separately. By decomposing each time-varying structural parameter using one wavelet multi-resolution approximation, the time-varying parametric identification problem is transformed into a time-invariant non-parametric one. In solving the high number of regressors in the non-parametric regression program, the modified orthogonal forward regression algorithm is proposed for significant term selection and parameter estimation. This work is demonstrated through numerical examples which consider both gradual variation and abrupt changes in the structural parameters.

scholarly journals Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

2013 ◽  
Vol 20 (6) ◽  
pp. 1033-1047 ◽  
Author(s):  
J. Warminski ◽  
M. P. Cartmell ◽  
A. Mitura ◽  
M. Bochenski
Keyword(s):  
Analytical Solutions ◽  
Order Approximation ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Harmonic Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Beam ◽  
Approximate Analytical Solutions ◽  
Full Structure

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.

Trajectory Synthesis and Redundancy Resolution for High Speed Point to Point Motions of Redundant Robot Manipulators

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic Performance ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Redundancy Resolution ◽  
Tracking Accuracy ◽  
Point To Point

Abstract Trajectory synthesis for robot manipulators with redundant kinematic degrees-of-freedom has been studied by numerous investigators. Redundant manipulators are of interest since the redundant degrees-of-freedom can be used to improve the local and global kinematic and dynamic performance of a system. As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Noting that manipulators with revolute joints have nonlinear dynamics, high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. In this paper, a redundancy resolution method is developed based on the Trajectory Pattern Method (TPM) to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. As an example, optimal trajectories are synthesized for point to point motions of a plane 3R manipulator.

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Sign in / Sign up

Export Citation Format

Share Document