scholarly journals Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 180
Author(s):  
Zuguang Ying ◽  
Yiqing Ni
Keyword(s):  
Harmonic Balance ◽  
Frequency Characteristics ◽  
Vibration Response ◽  
Periodic Response ◽  
General Analytical Expression ◽  
Analytical Expression ◽  
Periodic Vibration ◽  
Balance Solution ◽  
Frequency Relation ◽  
Meso Scale

Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration analyses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response variation have potential application to the vibration control design of nonlinear meso-scale structure systems.

Experimental Investigation into the Vibration Response of an Aero-Engine Rotor-Damper Assembly

1994 ◽  
Vol 208 (1) ◽  
pp. 52-66 ◽  
Author(s):  
M C Levesley ◽  
R Holmes
Keyword(s):  
Experimental Investigation ◽  
Harmonic Balance ◽  
Vibration Response ◽  
Linear Vibration ◽  
Film Rupture ◽  
Supply Pressure ◽  
Balance Principle ◽  
Aero Engine ◽  
Rupture Pressure ◽  
Engine Rotor

This paper presents experimental results on the non-linear vibration response of a rotating assembly comprising a rotor, flexible bearing housing and oil film damper. For the latter, due consideration is given to the effects of oil-supply pressure, film-rupture pressure and end sealing. The results are compared with predictions based on the Harmonic Balance principle described in a complementary paper (1).

A theoretical and experimental investigation into the vibration response of a flexible rotor and squeeze-film damper assembly

2001 ◽  
Vol 215 (10) ◽  
pp. 1251-1269 ◽  
Author(s):  
C-C Siew ◽  
M Hill ◽  
R Holmes ◽  
M Brennan
Keyword(s):  
Harmonic Balance ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Vibration Response ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Linear Vibration ◽  
Squeeze Film Damper ◽  
Good Agreement

This paper presents two efficient methods to calculate the unbalance vibration response of a flexible rotor provided with a squeeze-film damper (SFD) with retainer springs. Both methods are iterative and combine the harmonic balance and receptance approaches. The first method, called the modified iteration method (MIM), is suitable for predicting the three-dimensional mode shapes of a concentric SFD-rotor system. The second method, called the modified harmonic balance method (MHBM), is developed to calculate the non-linear vibration response of a flexible shaft provided with either a concentric or eccentric SFD. The system is also investigated experimentally under different conditions. The predictions computed by these methods are compared with experimental measurements and reasonably good agreement is obtained.

scholarly journals Frequency characteristics of the fractional oscillator Van der Pol

2019 ◽  
Vol 127 ◽  
pp. 02010
Author(s):  
Roman Parovik
Keyword(s):  
Quality Factor ◽  
Harmonic Balance ◽  
Fractional Derivatives ◽  
Harmonic Balance Method ◽  
Oscillatory System ◽  
Frequency Characteristics ◽  
Van Der Pol ◽  
Fractional Oscillator ◽  
Analytical Formulas ◽  
Frequency Phase

Into this paper, the amplitude-frequency and phase-frequency characteristics of the Van der Polar fractional oscillator are studied in order to establish their relationship with the orders of fractional derivatives included in the model equation. Using the harmonic balance method, analytical formulas were obtained for the amplitude-frequency, phase-frequency characteristics, as well as the quality factor – the energy characteristic of the oscillatory system. It was shown that the quality factor depends on the orders of fractional derivatives, and change in their values can lead to both an increase and a decrease in the quality factor.

Expression analytique generale de la granulometrie des sediments meubles; indices caracteristiques et interpretation geologique; notion de facies granulometriques

1952 ◽  
Vol S6-II (1-3) ◽  
pp. 155-167
Author(s):  
Andre Riviere
Keyword(s):  
Granulometric Composition ◽  
Sedimentary Facies ◽  
Unconsolidated Sediments ◽  
Algebraic Functions ◽  
General Analytical Expression ◽  
Analytical Expression ◽  
Fine Sediments ◽  
Two Indices

Abstract The granulometric composition of most unconsolidated sediments is susceptible to general analytical expression and can be represented by simple algebraic functions defined by the two indices of evolution (n) and sorting (g).In the case of fine sediments, where dispersion is weak, these functions correspond rather precisely to the actual granulometric curves. Four granulometric facies corresponding to true sedimentary facies can be defined according to the index n.

scholarly journals Harmonic Balance Solution Of Coupled Nonlinear Non-Conservative Differential Equation

2013 ◽  
Vol 32 ◽  
pp. 1-14
Author(s):  
M Saifur Rahman ◽  
M Majedur Rahman ◽  
M Sajedur Rahaman ◽  
M Shamsul Alam
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Limit Cycle ◽  
Nonlinear Differential Equation ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Balance Method ◽  
Balance Solution ◽  
Good Agreement

A modified harmonic balance method is employed to determine the second approximate solutions to a coupled nonlinear differential equation near the limit cycle. The solution shows a good agreement with the numerical solution. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13640 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 1 – 14

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