Reduction of Harmonic Response of Cylindrical Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1371-1377 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cantilever Beams ◽  
Steady State Response ◽  
Optimum Conditions ◽  
Harmonic Force ◽  
Shell Surface ◽  
Single Degree Of Freedom ◽  
Harmonic Response ◽  
State Response ◽  
Single Degree ◽  
Mode Method

The normal mode method is used to investigate the reduction in the steady-state response of a simply supported cylindrical shell when conventional absorbers are attached to the shell. Two types of excitation are considered: (a) a single radial harmonic force, and (b) a harmonic pressure distributed over the shell surface. The effect upon response of varying the absorber parameters is studied. Optimum conditions for specific cases are obtained and compared with those required to minimize response when absorbers are added to cantilever beams and to the classical single degree of freedom system.

Predictions of the Periodic Response of a Single-Degree-of-Freedom Foam-Mass System by Using Incremental Harmonic Balance

2012 ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Driving Frequency ◽  
Steady State Response ◽  
Base Excitation ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Incremental Harmonic Balance

Vehicle occupants are exposed to low frequency vibration that can cause fatigue, lower back pain, spine injuries. Therefore, understanding the behavior of a seat-occupant system is important in order to minimize these undesirable vibrations. The properties of seating foam affect the response of the occupant, so there is a need for good models of seat-occupant systems through which the effects of foam properties on the dynamic response can be directly evaluated. In order to understand the role of flexible polyurethane foam in characterizing the complex seat-occupant system behavior better, the response of a single-degree-of-freedom foam-mass system, which is the simplest model representing a seat-occupant system, is studied. The incremental harmonic balance method is used to determine the steady-state behavior of the foam-mass system subjected to sinusoidal base excitation. This method is used to reduce the time required to generate the steady-state response at the driving frequency and at harmonics of the driving frequency from that required when using direct time-integration of the governing equations to determine the steady state response. Using this method, the effects of different viscoelastic models, riding masses, base excitation levels and damping coefficients on the response are investigated.

The Steady State Response of Systems With Hardening Hysteresis

1978 ◽  
Vol 100 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. K. Miller
Keyword(s):  
Steady State ◽  
Degree Of Freedom ◽  
General Nature ◽  
Model Parameters ◽  
Steady State Response ◽  
Single Degree Of Freedom ◽  
Analytical Technique ◽  
State Response ◽  
Single Degree ◽  
Critical Model

A physical model for hardening hysteresis is presented. An approximate analytical technique is used to determine the steady-state response of a single-degree-of-freedom system and a multi-degree-of-freedom system incorporating this model. Certain critical model parameters which determine the general nature of the responses are identified.

scholarly journals On the Steady State Response of a Cantilever Beam Partially Immersed in a Fluid and Carrying an Intermediate Mass

2000 ◽  
Vol 7 (4) ◽  
pp. 179-194 ◽  
Author(s):  
A.A. Al-Qaisia ◽  
M.N. Hamdan ◽  
B.O. Al-Bedoor
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Equation Of Motion ◽  
Steady State Response ◽  
Intermediate Mass ◽  
Assumed Mode Method ◽  
State Response ◽  
Non Linear ◽  
Mode Method ◽  
Assumed Mode

This paper presents a study on the nonlinear steady state response of a slender beam partially immersed in a fluid and carrying an intermediate mass. The model is developed based on the large deformation theory with the constraint of inextensible beam, which is valid for most engineering structures. The Lagrangian dynamics in conjunction with the assumed mode method is utilized in deriving the non-linear unimodal temporal equation of motion. The distributed and concentrated sinusoidal loads are accounted for in a consistent manner using the assumed mode method. The non-linear equation of motion is, analytically, solved using the single term harmonic balance (SHB) and the two terms harmonic balance (2HB) methods. The stability of the system, under various loading conditions, is investigated. The results are presented, discussed and some conclusions on the partially immersed beam nonlinear dynamics are extracted.

Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

Harmonic Response of Cylindrical Shells

1974 ◽  
Vol 96 (3) ◽  
pp. 994-999 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Shell Theory ◽  
Excitation Frequency ◽  
Radial Component ◽  
Resonant Response ◽  
Thin Cylindrical Shell ◽  
Harmonic Force ◽  
State Response ◽  
Hysteretic Damping ◽  
Mode Method ◽  
Thin Shell Theory

The normal mode method is used to determine the steady state response of a simply supported, uniform thin cylindrical shell to a radical harmonic force with hysteretic damping included in the analysis. Numerical results are given for the variation with excitation frequency of the radial component of amplitude at different points along the shell for three levels of damping. The response at the resonances, corresponding to the first few modes of each shell, and their convergence, as the number of modes included in the solution is increased, are considered in detail. Novozhilov’s thin shell theory is used in the analysis, but the effects upon resonant response of using other shell theories are discussed.

Forced Harmonic Response of a Continuous System Displaying Eigenvalue Veering Phenomena

1993 ◽  
Author(s):  
Jerry H. Ginsberg ◽  
Hoang Pham
Keyword(s):  
Natural Frequencies ◽  
Continuous System ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Steady State Response ◽  
Concentrated Force ◽  
Peak Displacement ◽  
Harmonic Response ◽  
State Response ◽  
Exact Eigenvalue

Abstract Prior studies of self-adjoint linear vibratory systems have extensively explored the phenomenon of veering of eigenvalue loci that depict the dependence of natural frequencies on a system parameter. The present work is an exploration of the effect of such phenomena on the response of a continuum to harmonic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pin support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state response of the beam to a harmonic concentrated force applied to the middle of one span. The analysis is used to identify situations in which the forced response is localized to one span, as well as the degree to which the location and magnitude of the peak displacement displays parameter sensitivity.

A Nonlinear Analysis of the Axial Steady State Response of the Hydrodynamic Thrust Bearing-Rotor System Subjected to a Harmonic Excitation

2005 ◽  
Author(s):  
T. N. Shiau ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Harmonic Excitation ◽  
Rotor System ◽  
Time Dependent ◽  
Steady State Response ◽  
Harmonic Force ◽  
Oil Film ◽  
State Response

The purpose of this study is to investigate the nonlinear axial response of a thrust bearing-rotor system, which is subjected to an axial harmonic force. For the axial vibration of the rotor, the system forces include the external axial harmonic force and the reacting oil film forces, which are obtained by solving a time-dependent Reynolds Equation within the thrust pads of the thrust bearing. The time-dependent Reynolds Equation is solved by a finite difference method, and the system equation of motion is solved by the fourth-order Runge-Kutta method. A linear analysis is attempted in to evaluate its suitability for the situation under consideration. And the bearing stiffness and damping coefficients are investigated with parameters including the dimensionless wedge thickness, the initial oil film thickness and the rotor spin speed. The results show that the average steady state response will decrease as the harmonic axial force intensifies its fluctuating magnitude. The results also indicate that it will induce ultra-super harmonics when the axial harmonic force intensifies its fluctuating magnitude.

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