The Effect of Rotation on the Steady State Response of a Spring-Mass System under Harmonic Excitation

Gyrodynamics ◽  
1974 ◽  
pp. 44-48
Author(s):  
J. A. Linnett
Keyword(s):  
Steady State ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Mass System ◽  
State Response

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.

scholarly journals Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

2015 ◽  
Author(s):  
W. Xu ◽  
W. D. Zhu ◽  
S. A. Smith
Keyword(s):  
Steady State ◽  
Damage Detection ◽  
Structural Damage ◽  
Longitudinal Vibration ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Noise Robustness ◽  
Steady State Response ◽  
Structural Damage Detection ◽  
State Response

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, a slope vibration shape is transformed to a multiscale slope vibration shape in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that multiscale slope vibration shapes can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

scholarly journals Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
W. Xu ◽  
W. D. Zhu ◽  
S. A. Smith ◽  
M. S. Cao
Keyword(s):  
Steady State ◽  
Damage Detection ◽  
Structural Damage ◽  
Longitudinal Vibration ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Noise Robustness ◽  
Steady State Response ◽  
Structural Damage Detection ◽  
State Response

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape (SVS) for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, an SVS is transformed to a multiscale slope vibration shape (MSVS) in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that MSVSs can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer (SLV) is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

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.

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

2020 ◽  
pp. 095440622095910
Author(s):  
Mohammad Noroozi ◽  
Majid Ghadiri
Keyword(s):  
Steady State ◽  
Bifurcation Point ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Multiple Scale ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Size Dependent ◽  
State Response ◽  
Point Types

In the present paper, nonlinear forced vibrations of an axial moving nanobeam which is vertically influenced by an external harmonic excitation and gravity is analyzed by considering the effects of linear damping. Considering certain assumptions, a nonlinear Euler-Bernoulli beam theory is developed. With the implementation of the nonlocal elasticity theory, the governing integro-partial-differential equation is obtained by using the Hamilton principle. The multiple scale method is employed to obtain a steady-state response for the size-dependent viscoelastic nanobeam with fixed-free boundary conditions. Subsequently, the trivial and non-trivial steady-state response and the bifurcation point types are examined. Finally, the effects of damping coefficient and nonlocal parameter on stability and bifurcation of trivial and non-trivial solutions are studied. It is found that the effect of nonlocal parameter on the steady-state response and the bifurcation point types is quite important.

Sign in / Sign up

Export Citation Format

Share Document