Analytical Method of Response of Piping System With Nonlinear Support

2000 ◽  
Vol 122 (4) ◽  
pp. 437-442
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Analytical Method ◽  
Mode Shapes ◽  
Piping System ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
Damping Characteristics ◽  
Nonlinear Support

This paper deals with steady-state response of the piping system with nonlinear support having hysteresis damping characteristics. Considering the energy loss for contact with a support, an analytical method of approximate solution for the beam, a one-span model of the piping system, with quadrilateral hysteresis loop characteristics is presented. Some numerical results of the approximate solution for the response curves and the mode shapes are shown. [S0094-9930(00)00204-3]

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

scholarly journals Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Atta Oveisi ◽  
Mohammad Gudarzi ◽  
Seyyed Mohammad Hasheminejad
Keyword(s):  
Steady State ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cylindrical Panel ◽  
Mode Shapes ◽  
Steady State Response ◽  
Two Dimensional ◽  
Finite Element Software ◽  
State Response ◽  
Thick Shells

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally.

Forced Response of Continuous System With Hysteresis Loop Characteristics: System With Quadrilateral Hysteresis Loop Characteristics

2005 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Energy Loss ◽  
Hysteresis Loop ◽  
Nonlinear Response ◽  
Continuous System ◽  
Forced Response ◽  
Steady State Response ◽  
State Response ◽  
Discontinuous Line

This paper deals with steady-state response of a continuous system with collision characteristics. Considering the energy loss in a collision, an analytical method of approximate solution for the continuous system with symmetrical hysteresis loop characteristics is presented. The resonance curves of nonlinear response obtained from approximate solution are shown as discontinuous line, and are discussed the phenomenon.

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.

Dynamic Response of a Geared Rotor-Bearing System Under Residual Shaft Bow Effect

2006 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
Y. C. Chen ◽  
T. H. Young
Keyword(s):  
Steady State ◽  
Natural Frequencies ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Transmission Error ◽  
Mode Shapes ◽  
Steady State Response ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

The paper presents the dynamic behaviors of a geared rotor-bearing system under the effects of the residual shaft bow, the gear eccentricity and excitation of gear’s transmission error. The coupling effect of lateral and torsional motions is considered in the dynamic analysis of the geared rotor-bearing system. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The dynamic characteristics including system natural frequencies, mode shapes and steady-state response are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between gear eccentricity and residual shaft bow will significantly affect system natural frequencies and steady-state response. When the spin speed closes to the second critical speed, the system steady state response will be dramatically increased by the residual shaft bow for the in-phase case. Moreover the zero response can be obtained when the system is set on special conditions.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

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.

scholarly journals Sine Sweep and Steady-State Response of a Simplified Solar Array Model With Nonlinear Support

1999 ◽  
Author(s):  
Rob H. B. Fey ◽  
Berend Winter ◽  
Jaap J. Wijker
Keyword(s):  
Steady State ◽  
Dynamic Behaviour ◽  
Solar Array ◽  
Beam Model ◽  
Steady State Response ◽  
Good Correspondence ◽  
State Response ◽  
Softening Behaviour ◽  
Nonlinear Support ◽  
Sine Sweep

Abstract In this paper the dynamic behaviour of a multi degree of freedom beam model of a solar array structure is investigated both experimentally and numerically. The beam is supported by one nonlinear element, a so-called snubber. This snubber can only take compressive forces. Two types of excitation are applied and compared: sine sweep excitation (with different sweep rates and directions) and steady-state excitation. Emphasis lies on the investigation of the dynamic behaviour of the system under prestress, which implies softening behaviour at the time when snubber and beam loose contact. The system displays rich nonlinear dynamic behaviour: multiple solutions (hysteresis loop), superharmonic resonances and subharmonic, quasi-periodic and chaotic solutions. Good correspondence between experimental and numerical results has been found.

scholarly journals Reduction of the Measurement Time by the Prediction of the Steady-State Response for Quartz Crystal Microbalance Gas Sensors

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2475 ◽  
Author(s):  
Diana Osorio-Arrieta ◽  
José Muñoz-Mata ◽  
Georgina Beltrán-Pérez ◽  
Juan Castillo-Mixcóatl ◽  
Claudia Mendoza-Barrera ◽  
...  
Keyword(s):  
Steady State ◽  
Quartz Crystal Microbalance ◽  
Gas Sensors ◽  
Quartz Crystal ◽  
Measurement Time ◽  
Steady State Response ◽  
Response Curves ◽  
Time Constants ◽  
State Response ◽  
Calculated Parameter

This paper presents a new approach to reduce the measurement time by the prediction of the steady-state using the transient response to ethanol for quartz crystal microbalance gas sensors coated with ethyl cellulose. The experimentally measured response curves were successively fitted using a mathematical model based on the sum of two exponentials with different time constants. The parameters of the model were determined, and the time constants and the magnitude of the steady-state response were analyzed. Even though the time constants did not stabilize well, the parameter corresponding to the magnitude of the steady-state response quickly converged and stabilized after 37 s. Moreover, this calculated parameter was highly correlated with the measured values of the steady-state response, which was measured at five times the longest time constant (83 s) of the model. Therefore, the steady-state response could be predicted with a 55% reduction in the measurement (detection) time.

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