Horizontal Ground Random Excitation of Structures Carrying a Rigid Container Partially Filled With Liquid

2006 ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim
Keyword(s):  
Natural Frequency ◽  
Vibration Suppression ◽  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Random Excitation ◽  
Center Frequency ◽  
System Response ◽  
Structure Response ◽  
Mean Square Response ◽  
The Mean

Nonlinear random interaction of an elastic structure carrying a container, partially filled with liquid, under horizontal narrowband random excitation is investigated. The modal equations of motion are derived by using Galerkin’s method, taking into account the nonlinearity of the hydrodynamic force when the natural frequency of the structure is close to the natural frequency of liquid sloshing. The system response statistics are numerically estimated using Monte Carlo simulation. The influences of the excitation center frequency, its bandwidth and liquid level on the system response are studied. As a result, it is found that the mean square response of the structure decreases as the center frequency approaches to the natural frequency of the structure, and that the sloshing in the container has an effect on the vibration suppression of the structure response.

Dynamic Modeling of a Piggybacked Cantilever Beam System

2014 ◽  
Author(s):  
Troy Lundstrom ◽  
Nader Jalili
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Continuous System ◽  
Element Model ◽  
System Response ◽  
Structure Response ◽  
Beam System ◽  
Geometric Boundary ◽  
Primary Base ◽  
Base Structure

Typically, active resonators for vibration suppression of flexible systems are uniaxial and can only affect structure response in the direction of the applied force. The application of piezoelectric bender actuators as active resonators may prove to be advantageous over typical, uniaxial actuators as they can dynamically apply both torque and translational force to the base structure attachment point; this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). In this paper, Hamilton’s Principle is used to develop the equations of motion for a continuous two-beam system composed of a cantilevered, primary base beam with a secondary piezoelectric bender mounted to its surface. A disturbance force is applied near the fixture location of the base beam and the system response is estimated using a sufficient quantity of assumed eigenfunctions that satisfy the geometric boundary conditions. A theoretical study is performed to compared the continuous system eigenfunctions to a finite element model (FEM) of the two-beam structure and the required number of eigenfunctions required to yield a convergent solution for an impulse excitation is explored. In addition, the frequency response function for the dynamic system is presented and compared to that of a FEM.

Passive Vibration Control of Structures Subjected to Random Ground Excitation Utilizing Sloshing in Rectangular Tanks

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim
Keyword(s):  
Vibration Control ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Correlation Coefficients ◽  
Liquid Sloshing ◽  
Center Frequency ◽  
System Response ◽  
Mean Square ◽  
Passive Vibration Control ◽  
Tuned Liquid Dampers

Passive vibration control of an elastic structure carrying a rectangular tank, partially filled with liquid, is investigated when the structure is subjected to horizontal, narrowband, random ground excitation. The modal equations of motion for liquid sloshing are derived using Galerkin's method, considering the nonlinearity of sloshing. The system response statistics including mean square values, correlation coefficients, and probability density functions (PDFs) are numerically estimated from the time histories using the Monte Carlo simulation when the natural frequency of the structure is close to that of liquid sloshing. The influences of the excitation center frequency, its bandwidth, and the liquid level on the system responses are examined. As a result, it is found that the mean square responses of the structure decrease when the center frequency is close to the natural frequency of the structure due to sloshing. Tuned liquid dampers (TLDs) are found to be most effective for comparatively low liquid levels.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Nonlinear Dynamic Analysis of Atomic Force Microscopy

2006 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Mehdi Behzad ◽  
Ali Meghdari
Keyword(s):  
Atomic Force Microscopy ◽  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Behavior ◽  
Random Excitation ◽  
System Response ◽  
Force Microscopy ◽  
Atomic Force ◽  
Exciting Frequency

This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as Averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.

Mean-Square Response of Thermoviscoelastic Medium to Nonstationary Random Excitation

1976 ◽  
Vol 43 (1) ◽  
pp. 150-158 ◽  
Author(s):  
W. Mosberg ◽  
M. Yildiz
Keyword(s):  
Random Excitation ◽  
Irreversible Thermodynamics ◽  
Envelope Function ◽  
Statistical Characteristics ◽  
Mean Square ◽  
Statistical Property ◽  
Step Functions ◽  
Mean Square Response ◽  
The Mean ◽  
Thermoviscoelastic Medium

The mean-square wave response of a lightly damped thermoviscoelastic medium to a special type of nonstationary random excitation is determined. The excitation function on the thermoviscoelastic medium is taken in the form of a product of a well-defined, slowly varying envelope function, and a part which prescribes the statistical characteristics of the excitation. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. By taking into consideration the slow variation envelope function and the wave characteristics of the lightly damped thermoviscoelastic medium, the mean-square response (as a function of temperature, excitation, and damping parameters with the aid of reversible and irreversible thermodynamics) is evaluated.

Random Response Relationships to Transfer Function and State-Space Properties

2007 ◽  
Vol 129 (5) ◽  
pp. 672-677
Author(s):  
Robin C. Redfield
Keyword(s):  
Transfer Function ◽  
State Space ◽  
Dynamic Systems ◽  
System Response ◽  
Mean Square ◽  
System Matrix ◽  
Matrix Transfer Function ◽  
Mean Square Response ◽  
The Mean ◽  
Insight Into

Output variables of dynamic systems subject to random inputs are often quantified by mean-square calculations. Computationally for linear systems, these typically involve integration of the output spectral density over frequency. Numerically, this is a straightforward task and, analytically, methods exist to find mean-square values as functions of transfer function (frequency response) coefficients. These formulations offer analytical relationships between system parameters and mean-square response. This paper develops further analytical relationships in calculating mean-square values as functions of transfer function and state-space properties. Specifically, mean-square response is formulated from (i) system pole-zero locations, (ii) as a spectral decomposition, and (iii) in terms of a system matrix transfer function. Direct, closed-form relationships between response and these properties are afforded. These new analytical representations of the mean-square calculation can provide significant insight into dynamic system response and optimal design/tuning of dynamic systems.

Mean-Square Response of Simple Mechanical Systems to Nonstationary Random Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 221-227 ◽  
Author(s):  
R. L. Barnoski ◽  
J. R. Maurer
Keyword(s):  
White Noise ◽  
Random Noise ◽  
Random Excitation ◽  
Correlated Noise ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Step Functions ◽  
Unit Step ◽  
Mean Square Response ◽  
The Mean

This paper concerns the mean-square response of a single-degree-of-freedom system to amplitude modulated random noise. The formulation is developed in terms of the frequency-response function of the system and generalized spectra of the nonstationary random excitation. Both the unit step and rectangular step functions are used for the amplitude modulation, and both white noise and noise with an exponentially decaying harmonic correlation function are considered. The time-varying mean-square response is shown not to exceed its stationary value for white noise. For correlated noise, however, it is shown that the system mean-square response may exceed its stationary value.

Vibration Suppression of a Linear Oscillator Force-Excited by Random Excitation via an Inerter Pendulum Vibration Absorber

2021 ◽  
Author(s):  
Joel A. Cosner ◽  
Wei-Che Tai
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Qualitative Change ◽  
Random Excitation ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Energy Transfer ◽  
Mass Damper ◽  
The Time Domain ◽  
Insight Into

Abstract In this theoretical study, the vibration suppression and nonlinear energy transfer, as a function of a dimensionless pendulum length parameter, is investigated for an Inerter Pendulum Vibration Absorber (IPVA) attached to a linear single-degree-of-freedom spring-mass-damper system, subject to white noise excitation. Stochastic differential equations of motion are first developed and integrated to determine the evolution of the response and associated mean and mean square values for long integration times. Dynamic statistical moment equations are then developed, while arc-length continuation is used to track stationary the moments as a function of the pendulum length. Two noise intensity and damping configurations are analyzed and a critical parameter value, in both cases, is found to produce a qualitative change in the system dynamics accompanied by optimal vibration suppression. The results are compared to the response of a linear system without an IPVA to quantify the vibration suppression. Realizations in the time domain are finally calculated to provide validation for the results and gain insight into the changing dynamics of the system as a function of the pendulum length, leading to the discovery of intermittent rotation for sufficiently large pendulum length.

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