Probabilistic Representation and Transmission of Nonstationary Processes in Multi-Degree-of-Freedom Systems

1998 ◽  
Vol 65 (2) ◽  
pp. 398-409 ◽  
Author(s):  
S. F. Masri ◽  
A. W. Smyth ◽  
M.-I. Traina
Keyword(s):  
Random Process ◽  
Structural Control ◽  
Extreme Values ◽  
Free Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Statistical Characteristics ◽  
Earthquake Ground Motion ◽  
Process Data

A relatively simple and straightforward procedure is presented for representing non-stationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom analytical random vibration studies. The method involves two main stages of compaction. The first stage is based on the spectral decomposition of the covariance matrix by the orthogonal Karhunen-Loeve expansion. The dominant eigenvectors are subsequently least-squares fitted with orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used to derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approach is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom system resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the rms response of representative multi-degree-of-freedom systems under the action of the subject earthquake are also presented. It is shown that the proposed random data-processing method is not only a useful data-archiving and earthquake feature-extraction tool, but also provides a probabilistic measure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a representation could be a valuable tool in risk management studies to quantify the average seismic risk over a spatially extended area.

INTERACTION OF TWO SEMI-CYLINDRICAL CANYONS EXCITED BY SH WAVES

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Abdul Hayir ◽  
Sinan Emre Cankaya
Keyword(s):  
Transfer Function ◽  
Infinite Series ◽  
Order Term ◽  
Closed Form Solution ◽  
Form Solution ◽  
Propagation Path ◽  
Earthquake Ground Motion ◽  
Dimensionless Frequency ◽  
Sh Waves ◽  
Incident Waves

The spectral analysis of strong earthquake ground motion needs detailed understanding of transfer function properties and source radiation along the wave propagation path. The main goal of this study is to evaluate the interaction of two semi-cylindrical canyons, which are subjected to the horizontally polarized shear-wave (SH-wave) and to find the transfer function properties of two canyons. In this study, the interaction of two semi-cylindrical canyons subjected to SH waves are considered and evaluated for a general angle of wave incidence. The method of Wave Function Expansion is derived, and the infinite series solution is obtained. Due to the complexity and convergence of infinite series including Bessel functions, the numerical results are limited. The convergence of the solution for the high frequencies requires the high order term. Moreover, the difficulties of this study come from convergence of the solution owing to interaction of two canyons having various dimensions and material properties. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves when the wavelengths of incident motion are short compared to the radius of a canyon. The parameters, dimensions of the canyons, distance between two canyons, and the amplifications of the displacement amplitudes are obtained with respect to the incident angles of the waves and dimensionless frequency.

Response of a bridge to a moving vehicle load

2006 ◽  
Vol 33 (1) ◽  
pp. 49-57 ◽  
Author(s):  
J H Lin
Keyword(s):  
Standard Deviation ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Statistical Characteristics ◽  
Roughness Coefficient ◽  
Vehicle Speed ◽  
Moving Vehicle ◽  
Bridge Span ◽  
Pavement Roughness

The determination of the statistical characteristics of bridge deflections due to a load of a vehicle moving across the span of a bridge is frequently a problem of great interest for bridge engineers. Developed herein is a spectral approach for evaluating the variation of bridge deflections due to a vehicle moving at constant speed along a rough bridge surface. Based on the above-mentioned approach, this study presents a closed-form solution for variances of bridge deflections. An example of application of the solution to the estimation of variances of bridge deflections is also presented. The effects of pavement type, vehicle speed, and bridge span on standard deviation of bridge deflections are investigated. The results of numerical examples show that if the effect of engine motions on vehicle vibrations is disregarded, the standard deviation of bridge deflections is proportional to the square root of the pavement roughness coefficient a for a specified vehicle speed.Key words: moving load, bridge deflection, pavement roughness.

On Occurrence of Reverse Full Annular Rub

2011 ◽  
Author(s):  
John J. Yu
Keyword(s):  
Contact Force ◽  
Dry Friction ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Free Region ◽  
Analytical Formulas

This paper discusses reverse full annular rub based on a two degree-of-freedom rotor/seal model where a rubbing location can be simulated away from the lumped rotor mass. The analytical model is much closer to the experimental setup for comparison of results, and real machines for analysis, than the previous one degree-of-freedom model. Its closed-form solution is given including reverse rub amplitudes and relative phases as well as the normal contact force. The exact frequency equation in polynomial form yields reverse full annular rub frequencies without having to neglect any parameters. Many conclusions can be drawn directly from explicit expressions without numerical calculations. The solution with non-positive normal contact force indicates a dry-friction whirl/whip-free region, usually accompanied by low friction and/or high damping. The analytical study covers both dry-friction whirl and dry-friction whip, and their relations with dry friction factor, damping, and rotor speed. Range of reverse rub frequencies, their relation with rotor and rotor/seal coupled natural frequencies, and direction of frictional force, are also revealed. Destructive dry-friction whip experimental results are given which have fully confirmed the analytical formulas.

On Occurrence of Reverse Full Annular Rub

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
John J. Yu
Keyword(s):  
Contact Force ◽  
Dry Friction ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Free Region ◽  
Analytical Formulas

This paper discusses reverse full annular rub based on a two degree-of-freedom rotor/seal model where a rubbing location can be simulated away from the lumped rotor mass. The analytical model is much closer to the experimental setup for comparison of results, and real machines for analysis, than the previous one degree-of-freedom model. Its closed-form solution is given including reverse rub amplitudes and relative phases, as well as the normal contact force. The exact frequency equation in polynomial form yields reverse full annular rub frequencies without having to neglect any parameters. Many conclusions can be drawn directly from explicit expressions without numerical calculations. The solution with nonpositive normal contact force indicates a dry-friction whirl/whip-free region, usually accompanied by low friction and/or high damping. The analytical study covers both dry-friction whirl and dry-friction whip, and their relations with dry-friction factor, damping, and rotor speed. Range of reverse rub frequencies, their relation with rotor and rotor/seal coupled natural frequencies, and direction of frictional force, are also revealed. Destructive dry-friction whip experimental results are given, which have fully confirmed the analytical formulas.

Predictions of Delamination Growth for Quasi-Static Loading of Composite Laminates

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Jiawen Xie ◽  
Anthony M. Waas
Keyword(s):  
Composite Laminates ◽  
Extreme Values ◽  
Plate Theory ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Form Solution ◽  
Multilayered Structures ◽  
Normal Contact ◽  
Fracture Models ◽  
2D Elasticity

This paper presents an exact, two-dimensional (2D) quasi-static elastic analysis of predelaminated composite panels subject to arbitrary transverse pressure loads. The piecewise linear spring model and the shear bridging model are, respectively, used to simulate the normal contact and shear frictional behavior between the interfaces of the existing delamination. This general contact model can be further reduced to the “friction-free model” and the “constrained model” by assigning extreme values to the spring stiffnesses. The analysis yields a closed-form solution for the 2D displacement and stress fields. To predict the delamination propagation, different propagation criteria as suggested in the literature are used. Calculated load–displacement responses and delamination threshold loads are in good agreement with existing experimental data. The results are further compared against simple fracture models and a model that uses a modified classical laminated plate theory for the predelaminated composite with fracture criteria, showing an overestimation of the delamination threshold loads. The 2D elasticity theory that is formulated can be used with confidence to study other multilayered structures with multiple delaminations and subject to arbitrary loading profiles.

A PLATE MODEL FOR THE EVALUATION OF PULL-IN INSTABILITY OCCURRENCE IN ELECTROSTATIC MICROPUMP DIAPHRAGMS

2011 ◽  
Vol 03 (01) ◽  
pp. 1-19 ◽  
Author(s):  
EMANUELE BERTARELLI ◽  
RAFFAELE ARDITO ◽  
RAFFAELE ARDITO ◽  
ALBERTO CORIGLIANO ◽  
ROBERTO CONTRO
Keyword(s):  
Nonlinear Dynamics ◽  
Loading Condition ◽  
Mechanical Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Plate Model ◽  
The One ◽  
Quality Factor Q ◽  
First Time

This work deals with the mechanical response of circular microplates undergoing electrostatic actuation. A one degree-of-freedom model and Finite Element approaches are exploited in a nondimensional framework. First, a quasi-static conventional approach is adopted. From the one degree-of-freedom model a closed form solution for the plate electromechanical problem is obtained for the first time. Then a strong attention is paid to pull-in phenomena in nonlinear dynamics. Dynamic behavior of the structure is explored, leading to the identification of a pull-in loading condition which is dependent on the quality factor Q. The outcomes are discussed and widely compared with those available in the literature for similar microsystems.

Parametric Identification of a Vibratory System With a Clearance

1993 ◽  
Vol 115 (1) ◽  
pp. 25-32 ◽  
Author(s):  
R. M. Alexander ◽  
S. T. Noah ◽  
C. G. Franck
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Closed Form ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Vibratory System ◽  
Experimental Structure

An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single-degree-of-freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multi-degree-of-freedom systems.

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