A Computationally Low-cost Method for Capturing Airframe Flexibility Effects in Landing Dynamic Simulations

2021 ◽  
Author(s):  
Terrin Stachiw ◽  
Fidel Khouli ◽  
Robert G. Langlois ◽  
Fred F. Afagh ◽  
Joseph Ricciardi
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Transfer Functions ◽  
Initial Conditions ◽  
Low Cost ◽  
Time History ◽  
Element Model ◽  
Landing Gear ◽  
Dynamic Simulations ◽  
Positive Time

Abstract Airframe flexibility effects have typically been captured by modal reduction of the airframe. Although efficient, this model may still be prohibitively expensive for preliminary design studies. This paper employs time- and frequency-domain system identification techniques to form a multi-objective optimization problem to identify equivalent transfer functions representing airframe flexibility effects. Pareto-optimal sets are first identified for an equivalent transfer function of a force element between the landing gear attachment point and the centre of gravity of a 150-passenger regional jet, and a second transfer function from the input landing gear force to the cockpit acceleration. The reduced models demonstrate the ability to generally capture flexibility effects with reduced computation times. The combination of time-domain and frequency-domain information ensures the positive time-history matches while the model remains physically realizable as it is rooted to frequency response obtained from the finite element model. It is hypothesized that this physical link allowed the model to be robust to the landing initial conditions.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

Integrated and frequency-band magnitude, two alternative measures of the size of an earthquake

1970 ◽  
Vol 60 (3) ◽  
pp. 917-937 ◽  
Author(s):  
B. F. Howell ◽  
G. M. Lundquist ◽  
S. K. Yiu
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Frequency Band ◽  
Transfer Functions ◽  
Body Wave ◽  
Average Amplitude ◽  
Equivalent Quantity ◽  
Short Period ◽  
Alternative Measures ◽  
Body Wave Magnitude

Abstract Integrated magnitude substitutes the r.m.s. average amplitude over a pre-selected interval for the peak amplitude in the conventional body-wave magnitude formula. Frequency-band magnitude uses an equivalent quantity in the frequency domain. Integrated magnitude exhibits less scatter than conventional body-wave magnitude for short-period seismograms. Frequency-band magnitude exhibits less scatter than body-wave magnitude or integrated magnitude for both long- and short-period seismograms. The scatter of frequency-band magnitude is probably due to real azimuthal effects, crustal-transfer-function variations, errors in compensation for seismograph response, microseismic moise and uncertainties in the compensation for attenuation with distance. To observe azimuthal variations clearly, the crustal-transfer functions and seismograph response need to be known more precisely than was the case in this experiment, because these two sources of scatter can be large enough to explain all of the observed variations.

scholarly journals Characterization of Raman Spectroscopy System Transfer Functions in Intensity, Wavelength, and Time

Instruments ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 22
Author(s):  
Yu-Chung Lin ◽  
Joseph V. Sinfield
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Low Cost ◽  
Instrument Design ◽  
Spectroscopic Techniques ◽  
Measurement Science ◽  
Broad Array ◽  
Spectroscopy System ◽  
System Transfer Function

The emergence of a wide variety of relatively low-cost compact spectrometers has led to an increase in the use of spectroscopic techniques by researchers in a broad array of fields beyond those that have traditionally employed these analytical methods. While the fundamental elements and functions of Raman systems are generally consistent, the specific components that compose a system may vary in number, design, and configuration, and researchers often modify off-the-shelf spectrometers for unique applications. Understanding the effect of instrument design and components on acquired information is thus crucial and provides the prospect to optimize the system to individual needs and to properly compare results obtained with different systems while also reducing the potential for unintended misinterpretation of data. This paper provides a practical treatment of the influences in a typical compact spectroscopy system that can impact the extent to which the output of the system is representative of the observed environment, a relationship that in measurement science is classically termed the system transfer function. For clarity, the transfer function is developed in terms of traditional Raman output parameters, namely intensity, wavelength, and time.

Simplified Methodology for Analysis of Reflected Detonation and DDT: Part 1 — Elastic Analysis

2014 ◽  
Author(s):  
Thomas C. Ligon ◽  
David J. Gross ◽  
Stephen D. Ahnert ◽  
John C. Minichiello
Keyword(s):  
Initial Conditions ◽  
Time History ◽  
Initial Pressure ◽  
Propagation Distance ◽  
Element Model ◽  
Simplified Approach ◽  
Pressure Time ◽  
Unburned Fuel ◽  
Reflecting Surface ◽  
Peak Pressures

This paper introduces a simplified approach for analyzing local elastic hoop response of piping to reflected gaseous detonations and deflagration-to-detonation transitions (DDT). A consequence associated with gaseous explosions is the potential for DDT to occur near the end of a closed pipe or gas pocket. As an accelerating deflagration flame approaches a closed end, the unburned fuel ahead of the flame front is compressed to an elevated initial pressure. This process is often referred to as pressure piling or pre-compression, and the combination of detonation reflection with the elevated initial pressure, can produce extremely high peak pressures and large values of impulse. In this paper, the event where DDT occurs immediately ahead of the reflecting surface is referred to as a reflected-DDT (R-DDT). In addition to gas mixture and initial conditions, the peak pressure and shape of the pressure time-history associated with a reflected detonation or DDT is a function of the detonation propagation distance prior to reflection and the relative distance between the ignition location, the DDT location, and the reflecting surface. An empirical pressure time-history has been developed using pressure data from approximately 190 explosion tests using hydrogen and nitrous oxide mixtures in 2-inch and 4-inch pipe to describe events ranging from fully-developed reflected detonations to R-DDTs. The empirical model of the pressure time-history was validated by comparing measured elastic hoop strains to finite-element model predictions using the pressure time-history model. Part 2 of this paper compares the methodology to plastic response data.

An Investigation of the Aeroelastic Response of a Two-Dimensional, Structurally Nonlinear Airfoil Subject to External Excitation

2002 ◽  
Author(s):  
Catharine C. Marsden ◽  
Stuart J. Price
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Nonlinear Response ◽  
Transfer Functions ◽  
Time History ◽  
System Response ◽  
Two Dimensional ◽  
Aeroelastic System ◽  
Aeroelastic Response ◽  
Band Limited

The results of an analytical investigation are presented for the aeroelastic response of a two-dimensional, structurally nonlinear airfoil subject to a forced excitation. The system is modeled as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap motion is used to provide the forcing input to the system. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion for the aeroelastic system are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. The time-histories are analysed using Fourier transform-based techniques to obtain frequency-domain response and transfer functions. Results show that the nonlinear response of the aeroelastic system contains frequencies other than the forcing frequency. When modal frequencies and damping values are calculated using standard Fourier-based techniques, it is shown that the super- and sub-harmonic frequency content in the nonlinear response can contribute to errors when results are compared to those obtained for the equivalent linear system. This paper describes an investigation of a method of analysis that, while based on the Fourier transform, has been modified to recognize and accommodate the nonlinear contribution to the system response. The method, developed by Bendat [1], uses a band-limited random input and separates the linear and nonlinear components of the response within the frequency domain. Results are given for the application of this method to the specific case of the structurally nonlinear aeroelastic system. It is shown that the method may be used to successfully recover the linear frequency response function using the input and output data for the nonlinear system.

A Numerical Evaluation of the Quadratic Transfer Function for a Floating Structure

2019 ◽  
Author(s):  
Zhitian Xie ◽  
Yujie Liu ◽  
Jeffrey Falzarano
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Transfer Functions ◽  
Second Order ◽  
Wave Frequency ◽  
Wave Forces ◽  
Floating Structure ◽  
Transfer Function Matrix ◽  
Wave Induced ◽  
Function Matrix

Abstract The second order force of a floating structure can be expressed in terms of a time independent quadratic transfer functions along with the incident wave elevation, through which it is possible to evaluate the second order wave exciting forces in the frequency domain. Newman’s approximation has been widely applied in approximating the elements of the quadratic transfer function matrix while numerically evaluating the second order wave induced force. Through Newman’s approximation, the off-diagonal elements can be numerically approximated with the diagonal elements and thus the numerical calculation efficiency can be enhanced. Newman’s approximation assumes that the off-diagonal elements do not change significantly with the wave frequency and that hydrodynamic phenomenon regarding the low difference frequency are usually of interest. However, it is obviously less satisfying when an element that is close to the diagonal line in the quadratic transfer function matrix shows an extremum if the corresponding wave frequency is close to the natural frequency of the certain motion. In this paper, the full derivation and expression of the second order wave forces and moments applied to a floating structure have been presented, through which the numerical results of the quadratic transfer function matrix including the diagonal and the off-diagonal elements will be illustrated. This work will present the basis of numerically evaluating the second order forces in the frequency domain. The comparisons among various approximations regarding the second order forces in deep water will also be presented as a meaningful reference.

Rotordynamic Analysis of a Large Industrial Turbo-Compressor Including Finite Element Substructure Modeling

2006 ◽  
Author(s):  
J. Jeffrey Moore ◽  
Giuseppe Vannini ◽  
Massimo Camatti ◽  
Paolo Bianchi
Keyword(s):  
Finite Element ◽  
Transfer Function ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Coupled Model ◽  
Element Model ◽  
7Th Edition ◽  
Curve Fit ◽  
Turbo Compressor ◽  
Fully Coupled

A rotordynamic analysis of a large turbo-compressor that models both the casing and supports along with the rotor-bearing system was performed. A three-dimensional (3-D) finite element model of the casing captures the intricate details of the casing and support structure. Two approaches are presented, including development of transfer functions of the casing and foundation, as well as a fully coupled rotor-casing-foundation model. The effect of bearing support compliance is captured, as well as the influence of casing modes on the rotor response. The first approach generates frequency response functions (FRF’s) from the finite element case model at the bearing support locations. A high-order polynomial in numerator-denominator transfer function format is generated from a curve-fit of the FRF. These transfer functions are then incorporated into the rotordynamics model. The second approach is a fully coupled rotor and casing model that is solved together. An unbalance response calculation is performed in both cases to predict the resulting rotor critical speeds and response of the casing modes. The effect of the compressor case and supports caused the second critical speed to drop to a value close to the operating speed and not compliant with API 617 7th edition requirements. A combination of rotor, journal bearing, casing, and support modifications resulted in a satisfactory and API compliant solution. The results of the fully coupled model validated the transfer function approach.

scholarly journals The research into the propagation law of the shock wave of a gas explosion inside a building

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shu-Chao Lin ◽  
You-Chun Xu ◽  
Pei-Dong Yang ◽  
Shan Gao ◽  
Yi-Jun Zhou ◽  
...  
Keyword(s):  
Shock Wave ◽  
Peak Pressure ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Time History ◽  
Element Model ◽  
Space Distribution ◽  
Gas Explosion ◽  
Propagation Law ◽  
Three Dimensional Finite Element

Based on the dissipation rate conservation equations of turbulent kinetic energy in the k-ε turbulence model, a complicated three-dimensional finite element model of a kitchen filled with gas mixture is developed by using the open source field operation and manipulation (OpenFOAM). Two representative kitchens were used to investigate the propagation law of the shock wave of a gas explosion inside a building by considering the key characteristics of the blast shock wave. The influence of some crucial parameters, such as initial conditions and kitchen parameters, on the properties of the blast shock wave is investigated. The basic steps to predict the peak pressure of the blast shock wave are given in consideration of the initial condition and the kitchen whilst the injury effect of the blast shock wave on the humans and animals is evaluated. The research results indicate that the pressure time history and the peak pressure space distribution are greatly influenced by the kitchen design layout. The coupled interaction between the initial temperature and gas volume concentration, especially at the upper and lower explosion limits of the gas, significantly affects the peak pressure. The peak pressure varies significantly with the opening and the buffer; however, it has little relation with the width, length, and height of the kitchen. The proposed method can accurately and effectively predict the peak pressure of the blast shock wave inside buildings. In terms of the peak pressure space distribution of the explosion shock wave, the peak pressure is much higher than the threshold of the killing pressure, which is unsafe for the humans and animals in the building.

scholarly journals Low-Cost Experimental Methodology for the Dynamic Model Approximation of Multirotor Actuators

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Walter A. Mayorga-Macías ◽  
Luis E. González-Jiménez ◽  
Marco A. Meza-Aguilar ◽  
Luis F. Luque-Vega
Keyword(s):  
Transfer Function ◽  
Embedded System ◽  
Duty Cycle ◽  
Transfer Functions ◽  
Electronic Control Unit ◽  
Low Cost ◽  
Design Procedure ◽  
Open Loop ◽  
Experimental Methodology ◽  
Model Approximation

A methodology for the experimental modelling of the electric actuators of a multirotor is presented in this work. These actuators are usually brushless DC motors which are driven by electronic speed controllers in an open loop. The duty cycle of a PWM signal, generated by the electronic control unit, is the input of the electronic controller. However, during the control design procedure for the multirotor, it is important to account with a model of the actuators as its dynamical features define the closed-loop performance of the overall aircraft. Hence, a procedure, based on low-cost electronic components, to obtain approximated transfer functions of the actuators of a multirotor is presented. Moreover, as the proposed signal processing algorithms are simple, the computational capabilities of the required embedded system are also low. Given that different control schemes require different information from the actuator, two models were obtained: a duty cycle vs. angular velocity transfer function and a duty cycle vs. consumed current transfer function. The effectivity of the proposal is validated with experimental results on common electric actuators of a multirotor.

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