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Open Mobile Search. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. R SW on 12 Dec Vote 0. Answered: Jose Ordaz on 19 Dec I am experimentally testing a material to retrieve its natural frequencies through modal analysis.

The type of testing is based around impulse response. My sampling frequency was 10kHz. My aim is to obtain an accurate FRF graph. My entire code:. Please tell me if you find any errors that can be the cause of an incorrect FRF.Sign in to comment. Sign in to answer this question. Unable to complete the action because of changes made to the page.

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## Frequency Response Function and FFT for Modal Analysis

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You may receive emails, depending on your notification preferences. How to obtain modal parameters from FRF. Enterprixe on 2 Oct Vote 0. Answered: Ahmed Sboui on 24 Jul Accepted Answer: Nick Choi. Recently i have received the data of the Frequency Response Function in a frequency invertal of a given system.

The system consists of a free-free beam with 21 points of measurement. I would like to know how, from this data, you can obtain in MATLAB all the modal parameters such as natural frequencies, damping coefficents and modes assuming viscous damping. All the examples i have seen, suppose you know how the system is modeled but in this case all i know is the FRF of all the points of measurement.

Accepted Answer. Nick Choi on 5 Oct Cancel Copy to Clipboard. Edited: Nick Choi on 5 Oct You could use the frequency response data to estimate the model for the system.Documentation Help Center. This example shows how to estimate frequency-response functions FRFs and modal parameters from experimental data.

The first section describes a simulated experiment that excites a three-degree-of-freedom 3DOF system with a sequence of hammer impacts and records the resulting displacement. Frequency-response functions, natural frequencies, damping ratios, and mode shape vectors are estimated for three modes of the structure.

The second section estimates mode shape vectors from frequency-response function estimates from a wind turbine blade experiment. The turbine blade measurement configuration and resulting mode shapes are visualized. A series of hammer strikes excite a 3DOF system, and sensors record the resulting displacements. The system is proportionally damped, such that the damping matrix is a linear combination of the mass and stiffness matrices. Import the data for two sets of measurements, including excitation signals, response signals, time signals, and ground truth frequency-response functions.

The first set of response signals, Y1measures the displacement of the first mass, and the second, Y2measures the second mass. Each excitation signal consists of ten concatenated hammer impacts, and each response signal contains the corresponding displacement. The duration for each impact signal is 2. Additive noise is present in the excitation and response signals. Visualize the first excitation and response channel of the first measurement.

Compute and plot the FRF for the first excitation and response channels in terms of dynamic flexibility, which is a measure of displacement over force [1]. By default, the FRF is computed by averaging spectra of windowed segments.

Since each hammer excitation decays substantially before the next excitation, a rectangular window can be used. Specify the sensor as displacement. The FRF, estimated using the default 'H1' estimator, contains three prominent peaks in the measured frequency band, corresponding to three flexible modes of vibration. The coherence is close to one near these peaks, and low in anti-resonance regions, where the signal-to-noise ratio of the response measurement is low.

Coherence near to one indicates a high quality estimate. The 'H1' estimate is optimal where noise exists only at the output measurement, whereas the 'H2' estimator is optimal when there is additive noise only on the input [2].

When there is significant measurement noise or the excitation is poor, parametric methods can offer additional options for accurately extracting the FRF from the data.

The 'subspace' method first fits a state-space model to the data [3] and then computes its frequency-response function.

The order of the state-space model equal to the number of poles and presence or lack of feedthrough can be specified to configure the state-space estimation. Here FRF3 is estimated by fitting a state-space model containing a feedthrough term and of the optimal order in the range The estimators perform comparably near response peaks, while the 'H2' estimator overestimates the response at the antiresonances.

The coherence is not affected by the choice of the estimator. Next, estimate the natural frequency of each mode using the peak-picking algorithm. The peak-picking algorithm is a simple and fast procedure for identifying peaks in the FRF. It is a local method, since each estimate is generated from a single frequency-response function. It is also a single-degree-of-freedom SDOF method, since the peak for each mode is considered independently.System Identification Toolbox.

Las tramas se limitan a las primeras cuatro excitaciones y cuatro respuestas. Especifique que las medidas de salida son desplazamientos. Utilice la funcionalidad de trazado de para visualizar las respuestas.

Generar muestras de tiempo. Las matrices de espacio-estado son. La masa es impulsada por la entrada aleatoria durante los primeros segundos y luego se deja volver al reposo. Especifique que la salida es el desplazamiento de la masa.

**How to find the Resonant frequency of an object (.wav files)**

Genera Especifique que las salidas medidas son desplazamientos. Trazar las estimaciones utilizando la sintaxis de sin argumentos de salida. El sistema se muestrea a Hz durante unos 3,9 segundos. Ventana de cada segmento mediante una ventana rectangular. Especifique un orden de modelo de Tipos de datos: single double. Ventana, especificada como un entero o como un vector de fila o columna. Si es un entero, divide y en segmentos de longitud y ventanas cada segmento con una ventana rectangular de esa longitud.

Si es un vector, se divide y se divide en segmentos de la misma longitud que el vector y windows cada segmento utilizando. Para obtener una lista de las ventanas disponibles, consulte. Si es un escalar, debe ser menor que. Si es un vector, debe ser menor que la longitud de. Tipos de datos: double single.

Especifique pares opcionales separados por comas de argumentos. Name,Value Name Value Name Puede especificar varios argumentos de par de nombre y valor en cualquier orden como. Estimador, especificado como el par separado por comas que consta de y,o. Se utiliza para minimizar la discrepancia entre los datos de respuesta modelados y los estimados minimizando el seguimiento de la matriz de errores.

Se utiliza para calcular las funciones de respuesta de frecuencia mediante un modelo de espacio de estado. Orden del modelo de espacio de estado, especificado como el par separado por comas que consta de un vector entero o de fila de enteros.Documentation Help Center. Identify state-space models of systems. Use the models to compute frequency-response functions and modal parameters. Specify the sample time as the inverse of the sample rate.

Store the data as iddata objects. Use the ssest function to estimate a 7th-order state-space model of the system that minimizes the simulation error between the measured outputs and the model outputs. Specify that the state-space model has feedthrough.

To find the model order that gives the best tradeoff between accuracy and complexity, set Orders to in the previous code. The function also recommends a model order of 7. Validate the model quality on the validation dataset. The model describes accurately the output signals of the validation data.

Estimate the frequency-response functions of the model. Display the functions using modalfrf without output arguments. Assume that the system is well described using three modes.

Compute the natural frequencies, damping ratios, and mode-shape vectors of the three modes. Compute and display the reconstructed frequency-response functions. Express the magnitudes in decibels. Load a file containing a high modal density frequency-response measurement.

The data corresponds to an unstable process maintained at equilibrium using feedback control. Store the data as an idfrd object for identification. Plot the Bode diagram. Extract the natural frequencies and damping ratios of the first 10 least-damped oscillatory modes.

Store the results in a table.

### How to obtain modal parameters from FRF

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Toggle Main Navigation. Buscar Answers Clear Filters. Answers Support MathWorks. Search Support Clear Filters. Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Software de prueba. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. R SW on 12 Dec Vote 0. Answered: Jose Ordaz on 19 Dec I am experimentally testing a material to retrieve its natural frequencies through modal analysis.

The type of testing is based around impulse response. My sampling frequency was 10kHz. My aim is to obtain an accurate FRF graph. My entire code:. Please tell me if you find any errors that can be the cause of an incorrect FRF. My suspect is the impulse FFT. Answers 3. Cancel Copy to Clipboard. Edited: durukan dilek on 1 Nov Deniz Kny on 6 Mar I have a accelerometer data and, trying to obtain fft like you.

You can actually check your resonance frequency or natural frequency. The sampling frequency must be twice of your natural frequency Nyquiste Theorem.Documentation Help Center. If x or y is a matrix, each column represents a signal. The frequency-response function matrix, frfis computed in terms of dynamic flexibility, and the system response, ycontains acceleration measurements.

Options include the estimator, the measurement configuration, and the type of sensor measuring the system response. Use estimation commands like ssestn4sidor tfest to create sys from time-domain input and output signals. This syntax allows use only of the 'Sensor' name-value pair argument. You must have a System Identification Toolbox license to use this syntax. The plots are limited to the first four excitations and four responses.

Xhammer — An input excitation signal consisting of five hammer blows delivered periodically. Yhammer — The response of a system to the input. Yhammer is measured as a displacement.

Compute and display the frequency-response function. Window the signals using a rectangular window.

Specify that the window covers the period between hammer blows. Load a data file that contains Xrandthe input excitation signal, and Yrandthe system response.

Specify that the output measurements are displacements. Use the plotting functionality of modalfrf to visualize the responses. Generate time samples. The state-space matrices are. The mass is driven by random input for the first seconds and then left to return to rest. Use the state-space model to compute the time evolution of the system starting from an all-zero initial state.

Plot the displacement of the mass as a function of time. Estimate the modal frequency-response function of the system. Use a Hann window half as long as the measured signals. Specify that the output is the displacement of the mass. The frequency-response function of a discrete-time system can be expressed as the Z-transform of the time-domain transfer function of the system, evaluated at the unit circle.

Compare the modalfrf estimate with the definition.

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