dynamics_frequency_response Module

The model parameter array. The elements of the array are stored as $$\left[ A_{1}, \omega_{n1}, \zeta_{1}, A_{2}, \omega_{n2}, \zeta_{2} ... \right]$$ .

The frequency value, in rad/s, at which to evaluate the model.

The model parameter array. The elements of the array are stored as $$\left[ A_{1}, \omega_{n1}, \zeta_{1}, A_{2}, \omega_{n2}, \zeta_{2} ... \right]$$ .

The frequency value, in rad/s, at which to evaluate the model.

The model parameter array. The elements of the array are stored as $$\left[ A_{1}, \omega_{n1}, \zeta_{1}, A_{2}, \omega_{n2}, \zeta_{2} ... \right]$$ .

The frequency value, in rad/s, at which to evaluate the model.

The model parameter array. The elements of the array are stored as $$\left[ A_{1}, \omega_{n1}, \zeta_{1}, A_{2}, \omega_{n2}, \zeta_{2} ... \right]$$ .

The frequency value, in rad/s, at which to evaluate the model.

The N-by-N mass matrix for the system. This matrix must be symmetric.

The N-by-N stiffness matrix for the system. This matrix must be symmetric.

The mass damping factor, $\alpha$.

The stiffness damping factor, $\beta$.

An M-element array of frequency values at which to evaluate the frequency response functions, in units of rad/s.

A pointer to a routine used to compute the modal forcing function.

An optional N-element allocatable array that, if supplied, will be used to retrieve the modal frequencies, in units of rad/s.

An optional N-by-N allocatable matrix that, if supplied, will be used to retrieve the N mode shapes with each vector occupying its own column.

An optional argument that can be used to communicate with the outside world.

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.
• DYN_MATRIX_SIZE_ERROR: Occurs if the mass or stiffness matrices are not square, or if the mass and stiffness matrices are different sized.
• DYN_NULL_POINTER_ERROR: Occurs if the forcing function pointer is undefined.

The N-by-N mass matrix for the system. This matrix must be symmetric.

The N-by-N stiffness matrix for the system. This matrix must be symmetric.

The mass damping factor, $\alpha$.

The stiffness damping factor, $\beta$.

The number of frequency values to analyze. This value must be at least 2.

The starting frequency, in units of rad/s.

The ending frequency, in units of rad/s.

A pointer to a routine used to compute the modal forcing function.

An optional N-element allocatable array that, if supplied, will be used to retrieve the modal frequencies, in units of rad/s.

An optional N-by-N allocatable matrix that, if supplied, will be used to retrieve the N mode shapes with each vector occupying its own column.

An optional argument that can be used to communicate with the outside world.

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.
• DYN_MATRIX_SIZE_ERROR: Occurs if the mass or stiffness matrices are not square, or if the mass and stiffness matrices are different sized.
• DYN_NULL_POINTER_ERROR: Occurs if the forcing function pointer is undefined.

An N-element array containing the excitation signal.

An N-element array containing the response signal.

The sampling frequency, in Hz.

The window to apply to the data. If nothing is supplied, no window is applied.

Enter 1 to utilize an H1 estimator; else, enter 2 to utilize an H2 estimator. The default is an H1 estimator.

An H1 estimator is defined as the cross-spectrum of the input and response signals divided by the energy spectral density of the input. An H2 estimator is defined as the energy spectral density of the response divided by the cross-spectrum of the input and response signals.

$$H_{1} = \frac{P_{xy}}{P_{xx}}$$

$$H_{2} = \frac{P_{yy}}{P_{xy}}$$

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.

• DYN_ARRAY_SIZE_ERROR: Occurs if x and y are not the same size.

An N-by-P array containing the P inputs to the system.

An N-by-M array containing the M outputs from the system.

The sampling frequency, in Hz.

The window to apply to the data. If nothing is supplied, no window is applied.

Enter 1 to utilize an H1 estimator; else, enter 2 to utilize an H2 estimator. The default is an H1 estimator.

An H1 estimator is defined as the cross-spectrum of the input and response signals divided by the energy spectral density of the input. An H2 estimator is defined as the energy spectral density of the response divided by the cross-spectrum of the input and response signals.

$$H_{1} = \frac{P_{xy}}{P_{xx}}$$

$$H_{2} = \frac{P_{yy}}{P_{xy}}$$

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.

• DYN_ARRAY_SIZE_ERROR: Occurs if x and y do not have the same number of rows.

A pointer to the routine containing the ODE's to integrate.

An M-element array containing the frequency points at which the solution should be computed. Notice, whatever units are utilized for this array are also the units of the excitation_frequency property in @p sys. It is recommended that the units be set to Hz. Additionally, this array cannot contain any zero-valued elements as the ODE solution time for each frequency is determined by the period of oscillation and number of cycles.

An N-element array containing the initial conditions for each of the N ODEs.

An optional differential equation solver. The default solver is the Dormand-Prince Runge-Kutta integrator from the DIFFEQ library.

An optional parameter controlling the number of cycles to analyze when determining the amplitude and phase of the response. The default is 20.

An optional parameter controlling how many of the initial "transient" cycles to ignore. The default is 200.

An optional parameter controlling how many evenly spaced solution points should be considered per cycle. The default is 1000. Notice, there must be at least 2 points per cycle for the analysis to be effective. The algorithm utilizes a discrete Fourier transform to determine the phase and amplitude, and in order to satisfy Nyquist conditions, the value must be at least 2.

An optional argument allowing for passing of data in/out of the fcn subroutine.

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.
• DYN_NULL_POINTER_ERROR: Occurs if a null pointer is supplied.
• DYN_INVALID_INPUT_ERROR: Occurs if an invalid parameter is given.
• DYN_ZERO_VALUED_FREQUENCY_ERROR: Occurs if a zero-valued frequency was supplied.

A pointer to the routine containing the ODE's to integrate.

The number of frequency values to analyze. This value must be at least 2.

The starting frequency. It is recommended that the units be set to Hz.

The ending frequency. It is recommended that the units be set to Hz.

An N-element array containing the initial conditions for each of the N ODEs.

An optional differential equation solver. The default solver is the Dormand-Prince Runge-Kutta integrator from the DIFFEQ library.

An optional parameter controlling the number of cycles to analyze when determining the amplitude and phase of the response. The default is 20.

An optional parameter controlling how many of the initial "transient" cycles to ignore. The default is 200.

An optional parameter controlling how many evenly spaced solution points should be considered per cycle. The default is 1000. Notice, there must be at least 2 points per cycle for the analysis to be effective. The algorithm utilizes a discrete Fourier transform to determine the phase and amplitude, and in order to satisfy Nyquist conditions, the value must be at least 2.

An optional argument allowing for passing of data in/out of the fcn subroutine.

An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

• DYN_MEMORY_ERROR: Occurs if there are issues allocating memory.
• DYN_NULL_POINTER_ERROR: Occurs if a null pointer is supplied.
• DYN_INVALID_INPUT_ERROR: Occurs if an invalid parameter is given.
• DYN_ZERO_VALUED_FREQUENCY_ERROR: Occurs if a zero-valued frequency was supplied.

The excitation frequency.

The current time step value.

The value of the solution estimate at time t.

The derivatives as computed by this routine.

An optional argument allowing the passing of data in/out of this routine.

The excitation frequency. When used as a part of a frequency response calculation, this value will have the same units as the frequency values provided to the frequency response routine.

An N-element array where the forcing function should be written.

An optional argument that can be used to communicate with the outside world.

The value of the independent variable at which to evaluate the excitation function.