dynamics_frequency_sweep

Uses

- iso_fortran_env
- dynamics_frequency_response
- dynamics_error_handling
- diffeq

Interfaces

frequency_sweep harmonic_ode ode_excite

Functions

chirp

Interfaces

public interface frequency_sweep

private function frf_sweep_1(fcn, freq, iv, solver, ncycles, ntransient, points, inHz, args) result(rst)

Computes the frequency response of each equation of a system of harmonically excited ODE's by sweeping through frequency.

The amplitude and phase are determined by means of a harmonic projection method.

For uniformly sampled data, the retained complex response is $Y = b + j a, \qquad |Y| = \sqrt{a^{2} + b^{2}},$ with phase $\phi = \operatorname{atan2}(a,b).$

where $a = \frac{2}{N} \sum_{k=0}^{N-1} y_k \cos(\omega t_k), \qquad b = \frac{2}{N} \sum_{k=0}^{N-1} y_k \sin(\omega t_k).$

Arguments

Type	Intent	Optional	Attributes		Name
procedure(harmonic_ode),	intent(in),		pointer	::	fcn	A pointer to the routine containing the ODE's to integrate.
real(kind=real64),	intent(in),		dimension(:)	::	freq	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 fcn. 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.
real(kind=real64),	intent(in),		dimension(:)	::	iv	An N-element array containing the initial conditions for each of the N ODEs.
class(ode_integrator),	intent(inout),	optional,	target	::	solver	An optional differential equation solver. The default solver is the Dormand-Prince Runge-Kutta integrator from the DIFFEQ library.
integer(kind=int32),	intent(in),	optional		::	ncycles	An optional parameter controlling the number of cycles to analyze when determining the amplitude and phase of the response. The default is 5.
integer(kind=int32),	intent(in),	optional		::	ntransient	An optional parameter controlling how many of the initial "transient" cycles to ignore. The default is 30.
integer(kind=int32),	intent(in),	optional		::	points	An optional parameter controlling how many evenly spaced solution points should be considered per cycle. The default is 1000.
logical,	intent(in),	optional		::	inHz	Set to true if the units of the frequency vector are in Hz. If false, the units are assumed as rad/s. The default is false such that the frequency units are assumed to be rad/s.
class(*),	intent(inout),	optional		::	args	An optional argument allowing for passing of data in/out of the fcn subroutine.

Return Value type(frf)

The resulting frequency responses.

private function frf_sweep_2(fcn, nfreq, freq1, freq2, iv, solver, ncycles, ntransient, points, inHz, args) result(rst)

Computes the frequency response of each equation of a system of harmonically excited ODE's by sweeping through frequency.

The amplitude and phase are determined by means of a harmonic projection method.

For uniformly sampled data, the retained complex response is $Y = b + j a, \qquad |Y| = \sqrt{a^{2} + b^{2}},$ with phase $\phi = \operatorname{atan2}(a,b).$

where $a = \frac{2}{N} \sum_{k=0}^{N-1} y_k \cos(\omega t_k), \qquad b = \frac{2}{N} \sum_{k=0}^{N-1} y_k \sin(\omega t_k).$

Arguments

Type	Intent	Optional	Attributes		Name
procedure(harmonic_ode),	intent(in),		pointer	::	fcn	A pointer to the routine containing the ODE's to integrate.
integer(kind=int32),	intent(in)			::	nfreq	The number of frequency values to analyze. This value must be at least 2.
real(kind=real64),	intent(in)			::	freq1	The starting frequency.
real(kind=real64),	intent(in)			::	freq2	The ending frequency.
real(kind=real64),	intent(in),		dimension(:)	::	iv	An N-element array containing the initial conditions for each of the N ODEs.
class(ode_integrator),	intent(inout),	optional,	target	::	solver	An optional differential equation solver. The default solver is the Dormand-Prince Runge-Kutta integrator from the DIFFEQ library.
integer(kind=int32),	intent(in),	optional		::	ncycles	An optional parameter controlling the number of cycles to analyze when determining the amplitude and phase of the response. The default is 5.
integer(kind=int32),	intent(in),	optional		::	ntransient	An optional parameter controlling how many of the initial "transient" cycles to ignore. The default is 30.
integer(kind=int32),	intent(in),	optional		::	points	An optional parameter controlling how many evenly spaced solution points should be considered per cycle. The default is 1000.
logical,	intent(in),	optional		::	inHz	Set to true if the units of the frequency units are in Hz. If false, the units are assumed as rad/s. The default is false such that the frequency units are assumed to be rad/s.
class(*),	intent(inout),	optional		::	args	An optional argument allowing for passing of data in/out of the fcn subroutine.

Return Value type(frf)

The resulting frequency responses.

interface

public subroutine harmonic_ode(freq, t, x, dxdt, args)

Defines a system of ODE's exposed to harmonic excitation.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	freq	The excitation frequency.
real(kind=real64),	intent(in)			::	t	The current time step value.
real(kind=real64),	intent(in),		dimension(:)	::	x	The value of the solution estimate at time t.
real(kind=real64),	intent(out),		dimension(:)	::	dxdt	The derivatives as computed by this routine.
class(*),	intent(inout),	optional		::	args	An optional argument allowing the passing of data in/out of this routine.

interface

public function ode_excite(t) result(rst)

Defines the interface for a ODE excitation function.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	t	The value of the independent variable at which to evaluate the excitation function.

Return Value real(kind=real64)

The result.

Functions

public pure elemental function chirp(t, amp, span, f1Hz, f2Hz) result(rst)

Evaluates a linear chirp function. The instantaneous frequency varies linearly, $f(t)=f_1+\frac{f_2-f_1}{T}t,$ giving phase $\phi(t)=2\pi(f_1t+(f_2-f_1)t^2/(2T))$ and response $x(t)=A\sin(\phi(t))$ .

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	t	The value of the independent variable at which to evaluate the chirp.
real(kind=real64),	intent(in)	::	amp	The amplitude.
real(kind=real64),	intent(in)	::	span	The duration of the time it takes to sweep from the start frequency to the end frequency.
real(kind=real64),	intent(in)	::	f1Hz	The lower excitation frequency, in Hz.
real(kind=real64),	intent(in)	::	f2Hz	The upper excitation frequency, in Hz.

Return Value real(kind=real64)

The value of the function at t.

dynamics_frequency_sweep Module

Contents

Interfaces

Functions

Uses

Contents

Interfaces

Functions

Interfaces

public interface frequency_sweep

private function frf_sweep_1(fcn, freq, iv, solver, ncycles, ntransient, points, inHz, args) result(rst)

Arguments

Return Value type(frf)

private function frf_sweep_2(fcn, nfreq, freq1, freq2, iv, solver, ncycles, ntransient, points, inHz, args) result(rst)

Arguments

Return Value type(frf)

interface

public subroutine harmonic_ode(freq, t, x, dxdt, args)

Arguments

interface

public function ode_excite(t) result(rst)

Arguments

Return Value real(kind=real64)

Functions

public pure elemental function chirp(t, amp, span, f1Hz, f2Hz) result(rst)

Arguments

Return Value real(kind=real64)