ARF

Examples using this class are:

Doinikov 2021 Viscous - Convergence Study

class osaft.solutions.doinikov2021viscous.arf.ARF(f, R_0, rho_s, E_s, nu_s, rho_f, c_f, eta_f, zeta_f, p_0, wave_type, position=None, N_max=5, inf_factor=60.0, inf_type=None, integration_rel_eps=0.001)[source]

Bases: StreamingField, BaseARF

ARF class for Doinikov (viscous fluid-elastic sphere; 2021)

Parameters

f (Frequency | float) – frequency [Hz]
R_0 (Sphere | float) – radius [m]
rho_s (float) – density of the particle [kg/m^3]
E_s (float) – Young’s modulus of the particle [Pa]
nu_s (float) – Poisson’s ratio of the particle [-]
rho_f (float) – density of the fluid [kg/m^3]
c_f (float) – speed of sound in the fluid [m/s]
eta_f (float) – fluid component shear viscosity [Pa s]
zeta_f (float) – fluid component bulk viscosity [Pa s]
p_0 (float) – pressure amplitude [Pa]
wave_type (WaveType) – wave type
position (None | float, optional) – position in the standing wave field [m]
Default: None
N_max (int, optional) – truncation of the summation index (highest order mode)
Default: 5
inf_factor (float, optional) – see inf_factor
Default: 60.0
inf_type (None | str, optional) – see inf_type
Default: None
integration_rel_eps (float, optional) – relative eps for adaptive integration
Default: 0.001

Public Data Attributes:

Inherited from StreamingField

`inf_factor`	Infinity factor
`inf_type`	Infinity type
`integration_rel_eps`	Relative integration error goal for adaptive integration
`C_0`	Container for integrals and errors \(C_{ml0}\)
`C_0_error`	Container for integrals and errors \(C_{ml0}\)
`inf`	Limit for the integration to the far-field / to infinity) [m]

Inherited from ScatteringField

`eta`	Wraps to `osaft.core.fluids.ViscousFluid.eta_f`
`zeta`	Wraps to `osaft.core.fluids.ViscousFluid.zeta_f`

Inherited from BaseScatteringDoinikov2021

`range_N_max`	Returns `range(0, N_max + 1)`
`range_1_N_max`	Returns `range(1, N_max + 1)`
`range_2_N_max`	Returns `range(2, N_max + 1)`

Inherited from BaseDoinikov

`supported_wavetypes`
`eta`	Wraps to `osaft.core.fluids.ViscousFluid.eta_f`
`zeta`	Wraps to `osaft.core.fluids.ViscousFluid.zeta_f`
`x_l`	Dimensionless primary wavenumber in the solid
`x_t`	Dimensionless secondary wavenumber in the solid
`x_f`	Dimensionless acoustic wavenumber in the fluid
`x_v`	Dimensionless viscous wavenumber in the fluid
`rho_s`	Wraps to `osaft.core.solids.ElasticSolid.rho_s`
`E_s`	Wraps to `osaft.core.solids.ElasticSolid.E_s`
`nu_s`	Wraps to `osaft.core.solids.ElasticSolid.nu_s`
`k_l`	Wraps to `osaft.core.solids.ElasticSolid.k_l`
`k_t`	Wraps to `osaft.core.solids.ElasticSolid.k_t`
`rho_f`	Wraps to `osaft.core.fluids.ViscousFluid.rho_0` or to `osaft.core.fluids.ViscoelasticFluid.rho_0`
`c_f`	Wraps to `osaft.core.fluids.ViscousFluid.c_f` or to `osaft.core.fluids.ViscoelasticFluid.c_f`
`eta_f`	Wraps to `osaft.core.fluids.ViscousFluid.eta_f` or to `osaft.core.fluids.ViscoelasticFluid.eta_f`
`zeta_f`	Wraps to `osaft.core.fluids.ViscousFluid.zeta_f` or to `osaft.core.fluids.ViscoelasticFluid.zeta_f`
`k_f`	Wraps to `osaft.core.fluids.ViscousFluid.k_f` or to `osaft.core.fluids.ViscoelasticFluid.k_f`
`k_v`	Wraps to `osaft.core.fluids.ViscousFluid.k_v` or to `osaft.core.fluids.ViscoelasticFluid.k_v`
`delta`	Wraps to `osaft.core.fluids.ViscousFluid.delta` or to `osaft.core.fluids.ViscoelasticFluid.delta`
`lambda_v`	Wraps to `osaft.core.fluids.ViscousFluid.lambda_v` or to `osaft.core.fluids.ViscoelasticFluid.lambda_v`
`position`	Wraps to `osaft.core.backgroundfields.BackgroundField.position`
`p_0`	Wraps to `osaft.core.backgroundfields.BackgroundField.p_0`
`wave_type`	Wraps to `osaft.core.backgroundfields.BackgroundField.wave_type`

Inherited from BaseSphereFrequencyComposite

`R_0`	Wrapper for `osaft.core.geometries.Sphere.R_0`
`area`	Wrapper for `osaft.core.geometries.Sphere.area`
`volume`	Wrapper for `osaft.core.geometries.Sphere.volume`

Inherited from BaseFrequencyComposite

`f`	wrapper for `osaft.core.frequency.Frequency.f`
`omega`	wrapper for `osaft.core.frequency.Frequency.omega`

Inherited from BaseSolution

`supported_wavetypes`
`wave_type`	Wraps to `osaft.core.backgroundfields.BackgroundField.wave_type`

Inherited from BaseScattering

N_max

Cutoff mode number for infinite sums

Public Methods:

`compute_arf`([return_error])	Returns the value for the ARF in Newton [N].
`I_1`()	Integral \(I_1\)
`I_1_error`()	Estimated numerical error for integral \(I_1\)

Inherited from StreamingField

`E`(l, r, ac)	\(E_l(r)\)
`F`(n, m, r, ac)	\(F_{mn}(r)\)
`G`(n, m, r, ac)	\(G_{mn}(r)\)
`V_S_r`(l, r, ac)	\(V_{Srl}(r)\)
`V_S_theta`(l, r, ac)	\(V_{S \theta l}(r)\)
`alpha`(l, r, ac)	\(\alpha_l(r)\)
`beta`(l, r, ac)	\(\beta_l(r)\)
`gamma`(l, r, ac)	\(\gamma_l(l, r)\)
`d_gamma`(l, r, ac)	\(\partial_r \gamma_l(r)\)

Inherited from BaseScatteringDoinikov2021

`radial_particle_displacement`(r, theta, t[, mode])	First-order radial particle displacements [m]
`radial_particle_velocity`(r, theta, t[, mode])	First-order radial particle velocity [m/s]
`tangential_particle_displacement`(r, theta, t)	First-order tangential particle displacements [m]
`tangential_particle_velocity`(r, theta, t[, mode])	First-order tangential particle displacements [m]
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`a`(n)	Coefficient \(a_n\) [m^2/s]
`a_hat`(n)	Coefficient \(\hat{a}_n\) [m^2/s]
`b`(n)	Coefficient \(b_n\) [m^2/s]
`b_hat`(n)	Coefficient \(\hat{b}_n\) [m^2/s]
`V_r_sc`(n, r)	Scattering contribution to \(V_{rn}(r)\) [m/s]
`d_V_r`(n, r, scattered, incident)	\(\partial_r V_{rn}(r)\) [m/s]
`d_V_r_sc`(n, r)	\(\partial_r V_{rn}^{sc}(r)\) [m/s]
`d_V_r_i`(n, r)	\(\partial_r V_{rn}^{i}(r)\) [m/s]
`d2_V_r`(n, r, scattered, incident)	\(\partial^2_r V_{rn}(r)\) [m/s]
`d2_V_r_i`(n, r)	\(\partial^2_r V_{rn}^{i}(r)\) [m/s]
`d2_V_r_sc`(n, r)	\(\partial^2_r V_{rn}^{sc}(r)\) [m/s]
`V_theta_sc`(n, r)	Scattering contribution to \(V_{\theta n}(r)\) [m/s]
`d_V_theta`(n, r, scattered, incident)	\(\partial_r V_{\theta n}(r)\) [m/s]
`d_V_theta_sc`(n, r)	\(\partial_r V_{\theta n}^{sc}(r)\) [m/s]
`d_V_theta_i`(n, r)	\(\partial_r V_{\theta n}^{i}(r)\) [m/s]
`d2_V_theta`(n, r, scattered, incident)	\(\partial^2_r V_{\theta n}(r)\) [m/s]
`d2_V_theta_sc`(n, r)	\(\partial^2_r V_{\theta n}^{sc}(r)\) [m/s]
`d2_V_theta_i`(n, r)	\(\partial^2_r V_{\theta n}^{i}(r)\) [m/s]
`phi`(n, r, scattered, incident)	\(\varphi_n(r)\)
`phi_sc`(n, r)	\(\varphi_n^{sc}(r)\)
`phi_i`(n, r)	\(\varphi_n^i(r)\)
`d_phi`(n, r, scattered, incident)	\(\partial_r \varphi_n(r)\)
`d_phi_sc`(n, r)	\(\partial_r \varphi_n^{sc}(r)\)
`d_phi_i`(n, r)	\(\partial_r \varphi_n^{i}(r)\)

Inherited from CoefficientMatrix

`det_M_n`(n[, column])	Determinant of the matrix M for the mode n
`matrix_M`(n)	Matrix \(M_l\)
`vector_n`(n)	Vector \(n_l\)
`viscosity_term`()	Often used function of fluids shear and bulk viscosity
`a_0`()	Coefficient \(a_0\) [m^2/s]
`a_hat_0`()	Coefficient \(\hat{a}_0\) [m^2/s]
`D_0`()	Coefficient \(D_0\)

Inherited from BaseDoinikov

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Inherited from BaseFrequencyComposite

input_variables()

Returns all properties that are settable.

Inherited from BaseSolution

`copy`()	Returns a copy of the object
`check_wave_type`()	Checks if `wave_type` is in `supported_wavetypes`

Inherited from BaseScattering

`radial_acoustic_fluid_velocity`(r, theta, t, ...)	Returns the value for the radial acoustic velocity in [m/s].
`tangential_acoustic_fluid_velocity`(r, theta, ...)	Returns the value for the tangential acoustic velocity in [m/s].
`pressure`(r, theta, t, scattered, incident[, ...])	Returns the acoustic pressure [Pa].
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`velocity_potential`(r, theta, t, scattered, ...)	Returns the velocity potential of the fluid in [m^2/s].
`radial_particle_velocity`(r, theta, t[, mode])	Returns the value for the radial particle velocity in [m/s].
`tangential_particle_velocity`(r, theta, t[, mode])	Returns the value for the tangential particle velocity in [m/s].
`radial_particle_displacement`(r, theta, t[, mode])	Particle displacement in radial direction
`tangential_particle_displacement`(r, theta, t)	Particle displacement in tangential direction
`radial_mode_superposition`(radial_func, r, ...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`tangential_mode_superposition`(...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`V_r_i`(n, r)	Radial incident field velocity term of mode n without Legendre coefficients
`V_theta_i`(n, r)	Tangential incident field velocity term of mode n without Legendre coefficients
`V_r_sc`(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
`V_theta_sc`(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
`V_r`(n, r, scattered, incident)	Superposition of `V_r_sc()` and `V_r_i()` depending on `scattered` and `incident`
`V_theta`(n, r, scattered, incident)	Superposition of `V_theta_sc()` and `V_theta_i()` depending on `scattered` and `incident`

Inherited from BaseARF

compute_arf()

Returns the value for the ARF in Newton [N].

A_in(n): Wraps to osaft.core.backgroundfields.BackgroundField.A_in

D_0()

Coefficient \(D_0\)

(Eq. A17)

Returns: coefficient D_0

E(l, r, ac)

\(E_l(r)\)

(Eq. C17)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

Returns

E(l, r)

F(n, m, r, ac)

\(F_{mn}(r)\)

(Eq. B5)

Parameters

n (int) – index n
m (int) – index m
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

complex

Returns

F(n, m, r)

G(n, m, r, ac)

\(G_{mn}(r)\)

(Eq. B6)

Parameters

n (int) – index n
m (int) – index m
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

complex

Returns

G(m, n, r)

I_1()[source]

Integral \(I_1\)

(Eq. 27)

Return type: float

I_1_error()[source]

Estimated numerical error for integral \(I_1\)

(Eq. 27)

Return type: float

V_S_r(l, r, ac)

\(V_{Srl}(r)\)

(Eq. F8)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

V_S_theta(l, r, ac)

\(V_{S \theta l}(r)\)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

V_r(n, r, scattered, incident)

Superposition of V_r_sc() and V_r_i() depending on scattered and incident

At least one of the two must be True.

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type

complex

V_r_i(n, r)

Radial incident field velocity term of mode n without Legendre coefficients

Returns radial incident field velocity in [m/s]

Parameters

n (int) – mode
r (float | Sequence) – radial coordinate [m]

Return type

complex

V_r_sc(n, r)

Scattering contribution to \(V_{rn}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

V_theta(n, r, scattered, incident)

Superposition of V_theta_sc() and V_theta_i() depending on scattered and incident

At least one of the two must be True.

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type

complex

V_theta_i(n, r)

Tangential incident field velocity term of mode n without Legendre coefficients

Returns tangential incident field velocity in [m/s]

Parameters

n (int) – mode
r (float | Sequence) – radial coordinate [m]

Return type

complex

V_theta_sc(n, r)

Scattering contribution to \(V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

a(n)

Coefficient \(a_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex
Returns: coefficient a_n

a_0()

Coefficient \(a_0\) [m^2/s]

(Eq. A15)

Returns: coefficient a_0

a_hat(n)

Coefficient \(\hat{a}_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex
Returns: coefficient a_hat_n

a_hat_0()

Coefficient \(\hat{a}_0\) [m^2/s]

(Eq. A15)

Returns: coefficient a_0

alpha(l, r, ac)

\(\alpha_l(r)\)

(Eq. B9)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

Returns

alpha(l, r)

b(n)

Coefficient \(b_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex

b_hat(n)

Coefficient \(\hat{b}_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex

beta(l, r, ac)

\(\beta_l(r)\)

(Eq. C5)

Parameters

l (int) – index l
r (float) – radial coordinate r
ac (bool) – if True only the contribution from the

Return type

float

Returns

beta(l, r)

check_wave_type()

Checks if wave_type is in supported_wavetypes

Raises: WrongWaveTypeError – If wave_type is not supported
Return type: None

compute_arf(return_error=False)[source]

Returns the value for the ARF in Newton [N]. This method must be implemented by every theory to have a common interface for other modules.

Parameters: return_error (bool, optional) –
Default: False
Return type: float | tuple[float, float]

copy()

Returns a copy of the object

Return type: BaseSolution

d2_V_r(n, r, scattered, incident)

\(\partial^2_r V_{rn}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d2_V_r_i(n, r)

\(\partial^2_r V_{rn}^{i}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_r_sc(n, r)

\(\partial^2_r V_{rn}^{sc}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_theta(n, r, scattered, incident)

\(\partial^2_r V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d2_V_theta_i(n, r)

\(\partial^2_r V_{\theta n}^{i}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_theta_sc(n, r)

\(\partial^2_r V_{\theta n}^{sc}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_r(n, r, scattered, incident)

\(\partial_r V_{rn}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_V_r_i(n, r)

\(\partial_r V_{rn}^{i}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_r_sc(n, r)

\(\partial_r V_{rn}^{sc}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_theta(n, r, scattered, incident)

\(\partial_r V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_V_theta_i(n, r)

\(\partial_r V_{\theta n}^{i}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_theta_sc(n, r)

\(\partial_r V_{\theta n}^{sc}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_gamma(l, r, ac)

\(\partial_r \gamma_l(r)\)

(Eq. C9)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

Returns

d_gamma(l, r)

d_phi(n, r, scattered, incident)

\(\partial_r \varphi_n(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_phi_i(n, r)

\(\partial_r \varphi_n^{i}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_phi_sc(n, r)

\(\partial_r \varphi_n^{sc}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

det_M_n(n, column=None)

Determinant of the matrix M for the mode n

Parameters

n (int) – mode
column (None | int, optional) – the l`th coefficient is replaced with the vector `N
Default: None

Return type

complex

gamma(l, r, ac)

\(\gamma_l(l, r)\)

(Eq. C9)

Parameters

l (int) – index l
r (float) – radial coordinate [m]
ac (bool) – if True only the incident field contribution

Return type

float

Returns

gamma(l, r)

classmethod input_variables()

Returns all properties that are settable.

Returns a list of the names of all properties that are settable, i.e. all properties that wrap a PassiveVariable.

Return type: list[str]

matrix_M(n)

Matrix \(M_l\)

(Eq. A19 - A 22)

Parameters: n (int) – mode
Return type: ndarray

phi(n, r, scattered, incident)

\(\varphi_n(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

phi_i(n, r)

\(\varphi_n^i(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

phi_sc(n, r)

\(\varphi_n^{sc}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

potential_coefficient(n)

Wrapper to the fluid scattering coefficients for an inviscid fluid

This method must be implemented by every theory to have a common interface for other modules.

Parameters: n (int) – mode
Return type: complex

pressure(r, theta, t, scattered, incident, mode=None)

Returns the acoustic pressure [Pa].

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type

complex

radial_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the radial acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type

complex | NDArray

radial_mode_superposition(radial_func, r, theta, t, mode=None)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_{\text{mode}}(r) \,P_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t} \sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P_n(\cos\theta)\]

where \(f_\text{n}(r)\) is the radial_func(n, r) passed to the method.

Parameters

radial_func (Callable[[int, float], complex]) – radial function dependent on r
r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type

complex | NDArray

radial_particle_displacement(r, theta, t, mode=None)

First-order radial particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order radial particle displacement

radial_particle_velocity(r, theta, t, mode=None)

First-order radial particle velocity [m/s]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

tangential_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the tangential acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type

complex | NDArray

tangential_mode_superposition(tangential_func, r, theta, t, mode)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_\text{mode}(r) \,P^1_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t}\sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P^1_n(\cos\theta)\]

where \(f_n(r)\) is the tangential_func(n, r) passed to the method.

Parameters

tangential_func (Callable[[int, float], complex]) – tangential function dependent on r
r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (int) – specific mode number of interest; if None then all modes until N_max

Return type

complex | NDArray

tangential_particle_displacement(r, theta, t, mode=None)

First-order tangential particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order tangential particle displacements

tangential_particle_velocity(r, theta, t, mode=None)

First-order tangential particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order tangential particle displacements

vector_n(n)

Vector \(n_l\)

(Eq. A19 - A 22)

Parameters: n (int) – mode
Return type: ndarray

velocity_potential(r, theta, t, scattered, incident, mode=None)

Returns the velocity potential of the fluid in [m^2/s].

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type

complex

viscosity_term()

Often used function of fluids shear and bulk viscosity

Return type: complex

property C_0: ndarray

Container for integrals and errors \(C_{ml0}\)

(Eq. E5 - E7)

Stores the integrals and the estimated errors for the integral \(C_{ml0}\)

Return type: ndarray

property C_0_error: ndarray

Container for integrals and errors \(C_{ml0}\)

(Eq. E5 - E7)

Stores the integrals and the estimated errors for the integral \(C_{ml0}\)

Return type: ndarray

property E_s: float

Wraps to osaft.core.solids.ElasticSolid.E_s

Return type: float

property N_max

Cutoff mode number for infinite sums

Getter: returns number of infinite sum term
Setter: automatically invokes osaft.core.variable.BaseVariable.notify()

property R_0: float

Wrapper for osaft.core.geometries.Sphere.R_0

Return type: float

property area: float

Wrapper for osaft.core.geometries.Sphere.area

Return type: float

property c_f: float

Wraps to osaft.core.fluids.ViscousFluid.c_f or to osaft.core.fluids.ViscoelasticFluid.c_f

Return type: float

property delta: float

Wraps to osaft.core.fluids.ViscousFluid.delta or to osaft.core.fluids.ViscoelasticFluid.delta

Return type: float

property eta: float

Wraps to osaft.core.fluids.ViscousFluid.eta_f

Return type: float

property eta_f: float

Wraps to osaft.core.fluids.ViscousFluid.eta_f or to osaft.core.fluids.ViscoelasticFluid.eta_f

Return type: float

property f: float

wrapper for osaft.core.frequency.Frequency.f

Return type: float

property inf: Limit for the integration to the far-field / to infinity) [m]

property inf_factor: float

Infinity factor

Factor that is multiplied with the length given through inf_type to get the upper limit for integration to the far-field.

Getter: returns the infinity factor
Return type: float
Setter: automatically invokes osaft.core.variable.BaseVariable.notify()
Type: float

property inf_type: str

Infinity type

the upper limit of the integration to the far-field is defined as a multiple of either radius, boundary layer thickness, acoustic wavelength, viscous wavelength, or a user-defined value. The options are - ‘delta’ - ‘radius’ - ‘1’ or 1 - None

The multiplier is set through inf_value