tmdsimpy.nlforces.GenPolyForce

class tmdsimpy.nlforces.GenPolyForce(Q, T, Emat, qq)

Bases: InstantaneousForce

Nonlinear force based on general polynomial combinations of nonlinear DOFs.

Parameters:

Q(Nnl, N) numpy.ndarray

Matrix tranform from the N degrees of freedom (DOFs) of the system to the Nnl local nonlinear DOFs.

T(N, Nnl) numpy.ndarray

Matrix tranform from the local Nnl forces to the N global DOFs.

Emat(Nnl,cnl) numpy.ndarray

Stiffness coefficients that multiply polynomial combinations of Nnl DOFs as defined by qq. cnl is the number of polynomial combinations considered.

qq(cnl,Nnl) numpy.ndarray

Matrix defining the exponents of the nonlinear DOFs for evaluating the force. Each of the cnl rows defines a different polynomial term. Within a row, the column i is the exponent for nonlinear DOF i of the Nnl nonlinear DOFs.

Notes

This class can commonly be used with cubic and quadratic polynomial nonlinearities to simulate geometric nonlinearity. Applications can be more general than geometric nonlinearity.

This class calculates an instantaneous force, but does not exactly match the template of tmdsimpy.nlforces.InstantaneousForce because here each of the force outputs can depend in a nonlinear fashion on other nonlinear DOFs.

__init__(Q, T, Emat, qq)

Methods

__init__(Q, T, Emat, qq)
aft(U, w, h[, Nt, tol, calc_grad])	Implementation of the alternating frequency-time method to extract harmonic nonlinear force coefficients.
force(X)	Calculate global nonlinear forces for some global displacement vector.
local_force_history(unlt, unltdot)	Evaluates the local nonlinear forces based on local nonlinear displacements for a time series.
nl_force_type()	Method to identify the force type as instantaneous.

aft(U, w, h, Nt=128, tol=1e-07, calc_grad=True)

Implementation of the alternating frequency-time method to extract harmonic nonlinear force coefficients.

Parameters:

U(N*Nhc,) numpy.ndarray

displacement harmonic DOFs

wfloat

Frequency in rad/s. Needed in case there is velocity dependency.

hnumpy.ndarray, sorted

List of harmonics. The list corresponds to Nhc harmonic components.

Ntint power of 2, optional

Number of time steps used in evaluation. The default is 128.

tolfloat, optional

This argument is ignored for instantaneous forces. It is included for compatability of interface. The default is 1e-7.

calc_gradboolean, optional

This argument is ignored for instantaneous forces. It is included for compatability of interface. The default is True.

Returns:

Fnl(N*Nhc,) numpy.ndarray

Nonlinear hamonic force coefficients

dFnldU(N*Nhc,N*Nhc) numpy.ndarray

Jacobian of Fnl with respect to U

dFnldw(N*Nhc,) numpy.ndarray

Jacobian of Fnl with respect to w

force(X)

Calculate global nonlinear forces for some global displacement vector.

Parameters:

X(N,) numpy.ndarray

Global displacements.

Returns:

F(N,) numpy.ndarray

Global nonlinear force.

dFdX(N,N) numpy.ndarray

Derivative of F with respect to X.

local_force_history(unlt, unltdot)

Evaluates the local nonlinear forces based on local nonlinear displacements for a time series.

Parameters:

unl(Nt,Nnl) numpy.ndarray

Local displacements, rows are different time instants and columns are different displacement DOFs.

unldot(Nt,Nnl) numpy.ndarray

Local velocities, rows are different time instants and columns are different displacement DOFs.

Returns:

ft(Nt,Nnl) numpy.ndarray

Local nonlinear forces, rows are different time instants and columns are different local force DOFs.

dfdu(Nt,Nnl,Nnl) numpy.ndarray

Derivative of forces of ft with resepct to displacements unl. Each index i, j, k is the derivative ft[i, j] with respect to unl[i, k].

dfdud(Nt,Nnl,Nnl) numpy.ndarray

Derivative of forces of ft with resepct to velocities unltdot. Each index i, j, k is the derivative ft[i, j] with respect to unltdot[i, k].

nl_force_type()

Method to identify the force type as instantaneous.

Returns:

int

0, indicating instanteous force type.