Made when setting up the harmonic balance solution. Were not determined in the solution are zero. The implication of this function is that the higher harmonics that Number of points desired in the “smooth” time history. realify: booleanįorce the returned results to be real.

Values representing the repeating solution. N x m array where m is the number of equations and m is the number of This function fills in the gaps using the Plotting these results implies that the solution isn’tĪctually a continuous one. The result is that the time history is usually a very limited Harmonic balance solutions presume a limited number of harmonics in the Generate refined time history from harmonic balance solution. time_history ( t, x, num_time_points=200, realify=True ) ¶ array (,]) > F = v * 0.1 > a = solmf ( x, v, M, C, K, F ) > print ( a ) ] har_bal. Options to the nonlinear solvers can be passed in by **kwargs (keywordĪrguments) identical to those available to the nonlinear solver. (default newton_krylov) to be minimized by the solver. Velocities (after an inverse FFT) then calls sdfunc to determineĪccelerations are also obtained using a Fourier representation of xĮrror in the accelerations (or state derivatives) are the functionalĮrror used by the nonlinear algebraic solver Hb_err uses a Fourier representation of x to obtain Solver should gently “walk” solution up to get to nonlinearities for hardĬalls hb_err with x as the variable to solve for. Results in 3 points in time over the cycle. This method is not reliable for a low number of harmonics.Įvaluates the differential equation/s at evenly spaced points in time. phases float arrayĪmplitudes of displacement (primary harmonic) in column vector format. Time, displacement history (time steps along columns), errors, amps float arrayĪmplitudes of displacement (primary harmonic) in column vector format. Other keyword arguments available to nonlinear solvers in

realify boolean, optionalįorce the returned results to be real. (second order is default) params dict, optionalĭictionary of parameters needed by sdfunc. Num_variables must be defined if x0 is not. An error will result ifīoth x0 and num_variables are left out of the function call. If x0 is defined, num_variables is inferred. Number of states for a state space model, or number of generalized If num_harmonics*2+1Įxceeds the number of columns of x0 then x0 will be expanded, usingįourier analaysis, to include additional harmonics with the starting Generalize allowable default values later.) omega floatĪssumed fundamental response frequency in radians per second. This is NOT a string (not the name of the function). Vector first derivative given x, and a dictionry of parameters. Parameters sdfunc functionįor eqform=’first_order’, name of function that returns column Parameters are used to calculate the state derivatives which are returnedīy the function. Prescribed response frequency and the current time. This dictionary should be used to obtain the In a second-order form solution the function must take the states and the Parameters sdfunc functionįunction in SciPy integrator form ( odeint or solve_ivp) Returns new_function functionįunction in Mousai form (accepting inputs like a standard Mousaiĭef duff_osc ( x, v, params ): # params is a dictionary of parameters omega = params # `omega` will be put into the dictionary # for you t = params # The time value is available as # `cur_time` in the dictionary return np. Inspect package to determine the form of the function being used and to This function returns a function compatible with Mousai by using the Integrators for good cause, but can make simultaneous usage diffucult. This is inconsistent with the SciPy numerical Sdfunc(x, t, params) where x are the current states as an n by 1Īrray, t is a scalar, and params is a dictionary of parameters, one of The form of the function returning state derivatives is function_to_mousai ( sdfunc ) ¶Ĭonvert scipy.integrate functions to Mousai form. Switch from complex form fft form to SciPy rfft form. duff_osc ( x, v, params ) ¶ĭuffing oscillator acceleration. condense_rfft ( X_full, num_harmonics ) ¶

condense_fft ( X_full, num_harmonics ) ¶Ĭreate equivalent amplitude reduced-size FFT from longer FFT. Harmonic balance solvers and other related tools. Harmonic Balance Tools ( mousai.har_bal) ¶

Har bal 3.7