Single Degree of Freedom Oscillator Parameters

Definition of the custom type, Oscillator to represent a single degree of freedom (SDOF) oscillator. Type simply stores the oscillator frequency and damping ratio.

StochasticGroundMotionSimulation.Oscillator — Type

Oscillator{T<:Float64}

Custom type to represent a SDOF oscillator. The type has two fields:

f_n is the natural frequency of the oscillator
ζ_n is the damping ratio

Examples

    sdof = Oscillator( 1.0, 0.05 )

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## Functionality

The main methods that are used to interact with Oscillator instances are:

StochasticGroundMotionSimulation.period — Function

period(sdof::Oscillator)

Natural period (s) of the sdof Oscillator.

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StochasticGroundMotionSimulation.transfer — Function

transfer(f::T, sdof::Oscillator) where {T<:Real}

Compute the modulus of the transfer function for a SDOF system.

The transfer function is defined as:

\[|H(f,f_n,\zeta_n)| = \frac{1}{\sqrt{ \left(1 - \beta^2 \right)^2 + \left(2\zeta_n\beta\right)^2 }}\]

where $\beta$ is the tuning ratio defined by $f/f_n$.

Examples

    f = 2.0
    sdof = Oscillator(1.0, 0.05)
    Hf = transfer(f, sdof)

See also: squared_transfer

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transfer(f::Vector{T}, sdof::Oscillator) where T<:Real

Computes the modulus of the transfer function of a SDOF for a vector of frequencies

f::Vector is the vector of frequencies
sdof::Oscillator is the oscillator instance

Examples

  f = collect(range(0.1, stop=10.0, step=0.01))
  sdof = Oscillator(1.0)
  Hf = transfer(f, sdof)

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StochasticGroundMotionSimulation.transfer! — Function

transfer!(Hf::Vector{T}, f::Vector{T}, sdof::Oscillator) where T<:Real

Computes the modulus of the transfer function of a SDOF for a vector of frequencies in place - Hf::Vector is the pre-allocated vector into which the results are stored - f::Vector is the vector of frequencies - sdof::Oscillator is the oscillator instance

Examples

    f = collect(range(0.1, stop=10.0, step=0.01))
    sdof = Oscillator(1.0)
    Hf = similar(f)
    transfer!(Hf, f, sdof)

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StochasticGroundMotionSimulation.squared_transfer — Function

squared_transfer(f, sdof::Oscillator)

Compute the square of the transfer function for a SDOF system, sdof, at frequency f.

Examples

	f = 2.0
	# create sdof with natural frequency f_n=1.0 and damping ζ=0.05
	sdof = Oscillator( 1.0, 0.05 )
	Hf2 = squared_transfer( f, sdof )

See also: transfer

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StochasticGroundMotionSimulation.squared_transfer! — Function

squared_transfer!(Hf2::Vector{T}, f::Vector{T}, sdof::Oscillator) where T<:Real

Computes the square of the modulus of the transfer function of a SDOF for a vector of frequencies in place: - Hf2::Vector is the pre-allocated vector into which the results are stored - f::Vector is the vector of frequencies - sdof::Oscillator is the oscillator instance Inputs derive from the Real type and so are differentiable.

Examples

    f = collect(range(0.1, stop=10.0, step=0.01))
    sdof = Oscillator(1.0)
    Hf2 = similar(f)
    squared_transfer!(Hf2, f, sdof)

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