pyva.systems.lumpedSystems.HarmonicOscillator

class pyva.systems.lumpedSystems.HarmonicOscillator(mass, stiffness, damping=0.0)

Bases: object

The harmonocOscillator class defines the dynamics of a simple damped or undamped harmonic oscillator.

The main purpose of this class is the presentation of the oscillator dynamics in [Pei2022]

mass

oscillating mass

Type:

float

stiffness

stiffness of spring

Type:

float

damping

viscous damping

Type:

float

__init__(mass, stiffness, damping=0.0)

Class contructor for HarmonicOscillator

Parameters:

• mass (float) – oscillating mass

• stiffness (float) – stiffness of spring

• damping (float) – viscous damping

Methods

__init__(mass, stiffness[, damping])	Class contructor for HarmonicOscillator
displacement(time, x0[, v0])	Displacement of harmonic oscillator over time
displacement_amplitude(time, x0[, v0])	Complex amplitude due to initial conditions
energy(time, x0[, v0])	total energy of harmonic oscillator over time
kinetic_energy(time, x0[, v0])	kinetic energy of harmonic oscillator over time
potential_energy(time, x0[, v0])	potential energy of harmonic oscillator over time
u_force(omega, F)	Harmonic forced response of harmonic oscillator
velocity(time, x0[, v0])	Velocity of harmonic oscillator over time
velocity_amplitude(time, x0[, v0])	Complex velocity amplitude due to initial conditions

Attributes

critical_damping_ratio	Ratio of viscous- to critical-viscous damping
critical_viscous_damping	The critical viscous damping
damping_loss	The damping loss
omega_mode	Resonance frequency or harmonic oscillator
omega_resonance	Resonance frequency or harmonic oscillator

property critical_damping_ratio

Ratio of viscous- to critical-viscous damping

Returns:

The ratio of damping to critical viscous damping

Return type:

float

property critical_viscous_damping

The critical viscous damping

Returns:

Critical viscous damping

Return type:

float

property damping_loss

The damping loss

Returns:

damping loss

Return type:

float

displacement(time, x0, v0=0)

Displacement of harmonic oscillator over time

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

displacement over time

Return type:

float

displacement_amplitude(time, x0, v0=0)

Complex amplitude due to initial conditions

This method separates between the tree cases. It provides the complex oscillation amplitude X(t) for underdamped case. And the real displacement over time for the damped cases

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

displacement amplitude over time

Return type:

complex

energy(time, x0, v0=0)

total energy of harmonic oscillator over time

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

energy over time

Return type:

float

kinetic_energy(time, x0, v0=0)

kinetic energy of harmonic oscillator over time

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

kinetic energy over time

Return type:

float

property omega_mode

Resonance frequency or harmonic oscillator

Returns:

angular resonance frequency without damping

Return type:

float

property omega_resonance

Resonance frequency or harmonic oscillator

Returns: float

angular resonance frequency with damping

potential_energy(time, x0, v0=0)

potential energy of harmonic oscillator over time

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

potential energy over time

Return type:

float

u_force(omega, F)

Harmonic forced response of harmonic oscillator

Parameters:

• omega (float) – angular frequency

• F (complex) – amplitude of force excitation

Returns:

displacement amplitude

Return type:

complex

velocity(time, x0, v0=0)

Velocity of harmonic oscillator over time

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

displacement over time

Return type:

float

velocity_amplitude(time, x0, v0=0)

Complex velocity amplitude due to initial conditions

This method separates between the tree cases. It provides the complex oscillation velocity V(t) for underdamped case. And the real velocity over time for the damped cases

Parameters:

• time (float) – time > 0

• x0 (float) – initial displacement at time=0

• v0 (float) – initial velocity at time=0

Returns:

velocity amplitude over time

Return type:

complex