Mechanics of particles and systems Nonlinear mechanical dynamics Concept
Random vibration
Builds on Stochastic processStationary processDamped harmonic oscillator
Summary
A random vibration is the motion of a mechanical system driven by a load that is a stochastic process. Examples of such loads are wind, road roughness, ocean waves and earthquakes. Such a motion cannot be predicted in detail, so it is described by statistics: mean values, correlation functions and spectral densities. Consider a linear system driven by a stationary process. The spectral density of its response is the spectral density of the load times the squared modulus of the frequency response. The theory is used to design structures and vehicles for fatigue and for extreme loads.
Reading path
To understand this page from the ground up, read these 60 pages in order. The foundations come first.
- Complex numbers object
- Construction of the reals from Cauchy sequences concept
- Differential equation concept
- Element definition
- Function concept
- Integers object
- Interval concept
- Ordered field definition
- Proposition concept
- Random experiment concept
- Rational numbers object
- Real numbers object
- Stationary process concept
- Euler's formula statement
- Ordinary differential equation definition
- Set definition
- Ring of integers statement
- Disjunction definition
- Implication definition
- Predicate definition
- Order of a differential equation definition
- Ordered pair definition
- Union definition
- Sample space definition
- Existential quantifier definition
- Universal quantifier definition
- The rationals form a field statement
- Cartesian product definition
- Linear differential equation of order n definition
- Subset definition
- Uniqueness quantifier definition
- The rationals form an ordered field statement
- Binary relation definition
- Homogeneous linear equation definition
- Linear equation with constant coefficients definition
- Power set definition
- Universal set definition
- Order on the reals definition
- Superposition principle statement
- Function definition
- Characteristic equation definition
- Complement definition
- Interval definition
- Solution space of a homogeneous linear equation has dimension n statement
- Preimage of a set definition
- Sigma-algebra definition
- Fundamental system of solutions definition
- Event definition
- Borel sigma-algebra definition
- Solutions for distinct real roots statement
- Probability axioms concept
- Solutions for repeated roots statement
- Probability measure definition
- Solutions for complex conjugate roots statement
- Probability space definition
- Harmonic oscillator example
- Random variable definition
- Damped harmonic oscillator example
- Stochastic process concept
- Random vibration concept
Further reading
About this page
| Tag | KSFW7GWB5T |
|---|---|
| URI | m2://KSFW7GWB5T |
| Kind | concept |
| Writing | W0 stub |
| MSC | 70L05, 60G10, 70J35 |
| Uses | Stochastic process, Stationary process, Damped harmonic oscillator |
| Same as | |
| Changed | 3 November 2026 |
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