Back to Search
Start Over
Dynamic Analysis of a Plate on the Generalized Foundation with Fractional Damping Subjected to Random Excitation
- Source :
- Mathematical Problems in Engineering, Vol 2018 (2018)
- Publication Year :
- 2018
- Publisher :
- Hindawi Limited, 2018.
-
Abstract
- Stochastic response of a plate on the generalized foundation driven by random excitation is solved in this paper. Governing differential equation is obtained by employing the Galerkin method. The generalized harmonic function technique is applied to the governing equation of motion. Using the stochastic averaging method (SAM), the system is approximated by the time homogeneous diffusive Markov process. Corresponding approximate stationary probability function is achieved by solving associated Fokker-Plank-Kolmogorov (FPK). An analytical solution is presented for the stationary probability of the amplitude and velocity. Validity of the stationary probability is verified by Monte-Carlo simulation. Parametric study is carried out to investigate effects of foundation parameters and excitation intensity on the stationary probability function. It is found that the fractional properties act similar to the foundation stiffness and damping and can be employed as a new control parameter for the support design.
- Subjects :
- Stationary distribution
Article Subject
Differential equation
lcsh:Mathematics
General Mathematics
Mathematical analysis
General Engineering
Markov process
02 engineering and technology
Function (mathematics)
lcsh:QA1-939
01 natural sciences
symbols.namesake
020303 mechanical engineering & transports
Amplitude
0203 mechanical engineering
Harmonic function
lcsh:TA1-2040
0103 physical sciences
symbols
lcsh:Engineering (General). Civil engineering (General)
Galerkin method
010301 acoustics
Mathematics
Parametric statistics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2018
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....6d6733031a8273eb13156c2ab7ff71e3