טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGreenberg Robert
SubjectFlexible Mast Under Stochastic Dynamic Base Excitation
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Eli Altus
Full Thesis textFull thesis text - English Version


Abstract

This study deals with modeling, analysis and evaluation of the elastic response, of a flexible sailing mast, subjected to stochastic dynamic excitations, in statistical terms. In particular, the goal is to find the probability that the elastic deflection and slope will be in a predetermined range.

The mast was modeled as a one dimensional, homogeneous, Euler-Bernoulli beam. More generalized cases can be analyzed by the same approach. The study was conducted in three stages: 1) Calculation of the probability density functions (pdfs) of the elastic response analytically by spectral analysis. 2) Validation of (1) by finite difference scheme and Monte-Carlo-Simulation. 3) Calculation of the Gaussian response (pdf) by a single excitation signal and a numerical solution.

The mast base excitation is composed of two components: stochastic base excitations caused by the vessel's ‘SWAY’ (translation) and ‘ROLL’ (rotation) motions. These excitations are both random stationary Gaussian processes and are usually characterized by their spectral densities.

It was found that for realistic loads and structure parameters, the linear assumptions of the model are justified. For any given signal which fits the input spectral densities, the pdf of the output signal is not Gaussian but has the same variance. Nevertheless, the pdf of a large ensemble of output signals is Gaussian with the above variance.

Using the above modeling, the following effects were studied: 1) Additional lumped mass at the mast's free edge. 2) Correlation (proportion) between the base excitation components. 3) Additional harmonic excitation originating from rotating machinery. 4) Wind effect estimation, where a velocity Weibull pdf time distribution is used. These effects were quantified in terms of the increase in the Probability of Exceeding a Specified Response Range (PESRR) compared to the case without the additional effects.

Major results and conclusions are: 1) The lumped mass effect is not negligible: 6.33% of the mast's mass, increases the PESRR for an elastic slope of 0.0002rad at the mast’s free-end by 1.28 times. 2) The effect of a correlation between the base excitation components is considerable: a constant proportion increases the above PESRR by up to 4.58 times. 3) Addition of a dominant harmonic excitation causes drastic increase in the PESRR. 4) A "Fresh breeze" wind (number 5 in the Beaufort scale) increases the above PESRR by 3.01 times. 5) Finding the Gaussian response by solving numerically a single base excitation signal of each type is very advantageous for complex dynamic models.