This study is concerned with the derivation of differential equation of motion for the free coupled vertical – torsional and lateral vibration of opened thin-walled curved beams. The curved beam to be considered in this study is of isotropic opened thin – walled (I) section with equal top and bottom flanges. The derivation depends on Hamilton's principle which required finding the potential and kinetic energy of the curved beam section due to internal stresses and all types of movements (Vertical,Torsional and Lateral) .The effect of restrained warping displacement is also considered in this study. Three differential equations are derived for vertical, torsional and lateral movement .and approximate solutions are developed by using the method of multiple scale via a perturbation technique. The resulting natural frequencies and modes for vertical , torsional and lateral movements are compared with those calculated by using finite element approach ( STAAD Pro. 2007 ) and with the results other studies.
COUPLED VERTICAL – TORSIONAL AND LATERAL FREE VIBRATION OF THIN-WALLED CURVED BEAM
Thin-walled curved beams
Free vibration
Differential Equation of Motion
Publication Date
Wed Apr 25 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Different Estimation Methods for System Reliability Multi-Components model: Exponentiated Weibull Distribution
Exponentiated Weibull Distribution (EWD)
Reliability of multi-component Stress – Strength models R(s
k)
Maximum likelihood estimator (MLE)
Moment estimator (MOM)
shrinkage method (Sh)
Least Squares Estimator (LS)
Rank Set Sampling (RSS). and mean squared error (MSE).
In this paper, estimation of system reliability of the multi-components in stress-strength model R(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through Monte Carlo simulation technique were made depend on mean squared error (MSE) criteria
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