Stochastic natural frequency of composite conical shells

The present study portrays the stochastic natural frequencies of laminated composite conical shells using a surrogate model (D-optimal design) approach. The rotary inertia and transverse shear deformation are incorporated in probabilistic finite element analysis with uncertainty due to variation in angle of twist. A sensitivity analysis is carried out to address the influence of different input parameters on the output natural frequencies. Typical fiber orientation angle and material properties are randomly varied to obtain the stochastic natural frequencies. The sampling size and computational cost are exorbitantly reduced by employing the present approach compared to direct Monte Carlo simulation. Statistical analysis is presented to illustrate the results. The stochastic natural frequencies obtained are the first known results for the type of analyses carried out here.

[1]  K. M. Liew,et al.  Vibration of pretwisted cantilever shallow conical shells , 1994 .

[2]  Moonsu Kang,et al.  Optimal sampling frequency for high frequency data using a finite mixture model , 2014 .

[3]  Toby J. Mitchell,et al.  An Algorithm for the Construction of “D-Optimal” Experimental Designs , 2000, Technometrics.

[4]  Sayan Gupta,et al.  Stochastic finite element analysis of layered composite beams with spatially varying non-Gaussian inhomogeneities , 2014 .

[5]  Slawomir Koziel,et al.  Computational Optimization, Methods and Algorithms , 2016, Computational Optimization, Methods and Algorithms.

[6]  Jakob Kuttenkeuler,et al.  A Finite Element Based Modal Method for Determination of Plate Stiffnesses Considering Uncertainties , 1999 .

[7]  Wael G. Abdelrahman,et al.  Stochastic Finite element analysis of the free vibration of functionally graded material plates , 2008 .

[8]  Douglas O. Stanley,et al.  Parametric Modeling Using Saturated Experimental Designs , 1996 .

[9]  Leonard Meirovitch,et al.  Dynamics And Control Of Structures , 1990 .

[10]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[11]  George S. Springer,et al.  Design of Composite Laminates by a Monte Carlo Method , 1993 .

[12]  Mohamad S. Qatu,et al.  Vibration studies for laminated composite twisted cantilever plates , 1991 .

[13]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[14]  Sudip Dey,et al.  Finite element analysis of bending-stiff composite conical shells with multiple delamination , 2012 .

[15]  Barry L. Nelson,et al.  Stochastic kriging for simulation metamodeling , 2008, WSC 2008.

[16]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[17]  Byeongdo Kim,et al.  Comparison study on the accuracy of metamodeling technique for non-convex functions , 2009 .

[18]  Sondipon Adhikari,et al.  Stochastic free vibration analysis of angle-ply composite plates – A RS-HDMR approach , 2015 .

[19]  Rakesh K. Kapania,et al.  Dynamic stability of uncertain laminated beams subjected to subtangential loads , 2008 .

[20]  Radoslav Harman,et al.  Multiplicative methods for computing D-optimal stratified designs of experiments , 2014 .

[21]  Art B. Owen,et al.  9 Computer experiments , 1996, Design and analysis of experiments.

[22]  Rajamohan Ganesan,et al.  Free-vibration of Composite Beam-columns with Stochastic Material and Geometric Properties Subjected to Random Axial Loads , 2005 .

[23]  R. Yue,et al.  D-optimal designs for multiresponse linear models with a qualitative factor , 2014, J. Multivar. Anal..

[24]  Tanmoy Mukhopadhyay,et al.  Optimisation of Fibre-Reinforced Polymer Web Core Bridge Deck—A Hybrid Approach , 2015 .

[25]  William C. Carpenter,et al.  Effect of design selection on response surface performance , 1993 .

[26]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[27]  Anupam Chakrabarti,et al.  Structural Damage Identification Using Response Surface-Based Multi-objective Optimization: A Comparative Study , 2015, Arabian Journal for Science and Engineering.

[28]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[29]  Ranjan Ganguli,et al.  Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion , 2011 .

[30]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[31]  Chun-Gon Kim,et al.  Stochastic Finite Element Method for Laminated Composite Structures , 1995 .

[32]  Mohamad S. Qatu,et al.  Natural frequencies for cantilevered doubly-curved laminated composite shallow shells , 1991 .

[33]  M. J. Box,et al.  On Minimum-Point Second-Order Designs , 1974 .

[34]  Xiaojun Wang,et al.  Uncertainty propagation in SEA for structural–acoustic coupled systems with non-deterministic parameters , 2014 .

[35]  S. Adhikari,et al.  Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach , 2015 .

[36]  George Z. Voyiadjis,et al.  Mechanics of Composite Materials with MATLAB , 2005 .

[37]  P. Sinha,et al.  Failure Analysis of Laminated Composite Pretwisted Rotating Plates , 2001 .

[38]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[39]  Wael G. Abdelrahman,et al.  Stochastic finite element analysis of the free vibration of laminated composite plates , 2007 .