Effect of Stochastic Randomness in Natural Frequency Increment of a Trapezoidal Laminated Composite Plate

This paper highlights the considerable stochastic effects while taking a deterministic approach to satisfy a dynamic objective function involving the free vibration behavior of a laminated composite trapezoidal plate.The study considers relevant material and geometric parameters of the plate under investigation as stochastic without changing the plan area of the plate which generally happens in many industrial and engineering applications.Investigation of the stochastic effects of material properties, ply thickness, and ply orientation on the objective of reaching an increased natural frequency is carried out by Monte Carlo simulation.Abaqus CAE is used to calculate the increment in the thickness required for the desired rise in the natural frequency of a symmetrically laminated plate.It is shown that variation in reaching the desired frequency increases with the increase of the coefficient of variation of the input variables.A positive linear trend between the coefficients of variation of the desired frequency and input variables is found, whose slope increases as randomness is considered for a greater number of input variables.Probability of failure in reaching the desired frequency is shown to be heavily dependent on the combined variation of material and geometry.In particular, the probability of failure in reaching a desired frequency shows an undulating trend for both types of variation considered.In general, it is also shown that randomness in geometry has a more pronounced effect compared to that in material only.