In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.

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An analytical model is developed for active control of nonlinear flexural vibrations of cylindrical shells under random excitation. A velocity feedback control scheme is integrated into the governing equations of motion using discrete surface-bonded piezoelectric materials as collocated sensors/actuators. Donnell's thin shell theory is used to develop the governing equations of motion. A Monte Carlo simulation of stationary random processes, multi-mode Galerkin like approach, and numerical integration procedures are used to develop nonlinear response solutions of simply-supported cylindrical shells. Numerical results include time domain response histories, root mean square values and histograms of probability density. Parametric studies are performed to investigate the effect of nonlinearity, actuator placement, actuator number and size, and control gains.

PurposeThe transverse shear deformation and rotary inertia effects need to be included for an accurate analysis in the response of the relatively thick plates. This paper seeks to use, one of the refined theories which takes into account those effects, The First Order Shear Deformation Theory, to obtain linear and non‐linear responses for anti‐symmetric angle‐ply composite plates under random excitation.Design/methodology/approachThe random excitation is assumed to be stationary, ergodic and Gaussian with zero‐mean. A Monte Carlo Simulation of stationary random process is used. A multi‐mode Galerkin approach and numerical integration procedure are employed to find linear and non‐linear response solutions. Laminated composite plate is taken to be simply‐supported along four edges.FindingsThe vibration of composite plates at elevated temperatures is also investigated. The linear and non‐linear deflections root‐mean‐square (RMS) are obtained for various input levels, the different lamination angles and the number of layers.Practical implicationsFurther, case studies might lead to a lighter design of thick panels used in high‐performance systems such as aerospace structures.Originality/valueThe paper provides information on the linear and more realistic non‐linear vibrations of thick composite plates in time domain so that it would be possible to obtain key statistical information directly from time‐response history.

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