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Stochastic response of a plate on the generalized foundation driven by random excitation is solved in this paper. Governing differential equation is obtained by employing the Galerkin method. The generalized harmonic function technique is applied to the governing equation of motion. Using the stochastic averaging method (SAM), the system is approximated by the time homogeneous diffusive Markov process. Corresponding approximate stationary probability function is achieved by solving associated FokkerPlank-Kolmogorov (FPK). An analytical solution is presented for the stationary probability of the amplitude and velocity. Validity of the stationary probability is verified by Monte-Carlo simulation. Parametric study is carried out to investigate effects of foundation parameters and excitation intensity on the stationary probability function. It is found that the fractional properties act similar to the foundation stiffness and damping and can be employed as a new control parameter for the support design.

Material models are widely used in finite element codes for analysis of material deformations particularly at high strain rates and elevated temperatures. The problems such as necking and bulging limit the conventional test techniques to measure the stress–strain curves only up to small strains. This is while in some deformation processes, the strain can be greater than 1. In this study, steel shots of 6 mm in diameter are impacted on specimens at high impact velocities and at elevated temperatures using shot impact test. Strains up to 1.6 and strain rates up to about 4 × 106 s−1 are achieved in this study. The geometry of the crater created by the shot impact on the specimen is used for determination of the constants of Johnson–Cook material model. A combined experimental, numerical and optimization approach is used for determination of the constants. The experimental and numerical crater geometries coincide when the constants of material are chosen correctly. The selection of the constants is performed using an optimization technique such as genetic algorithm. The computed constants are verified by quasi-static tests. With this new technique, stress–strain curves are no longer needed to be obtained by experiment at high strain rates and elevated temperatures.

In this paper, we study vibro-acoustic behavior of auxetic sandwich panels subjected to different excitations and boundary conditions. The core of this panel has the auxetic feature (with negative Poisson’s ratio or NPR) with anti-tetrachiral honeycomb structure. Mechanical behavior of the core is formulated using theoretical relations presented for this kind of auxetic. Using the Finite Element Method, the modal analysis and spectral analysis of the structure are accomplished. Different random colored noises are applied as the system excitation. First, a parametric study is performed; and some interesting results are observed from investigating the effects of geometric parameters, boundary conditions, and noise color on the vibro-acoustic behavior of the structure. These parameters affect the natural frequencies, level of radiated sound, and mass of the structure. An optimization algorithm is applied to the geometrical parameters in order to simultaneously reduce the level of radiated sound and preserve the amount of total mass. By the use of the Genetic Algorithm (GA), we could achieve a remarkable noise attenuation gain. It is shown that the GA choses different optimized parameters for the structure according to the location of the load and frequency content of the load spectrum.

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