Determination of Notched Input for Equipment Under Random Vibrations

Equipment that is mounted on a spacecraft is subjected to random vibration tests to verify whether they can withstand the specified random loads. These tests are generally carried out by using shaker systems during which equipment experiences very high responses at the natural frequencies of the equipment. To reduce such over-testing, notching of the input is done. Notching of the input is normally carried out by considering the force generated at the base and limiting it to a specified value. To accomplish the notching, the force spectrum to be limited and measurement of base force during the tests are needed. This work shows that the acceleration input at the interface of equipment gets reduced at its resonance frequency and this feature can be utilized in arriving at the notched input. An expression to determine the depth of notching is derived and the results are compared with those obtained using numerical simulations. The depth of the notch increases with the response of the oscillator and it is sensitive to the stiffness ratios rather than the mass ratios of the oscillator and the mounting panel. This behavior and the expressions derived can be effectively used in arriving at the notched input for an equipment without the need for measuring the base force, especially for random vibration testing, which is demonstrated with an example.

Random vibration analysis with radial basis function neural networks

Random vibrations occur in many engineering systems including buildings subject to earthquake excitation, vehicles traveling on a rough road and off-shore platform in random waves. Analysis of random vibrations for linear systems has been well studied. For nonlinear systems, particularly for multi-degree-of-freedom systems, however, there are still many challenges including analyzing the probability distribution of transient responses of the system. Monte Carlo simulation was considered the only viable method for this task. In this paper, We propose a method to construct semi-analytical transient solutions of the probability distribution of transient responses of nonlinear systems by using the radial basis function neural networks. The activation functions consist of normalized Gaussian probability density functions. Two examples are presented to show the effectiveness of the proposed solution method. The transient probability distributions and response moments of these examples are presented, which have not been reported in the literature before.

Numerical and Experimental Investigation of Cumulative Fatigue Damage under Random Dynamic Cyclic Loads of Lattice Structures Manufactured by Laser Powder Bed Fusion

Lattice structures are lightweight engineering components suitable for a great variety of applications, including those in which the structural integrity under vibration fatigue is of paramount importance. In this work, we experimentally and numerically investigate the dynamic response of two distinct lattice configurations, in terms of fatigue damage and life. Specifically, Face-Centered-Cubic (FCC) and Diamond lattice-based structures are numerically studied and experimentally tested under resonant conditions and random vibrations, until their failure. To this end, Finite Element (FE) models are employed to match the dynamic behavior of the system in the neighborhood of the first natural frequency. The FE models are employed to estimate the structural integrity by way of frequency and tip acceleration drops, which allow for the identification of the failure time and a corresponding number of cycles to failure. Fatigue life under resonant conditions is well predicted by the application of conventional multiaxial high cycle fatigue criteria to the local state of stress. The same approach, combined with the Rainflow algorithm and Miner’s rule, provides good results in predicting fatigue damage under random vibrations.

Non-Linear Random Vibrations Using Second-Order Adjoint and Projected Differentiation Methods

This paper proposes a new computationally efficient methodology for random vibrations of nonlinear vibratory systems using a time-dependent second-order adjoint variable (AV2) method, and a second-order projected differentiation (PD2) method. The proposed approach is called AV2-PD2. The vibratory system can be excited by stationary Gaussian or non-Gaussian random processes. A Karhunen-Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. A second-order adjoint approach is used to obtain the required first and second-order output derivatives accurately by solving as many sets of equations of motion (EOMs) as the number of KL random variables. These derivatives are used to compute the marginal CDF of the output process with second-order accuracy. Then, a second-order projected differentiation method calculates the autocorrelation function of each output process with second-order accuracy, at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). The total number of solutions of the EOM scales linearly with the number of input KL random variables and the number of output processes. The efficiency and accuracy of the proposed approach is demonstrated using a non-linear Duffing oscillator problem under a quadratic random excitation.