Impact problems arise in many practical applications. The need for obtaining an accurate model for the inelastic impact is a challenging problem. In general, two approaches are common in solving the impact problems: the impulse-momentum and the compliance based methods. The former approach included the coefficient of restitution which provides a mechanism to solve the problem explicitly. While the compliance methods are generally tailored to solve elastic problems, researchers in the field have proposed several mechanisms to include inelastic losses. In this paper, we present correlations between the coefficient of restitution in the impulse-momentum based method and the contact stiffness in the compliance methods. We conducted numerical analysis to show that the resulting solutions are indeed identical for a specific range of impact conditions. The impulse-momentum based model is considered as a reference case to compare the post impact velocities. The numerical results showed that, the impulse-momentum and the compliance based methods can produce similar outcomes for specific range of coefficient of restitution if they satisfied a set of end conditions. The correlations lead to introduce a new contact force model with hysteresis damping for low coefficient of restitution impact.
In this paper, we numerically solved the elastic multiple impact problem in a linear chain of balls using the impuhe momentum and Hertz contact theory based methods. The first method depends on a parameter called the impulse correlation ratio (ICR) while the latter one depends on the material properties and geometries of the colliding bodies. We compared the post impact velocities from the two methods and we found that the two methods yield similar solutions for elastic collisions. Then, we develop an energy absorption scheme using an arrangement of balls with different sizes. The impulse momentum method is used and the ICRs are e.xperimentally estimated. We u.se numerical and e.xperimental analyses to demomtrate that one can significantly improve the energy absorption by placing small balls in specific locations in a linear chain of large balls.
In this paper, we present a solution to the frictionless multiple impact problems that may arise in the rocking blocks. We use an approach based on the impulse-momentum methods, the energetic coefficient of restitution and the impulse correlation ratio. Subsequently, we present the results of an experimental study that is used to compare the results predicted by the proposed method with the experimental outcomes.
This paper proposes designing a static output feedback controller for a structural-acoustics coupling system using piezoelectric actuators. The system consists of a rectangular cavity with two flexible plates, one at the top of the cavity and the other at the bottom, and four other rigid boundaries. Piezoelectric pair patches are considered to be bonded to the top plate, and each pair is assumed to produce a pure moment actuation. The top plate is exposed to an external pressure excitation due to a planar wave generated by a sound source mounted above the cavity. The series solution is assumed for the displacements of the plates and the pressure inside the cavity. The responses of the coupled system are obtained using Galarkin’s method. In the control scheme, the controller gains have been optimally tuned using genetic algorithms. The proposed static output feedback controller shows an acceptable performance with simple implementation requirements compared to the linear quadratic Gaussian state feedback controller.
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