Dynamic Influence Function Research Articles

VIBRATION ANALYSIS OF ARBITRARILY SHAPED MEMBRANES USING NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTION

In the present study, a theoretical formulation based on the collocation method is presented for the vibration analysis of arbitrarily shaped membranes. The mathematical relation between the two points of selected collocation points is given by a special function, the so-called non-dimensional dynamic influence function. Unlike the collocation methods in the literature, approximate functions used in this paper are simple, one-dimensional functions of which the only independent variable is the distance between the two points. The function is also a wave-type solution that satisfies exactly the given governing differential equation and physically describes the displacement reponse of a point in an infinite membrane due to a unit displacement excited at another point. The approximate solution is obtained by linear superposition of non-dimensional dynamic influence functions, and then boundary conditions are applied at the discrete points. The system matrix is always symmetric regardless of the boundary shape of the membrane, and the calculated eigenvalues rapidly converge to the exact values thanks to the special function employed in this study. Moreover, the method gives the associated mode shapes successfully without using interpolation functions between the boundary nodes. The validity and efficiency of the method proposed in this paper are illustrated through several numerical examples.

Genetic Algorithm Optimization for the Active Control of a Beam by Means of PZT Actuators

The aim of this work is to optimize placement and sizing of a given number of piezoelectric (PZT) actuator patches on an Euler-Bernoulli beam, in order to control (or damp) desired modes in an optimal way. A modal approach for the dynamic influence functions is used to take directly into account the position, length and loading of a generic PZT. The optimization problem is solved from a stochastic point of view by means of Genetic Algorithms.

Spatially coupled vibrations of a suspension bridge under random highway traffic

AbstractThe problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single‐span thin‐walled beam underslung to two cables. The response of the bridge in the space‐time domain is described by a coupled system of non‐linear, integro‐differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross‐section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer‐oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.