Action of Transverse Non-Stationary Force on a Hinged Moment Elastic Rectangular Plate (Simplified Model)


Аuthors

Do N. D.*, Tarlakovskii D. V.**, Fedotenkov G. V.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: Ngocdatktqs@mail.ru
**e-mail: tdvhome@mail.ru
***e-mail: greghome@mail.ru

Abstract

The transient bending of a moment-elastic rectangular plate under a concentrated force is considered. A simplified model is applied, using the Kirchhoff-Love hypothesis and neglecting transverse shear deformation. The initial conditions are zero, indicating that the system is at rest at the moment the force is applied. Generalized hinge support is assumed at the boundaries, which sets the necessary boundary conditions.
To solve this problem, double trigonometric series in spatial coordinates are used. Such series allow the solution to be decomposed as a sum of modes with different frequency components, each describing an individual contribution to the deformation. The equation with respect to the coefficients of these series reduces to a system of ordinary differential equations in time. The Laplace transform is applied to integrate this system, allowing a transition to the time domain representation. The solution for the function’s original form is recovered using the residue calculation in the complex plane, ensuring accurate and stable restoration of the temporal dependence.
As an example of loading, a normal force applied at the center of the square plate is considered. The force’s time variation follows the Heaviside function, modeling an instantaneous load application, characteristic of dynamic impact effects. The plate is made from a composite based on aluminum shot in an epoxy matrix, which provides high strength at relatively low weight and good damping properties.
For numerical calculations, a summation procedure for the series with a pre-specified accuracy in the continuous norm is implemented. This avoids the accumulation of errors and ensures result convergence. This method can be useful for modeling various cases of dynamic loading on composite plates, which is crucial for the aerospace industry, where accurate prediction of structural behavior under transient loads is of critical importance.

Keywords:

moment elastic plate, Kirchhoff-Love hypothesis, equations of motion, physical relations, deflection, angle of rotation, internal force factors, double trigonometric series.

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