Variable Support Control for the Wave Equation - A Multiplier Approach

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations.

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Sensitivity analysis of sandwich beams and plates accounting for variable support conditions

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.2478/bpasts-2013-0019 ◽

2013 ◽

Vol 61 (1) ◽

pp. 201-210 ◽

Cited By ~ 1

Author(s):

R. Studziński ◽

Z. Pozorski ◽

A. Garstecki

Keyword(s):

Sensitivity Analysis ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Practical Applications ◽

The Core ◽

State Of Stress ◽

Thin Steel ◽

Influence Of Temperature On ◽

Support Conditions ◽

Variable Support

Abstract The paper addresses the problems of the sensitivity analysis and optimal design of multi-span sandwich panels with a soft core and flat thin steel facings. The response functional is formulated in a general form allowing wide practical applications. Sensitivity gradients of this functional with respect to dimensional, material and support parameters are derived using adjoint variable method. These operators account for the jump of the slope of a Timoshenko beam or a Reissner plate at the position of concentrated active load or reaction, thus extending the sensitivity operators known in literature. The jump of slope is the effect of shear deformation of the core. Special attention is focussed on sensitivity and optimisation allowing for variable support position and stiffness, because local phenomena observed in supporting area of sandwich plates often initiate failure mechanisms. Introducing optimally located elastic supports allows to reduce the unfavourable influence of temperature on the state of stress. Several examples illustrate the application of derived sensitivity operators and demonstrate their exactness

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