Numerical modeling conducting plates with complex form in a given magnetic field. (Q2743020)

The mode of deformation of conducting plates having complex form in a given magnetic field is investigated. The corresponding boundary value problem NEWLINE\[NEWLINE h\rho \frac{\partial^2W}{\partial t^2}+D\nabla^4W+ \frac{h^3}{48\pi}H^2\left(\frac{\partial^2W}{\partial x^2}+ \frac{\partial^4W}{\partial x^2\partial y^2}\right)+ \frac{h}{4\pi}H^2\Delta W-\frac{h_x}{4\pi}H^2 \frac{\partial^2W}{\partial y^2}=Q NEWLINE\]NEWLINE where \(h,\rho,H,D, h_x\) are given physical constants and \(W_{\mid t=t_0} =\dot W_{\mid t=t_0}=0\), \(W_{\mid\Gamma}= \frac{\partial W}{\partial n}_{\mid\Gamma}=0\) is numerically solved by combination of Galerkin method and \(R\)-functions method. As an example a plate of hexagonal form is considered.