On oscillations of the viscoelastic dam-plate at seismic loading. (Q2743035)

Oscillations of viscoelastic dam-plate when seismic loading and hydrodynamic water pressure take place are investigated. If \(w(y,z,t)\) is a cross bend of the dam then mathematical model of the problem is reduced to corresponding boundary value problem for integro-partial differential equation \((1-R^*)\nabla^4w+ \rho\frac{ \partial^2(w+w_0)}{\partial t^2}=F\), where \(R^*\) is integral operator of the form \(R^*f=\int_0^tR(t-\tau) f(\tau)\,d\tau\) and \(w_0(t)=a_0e^{-\varepsilon_0t} \sin\omega_0t\). The Galerkin method and quadrature formulas are used.