Propagation of Natural Waves on Plates of a Variable Cross Section

Abstract

In this paper, a conjugate spectral problem and biorthogonality conditions for the problem of extended plates of variable thickness are constructed. A technique for solving problems and numerical results on the propagation of waves in infinite extended viscoelastic plates of variable thickness is described. The viscous properties of the material are taken into account using the Voltaire integral operator. The investigation is carried out within the framework of the spatial theory of viscoelasticity. The technique is based on the separation of spatial variables and the formulation of a boundary value problem for Eigen values which are solved by the Godunov orthogonal sweep method and the Muller method. Numerical values of the real and imaginary parts of the phase velocity are obtained depending on the wave numbers. In this case, the coincidence of numerical results with known data is obtained.

Damping Properties of Vibrations of Three-Layer VIscoelastic Plate

“…In the case of an inhomogeneous system (R E2 =0) The role of the global damping coefficient is imaginary parts of both the first and second frequencies ( Figure 5). The mathematical and physical aspects of this effect are explained in [13,14,15,16]. The change in the parameter, on which the global coefficient of damping depends so substantially, can be achieved by varying the geometric dimensions or physical properties, thereby opening up the perspective possibility of effectively controlling the damping characteristics of dissipatively inhomogeneous viscoelastic systems.…”

Interaction of Nonstationary Waves on Cylindrical Body

“…given in [20]. The improper integral (10) is solved numerically using the developed algorithms [21]. Practically, the calculation (10) on a computer can be carried out as follows.…”

Own Waves in a Spatial Viscoelastic Cylinder With Radial Crack.

“…Relations (1) and (3) after identical algebraic transformations are reduced to a system of six differential equations resolved with respect to the first derivative with respect to the radial coordinate Where , , , , , -are the components of the stress tensor, respectively; , , , , , -respectively, the components of the strain tensor. the relationship between stress and strain is given in (1). The boundary conditions are set in the form:…”

“…In a number of works, for the control of linearly extended objects, the use of a rod wave is proposed to give rise to the minimum velocity dispersion and torsion wave mode, in which there is no dispersion [1,2]. As an informative parameter in the waveguide control of linearly extended objects, as a rule, the reflection coefficient is used.…”