This paper is devoted to correct method of analytical solution of multipoint boundary problems of structural analysis for systems of ordinary differential equations with piecewise constant coefficients. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems and partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors.

In the present paper, the nonlocal-in-time damping models, called “damping-with-memory” models, are reviewed. Since such models do not involve the distribution along the longitudinal coordinate, they are easily adjustable for the FEM (Finite Element Model) algorithm, which is a big advantage due to the fact that FEM is the most-used method in engineering calculations. Within damping-with-memory models, the internal damping of a structure at the current time, is assumed to be dependent not only on the instant strain-rate magnitude or displacement-velocity magnitude but also on the strain-rate or velocity values along the previous time history. The greater the gap between the two time points, the lower the influence that one of them has on the other. To implement a composite beam vibration simulation involving damping with memory, the equation of motion of a structure written in the matrix form could be solved using the central difference method. The models constructed could be calibrated based on 3D numerical simulation data with the least squares method. It has been shown that the results obtained using the implementation of a calibrated damping-with-memory model within the 1D finite-element beam algorithm are in good correlation with those given by the 3D-FEM numerical simulation data.

This paper is devoted to a new gauge of small dynamic bending deformations of structures. Unlike previously existing strain gauges that measure elongation or compression at a certain point on the surface of a deformable body, the proposed gauge measures the change in curvature at a point on the surface of a deformable body and does not respond to elongation–compression strains. The gauge is a layered bar made of piezoelectric and elastic materials. It functions using the direct piezoelectric effect. In order to competently study the deformed state of a structure at points on a surface, it is necessary to determine all components of the strain tensor. The gauges currently used measure only elongational or compressive strains, which does not provide a complete picture of the strain state. It is very important to complement these deformations with bending strains measured by the new gauge.

The nonlocal model of internal damping is considered in this paper using the Euler-Bernoulli beam with fixed ends as an example. Equation of beam motion considering nonlocal damping is solved by Galerkin method to develop the model. The required number ofeigenmodes is obtained for the beam under an instantly applied distributed load. The influenceof nonlocal damping model parameters variation on the beam vibration process simulation results is shown. The beam is considered under a periodic deterministic distributed load. Defining of nonlocal damping model parameters is carried out using results of numerical three-dimensional finite element simulation. The parameters are defined for the glass fibre reinforced plastic beam with the fixed ends under the instantly applied distributed load. The parameters obtained for two different kernel functions and corresponding standard errors are compared. An opportunity of one-dimensional beam model use for the design of composite elements is shown and justified.