Dynamics of Structurally Inhomogeneous Lamellar and Shell Mechanical Systems. Part 1

Abstract

A vibrational statement, method and algorithm to assess the damping capacity of structurally inhomogeneous viscoelastic mechanical systems, consisting of a package of rectangular plates and shells with point relations and concentrated masses at different rheological properties of deformable elements, are proposed in the paper. To describe rheological properties of the material, the linear hereditary Boltzmann-Volter theory was used. To assess the damping capacity of the system, the problem in question in each case was reduced to solving the proper problems of algebraic equations with complex parameters solved by the Muller method. The accuracy of the methods was demonstrated by comparing the calculated results with known published data and a numerical experiment. Complex natural frequency of the system was used to assess the damping capacity of inhomogeneous viscoelastic systems. Various eigenvalue problems have been solved for structurally inhomogeneous mechanical systems consisting of a package of plate and shell systems with concentrated masses and shock absorbers. A number of new mechanical effects have been discovered, related to the manifestation of the damping capacity of mechanical systems under consideration.

Spatial forced oscillations of axisymmetric inhomogeneous systems

“…Substitution of (10) into system (9) leads to a system oflinear algebraic equations for the sought for constants of the form 1). For this, at various frequencies "p" of external action it is necessary to solve equation (11), and the results of solution must be included in (10) and (6).…”

“…Along with this, the dynamic behavior and stress-strain state (SSS) of various structures, with account for features and operating conditions, were studied in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

“…A plane longitudinal wave with potential ( ) falls on a cylindrical shell with radius R, the frequency and amplitude of the incident waves 0 in the form ( ) = 0 (⃗⃗ ⋅ − ) , ( ) = 0 (12) where = ( 0 + 0 ), = ( 0 + 0 ), = / 1 , 0 -the angle of the cylindrical shell in the main coordinate system, 0 is the angle of inclination of the falling loads, , are the unit vectors along the x and y axes, respectively (Figure 1). Further, the incident wave ( ) in cylindrical coordinates has the form [19].…”