Issue 1
JTAM, Sofia, vol. 1 Issue 1 (1970)

Theoretical and Applied Mechanics

G. Bradistilov


JTAM, Sofia, vol. 1 Issue 1 pp. 009-010 (1970)

On the Periodic Solutions of an Autonomous System of Differential Equations of Second Order in a Critical Case

G. Bradistilov, G. Ð’oyadjiev

A normal autonomous quasilinear system of n differential equations of second order in which the nonlinear functions are odd towards the unknown variables is considered. This system possesses the following property: the periodicity conditions are reduced to n only, and not to 2n as it is in the general case. The existence of periodic solutions in a critical case when several frequences are divisible to a certain one, is proved. A method for construction of these solutions is given. An example for a double physical pendulum is given.

JTAM, Sofia, vol. 1 Issue 1 pp. 011-018 (1970), [Full Article]

Investigation of Visco-Elastic Shells

G. Brankov

The contemporary stage of the development of shell structures is characterized with the wide application of the polymeric materials and in particular of the fiber-glass reinforced plastics. This imposes a more thorough investigation of the shells on the basis of a visco-elastic model and some new factors being taken into account. An attempt is made to examine the set problem according to the general laws on the mechanics of continuous media on the basis of the carried out investigations. These laws do not depend on the properties of the material. The specific properties of the material are given with physical equations which determine the stress strain relations or with a relation between the stresses and one or several energetic functions.

JTAM, Sofia, vol. 1 Issue 1 pp. 019-024 (1970)
Characteristic Equations in the Theory of the Dynamic Thermo-Visco-Plasticity

D. Kolarov, А. Вaltov

The main system of partial differential equations describing the spatial dynamic problem of thermo-visco-plasticity is examined. The investigation is carried out for a general case comprising wide variety of visco-plastic models. The type of the main system of differential equations is determined. Its characteristic elements are obtained and studied. The characteristic and bicharacteristic conditions are given. A parametrization of the characteristic elements suitable for applying approximate methods of calculation, using the bicha¬racteristic conditions, is proposed.

JTAM, Sofia, vol. 1 Issue 1 pp. 025-038 (1970)
Vibrations of Orthotropic Conical Shells

M. Kozarov

The vibrations of a cutoff ortotropic conical shell reinforced with stringers and shpangouts are investigated. The type of the main equations are obtained by Hammilton-Ostrogradski method in linear formulation. The solution is obtained with Bubnov-Gal’orkin’s method. The frequency equation is given as a determinant. The general solution makes possible the obtaining of many partial solutions.

JTAM, Sofia, vol. 1 Issue 1 pp. 039-046 (1970)
Degree of Irregularity of a Machine Aggregate with Elastic Asynchronous Cardan Transmission

A. Pisarev

The motion law of two rotors of a machine aggregate with asynchronous cardan transmission is deduced. The elastic, inertial and energetic properties of the aggregate are studied. The cardan shaft clasps different angles with the shafts of the driving and driven masses. The investigation is rather simplified because of the introduction of a co-ordinate which is analogic to the mass center of the mechanic system. Fire theoretical deductions are proved experimentally as well.

JTAM, Sofia, vol. 1 Issue 1 pp. 047-058 (1970)
Iterative Analysis of the Stationary Motion of a Machine Agregate

M.S. Konstantinov, P. Genova, M.M. Konstantinov

The stationary process of a machine agregate (motor-transmission-operating machine) with a variable inertional characteristic, subjected to positional and kinematic forces, is investigated. Approximate analytical methods for two cases are given: (i) determining the motion law for the case of a separable function of the set forces. Unlike the preceding investigation of the authors [2], in this case the dynamic characteristic of the motor, accounting the inertion (electro¬magnetic and hydraulic) is introduced; (ii) determining the motion law for the case of nonseparable function of the set forces.

JTAM, Sofia, vol. 1 Issue 1 pp. 059-066 (1970)
Stability of a Straight Bar at Dynamic Loading in Creep Conditions

S. Kislyakov, P. Kolev

The stability of a straight bar subjected to an axis force which varries witli time after an arbitrary given law is investigated. The transversal inertional forces are taken into account. In conditions of the nonlinear theory of the heredity creep of the material is accepted according the Kelwin model scheme. A partial differential equation describing this case is deduced. An approximate solution is proposed. An estimation for the accuracy at determining the Fourier’s functional coefficients is done. An example is given.

JTAM, Sofia, vol. 1 Issue 1 pp. 067-074 (1970)
On a Solution in Displacements of the Spatial Problem of Elastic Orthogonal-Anisotropic Body when Volume Forces Are Available

Chr. Karanikolov, I. Minchev

A solution of the spatial problem of the elasticity theory in displacements is given, the mass forces being taken into account. The stressed and strain state of an clastic orthogonal anysotropic body subjected to mass forces which can be presented as (1), is considered. The problem is to find a partial solution of the nonhomogeneous system of partial differential equations (2). A partial integral of the system (2) is found (3). The nonhomogeneous system of partial differential equations is transformed into a homogeneous one which solution is given. An example is given for the determination of the stresses and strains in a body subjected to gravity forces. This example shows the application of the given solution.

JTAM, Sofia, vol. 1 Issue 1 pp. 075-080 (1970)
Resonance Oscillations of Two Combined Pendula

Ð’. Cheshankov

Internal resonance in a conservative system of two combined pendula is considered. A transfer of energy between the two normal co-ordinates of the system is observed at certain conditions. The stroboscopic images of the motion at different disturbances are drawn.

JTAM, Sofia, vol. 1 Issue 1 pp. 081-092 (1970)