Quasi-static method of investigating the dynamic properties of rigid polymers

The mechanical properties of polymers have been investigated at medium impact velocities. The various experimental methods of constructing stress-strain diagrams are compared.     

Investigation of the fatigue properties of rigid polymers used in making harmonic drives

The fatigue properties of rigid polymers used for making harmonic drive components have been investigated. Certain data on the fatigue of flexible shells under complex loading conditions have been obtained. The effect of the polymer structure on the fatigue properties of a series of compounds with various antifriction fillers and plasticizing additives is evaluated.Translated from Mekhanika Polimerov, No. 6, pp. 1014–1019, November–December, 1970.     

Determination of fatigue life in bending with rotation

The fracture and stress redistribution processes in a specimen stressed in cyclic bending with rotation are considered. The calculations are based on the assumption of linear damage accumulation and a linear dependence of the modulus of elasticity on the damage; the fatigue strength curve for cyclic tension-compression is employed. The calculated damage accumulation and crack penetration times are compared. Specific calculations are made for the case of PMMA fatigue under isothermal conditions.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 875–880, September–October, 1971.     

Shrinkage properties of some rigid polymers

Experimental results from a study of the shrinkage of polymers based on epoxy and polyester resins during the polymerization process are presented. The shrinkage was determined by wire strain gauges from the moment of transition of the polymer into a solid medium. An equation has been found which satisfactorily describes the laws governing chemical shrinkage with time."Plastopolimer" Scientific-Manufacturing Union, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 236–240, March–April, 1972.     

Strength of rigid oriented amorphous polymers

A method is proposed for obtaining uniaxially oriented specimens of amorphous unfractionated polymer with a particular oriented chain length. The length of the oriented chains and their molecular weight M_c depend importantly on the conditions under which the polymer is stretched. It is shown that the strength of specimens obtained by stretching at constant M_c increases linearly with the relative fraction of oriented phase. The slope of this linear relation increases with the length of the oriented molecular chains. The ratio of the maximum strength of fully oriented polystyrene to the strength of the unoriented material is found to be 78 instead of the value of 6 given in [6].Mekhanika Polimerov, Vol. 3, No. 6, pp. 1048–1053, 1967     

Contact with break-off under bending of an elastic strip with a rigid disk

We consider the problem of the theory of elasticity of the contact interaction of a rigid circular disk and an elastic strip, which rests upon two supports with disturbance of contact in the middle part of the contact region. On the basis of the Wiener–Hopf method, an integral equation of the problem is reduced to an infinite system of algebraic equations. The size of the zone of break-off of the boundary of the strip from the disk and the distribution of contact stresses are determined.     

On bending an elastic plate with a delaminated thin rigid inclusion

Under study is the problem of bending an elastic plate with a thin rigid inclusion which may delaminate and form a crack. We find a system of boundary conditions valid on the faces of the crack and prove the existence of a solution. The problem of bending a plate with a volume rigid inclusion is also considered. We establish the convergence of solutions of this problem to a solution to the original problem as the size of the volume rigid inclusion tends to zero.     

Generation of random processes for fatigue testing

In fatigue testing there is a need to generate multivariate random processes meeting certain conditions on distributions, crossing properties and regularity. In this paper it is demonstrated how these conditions can be satisfied. The required process is generated by a random time deformation working on a Gaussian process.     

Multicycle fatigue resistance of brittle polymers

Conclusion A model of multicycle fatigue of polymers based on the hypothesis of self-simulation of the failure process was proposed and a method of predicting the durability was elaborated in the present study. It was found that in low-temperature conditions of self-heating, the crack is the basic cause of fatigue failure. A cyclic durability equation was obtained in the form of a modified time summation criterion for the stressed state in the failure zone in the vicinity of the apex of a fatigue crack. It was shown that in the case of brittle failure in multicycle fatigue, the maximum principal stresses which arise in the failure zone, one order of magnitude smaller than the size of the fatigue crack, are the criterion of failure.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 633–638, July–August, 1990.     

Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation

Using the averaged method, we investigate the dynamical characteristics of a single inertial neuron model with time delay under periodic external stimuli. It is shown that the system will lose its stability when the time delay is increased and will give rise to a quasi-periodic motion and chaos under the interaction of the periodic excitation. Numerical simulations show that the results of the analytical method are correct by a comparison with those of direct numerical integration.     

Mathieu equation with application to analysis of dynamic characteristics of resonant inertial sensors

In this paper, Mathieu equation is applied to analyze the dynamic characteristics of resonant inertial sensors. Unlike previous work, Mathieu equation is not just a differential equation and analyzes the stability of the transition curves, but become an important method in analyzing parametric resonant characteristics and approximate output of resonant inertial sensors. It is demonstrated that the mathematical model of resonant inertial sensors is described by Mathieu equation. The relevant Mathieu equation theory and dynamic characteristics analysis methods were proposed, which include both stability and dynamic linear output. Finally, theoretical and experimental analysis show that the correlation of the theoretical curve and the experimental result coincide so perfectly, which means proposed analysis methods for Mathieu equation could be used to analyze the dynamic output characteristic of resonant inertial sensors. The theoretical analyzing approach of Mathieu equation and experimental results of resonant inertial sensors are obtained, which provide an application area for Mathieu equation and a reference for the robust design for resonant inertial sensors.     

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing’s oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.     

Infrared spectroscopic study of the prefracture state of rigid polymers

A correspondence has been established between the effects of stress and temperature on the half-width and the position of the maximum of the 972-cm^–1 absorption band for polyethylene terephthalate. It is shown that the prefracture state of polyethylene terephthalate is a softened state.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 520–523, May–June, 1976.