N. P. Plakhtienko

On loads acting on a structure with a seismic damper

The problem on amplification of the translation acceleration by a seismoisolated structure is considered with regard for the nonlinearity of friction and the multifrequency nature of the external perturbation. The equivalent coefficients of Coulomb and turbulent friction that provide a transient time equal to that of a system with viscous friction are calculated. Spectral curves that reflect the dependence of the ratio of the maximum absolute acceleration to the maximum translation acceleration on the natural part of a vibrating system are plotted for various equivalent parameters of nonlinear friction

Methods of Identification of Nonlinear Mechanical Vibrating Systems

Methods for determination of the dynamic characteristics and parameters of mechanical vibrating systems by processing experimental data on controlled vibrations are presented. These methods are intended for construction of mathematical models of objects to be identified and classed as parametric and nonparametric methods. The quadrature formulas of the nonparametric-identification method are derived by inverting the integral parameters of approximate analytical solutions of nonlinear differential equations. The parametric-identification method involves setting up and solving systems of linear algebraic equations in the sought-for inertia, stiffness, and dissipation parameters by integrating experimental processes using special weighting functions. Depending on the type of the nonlinearity of the vibrating system and the method of representing experimental processes, the weighting functions can be oriented toward displacement, velocity, or acceleration gauges. The results of studies made mainly at the Institute of Mechanics of the National Academy of Sciences of Ukraine are presented

Nonlinear Translational Vibrations of a Solid with a Gravity–Friction Seismic Damper

A mathematical model of variable structure is constructed to describe translational motions of a solid on a fixed spherical support with regard for gravity forces and Coulomb friction. Generalized velocities determining transitions from one mathematical model to another are determined. The translational acceleration amplification factor is plotted against the natural period of vibrations of the solid under damped multifrequency disturbance

Double Transient Phase-Frequency Resonance in Vibratory Systems

Estimations are made of how an elastic structure or a pendulum system affects the accelerated motion of platforms. The platforms move at some angle to the horizontal plane. The perturbed motion of the platforms is represented as the sum of two damped harmonics. An analysis is made of how the initial phases of the harmonic perturbations affect the dynamic amplification factor of vibratory systems for certain angles between the perturbation direction and the horizontal plane. With some combinations of the frequency and dissipation parameters, the motion takes new features called the double transient resonance and antiresonance. They occur under the concurrent and partial actions of the parametric and external perturbations.

Selecting the Coefficients of Sliding Friction in the Problem on Frictional Interaction of Three Solids

The choice of the coefficients of sliding friction in the static equilibrium problem for a system of three solids with friction at two points is discussed. This system simulates the mechanism of gravitational seismic isolation of a solid. It is shown that the coefficients of friction must be identical at both points of frictional contact irrespective of the type of the material and surface finish. A formula for the balanced coefficient of friction is derived based on experimental data

On the motion stability of an airplane on a runway under wind loading

A nonlinear mathematical model is constructed for an airplane in high-speed plane-parallel motion along a runway when the airplanes weight exceeds slightly the lift of its wings in the presence of a cross wind. The airplane is considered a two-weight mechanical object. A system of second-order equations is obtained that describes the airplanes behavior. A system of three phase variables is suggested in which the dynamics of transverse motion is described by a set of three second-order equations. A stationary solution of this system is obtained. A stability criterion for the plane-parallel motion of the airplane is established using the Routh-Hurwitz criterion. Analysis of the data of other authors indicates that the mathematical model is adequate for some objects of aviation technology.

Transverse Elastic–Friction Vibrations of a Running Aircraft

An analytical model of the plane-parallel running of an aircraft under crosswind load is proposed. The compliance of the internal constraints of the aircraft and the nonlinearity of the side force on the landing gear wheels are taken into account. The model is intended to study the transverse elastic friction vibrations of the aircraft hull and landing gears. The steady motion of the aircraft is considered. The dependence of the lateral friction force on the slip angle is assumed to have the form of a sinusoidal segment. The Routh–Hurwitz instability conditions are derived in an explicit form

The Method of Abel-Type Integral Equations for Identification of Nonlinear Systems of Structural Seismodynamics

The problem on determination of the nonlinear dissipative and elastic characteristics of some vibrating systems that are encountered in structural seismodynamics is considered. Systems of integral Volterra equations of the first kind (Abel-type equations) are constructed on the basis of approximate analytical solutions to problems on the forced vibration of quasilinear vibrating systems. Such equations relate the nonlinear stiffness and dissipation characteristics with the characteristics of motion, which can be obtained experimentally. The solutions of the integral equations derived are represented in the form of quadrature Stieltjes-integral formulas