Some problems concerning the stability of nonlinear elastic bodies under finite and small subcritical strains

The stationary structure stability of discontinuous solutions to nonlinear hyperbolic equations describing the propagation of quasi-transverse waves with velocities close to characteristic ones are studied. A procedure to analyze spectral (linear) stability of these solutions is described. The main focus is the stability analysis of special discontinuities, the stationary structure of which is represented by the integral curve connecting two saddle points corresponding to the states in front of and behind the discontinuity. This analysis is done using the properties of the Evans function, an analytic function on the right complex half-plane, which has zeros in this domain if and only if there exist unstable modes of linearization around a solution representing a special discontinuity with the structure.

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A Basic Theory of Artery Buckling Under Internal Pressure

ASME 2009 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2009-204838 ◽

2009 ◽

Author(s):

Hai Chao Han

Keyword(s):

Internal Pressure ◽

Stretch Ratio ◽

External Pressure ◽

Mode Shapes ◽

Theoretical Base ◽

Linear And Nonlinear ◽

Elastic Artery ◽

The Stability ◽

Nonlinear Elastic ◽

Arteries And Veins

The stability of blood vessels under the lumen blood pressure load is essential to the maintenance of normal arterial function. It has been well documented that arteries and veins collapse when the internal lumen pressure is too low and/or the external pressure become higher than the internal pressure [1–3]. It has been demonstrated recently that arteries and veins also buckle (bend) due to hypertensive pressure or a reduced axial stretch ratio [4]. Buckling equations have been established recently for linear and nonlinear elastic artery and vein models based on assumed sinusoidal mode shapes [4–6]. However, the theoretical base for the assumption is lacking. It is necessary to determine whether arteries can bifurcate into the buckled shape under internal pressure.

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DYNAMICS FEATURES OF A VIBRATING MACHINE WITH ELASTIC ELEMENT HAVING EXPONENTIAL CHARACTERISTIC OF RESILIENT FORCE

Cybernetics and Physics ◽

10.35470/2226-4116-2021-10-2-59-62 ◽

2021 ◽

pp. 59-62

Author(s):

Grigory Altshul ◽

Alexander Gouskov ◽

Grigory PanovkoAlexander Shokhin ◽

Alexander Shokhin

Keyword(s):

Supply Voltage ◽

Elastic Characteristic ◽

Vibration Exciter ◽

Static Characteristics ◽

Power Supply Voltage ◽

Resonant Amplitude ◽

Processed Material ◽

Working Element ◽

The Stability ◽

Nonlinear Elastic

The article analyzes the possibility of using nonlinear elastic elements as a suspension of the working element of resonant vibrating machines with two unbalance vibration exciters is analyzed. The elastic characteristic of the suspension is described by an exponential law, which ensures that the natural frequency remains unchanged regardless of the system mass. Static characteristics of the vibration exciter motors are taken into account. A system of differential equations describing movement of the system depending on the processed material mass is obtained. Amplitude-frequency characteristics depending on the power supply voltage, as well as on the debalance rotational speed are obtained for different values of material mass. The stability of the obtained periodic solutions is analyzed. The constancy of resonant amplitude and frequency of the working element vibrations at various values of material mass is shown. The results obtained confirm the advisability of using an equalfrequency suspension of the working element for resonant vibrating machines.

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