Contents of Journal of Mechanical Engineering 58, 3 (2007) 




ZAHORANSKÝ, R., STEIN, J.: Modelling a simple oscillatory system 
with friction under bi-axial base random excitation                     117

BAKHSHANDEH, K., SARANJAM, B.: Orthotropy ratio effect on dynamic 
response of a cylinder tube under moving pressure                       133

KLIMAN, V.: A probabilistic approach to fatigue life estimation under 
biaxial non-proportional random loading. Part I. Methodology            147

KLIMAN, V.: A probabilistic approach to fatigue life estimation under 
biaxial non-proportional random loading. Part II. Model experiment      168

Abstracts



Modelling a simple oscillatory system with friction under bi-axial base random excitation

RADÚZ ZAHORANSKÝ, JURAJ STEIN

The paper deals with the modelling and simulation of a single degree of freedom (SDOF) oscillatory system with friction damping, excited from the base by a low-intensity random narrow band acceleration signal in two mutually perpendicular axis -- a horizontal one (x-axis) and vertical one (x-axis), in which the system can move. Such a state of system excitation leads to a time dependent normal force affecting the magnitude of friction force. The stick-slip approach to the simulation of such a system is briefly described. Simulation results are presented and compared to a simpler approach based on the use of the signum function. Field measured data have been used to indicate the mutual interaction due to bi-axial random excitation. The presented methodology is of a generic nature and can be used in seating dynamics research as well as in any mechanical system with friction exposed to comparable settings of excitation subject to reasonable knowledge of parameters describing the friction interface.

Orthotropy ratio effect on dynamic response of a cylinder tube under moving pressure

KAMBIZ BAKHSHANDEH, BAHADOR SARANJAM

In this study, the effect of orthotropy ratio on dynamic response of a cylinder tube subjected to an internal moving pressure travelling at a constant velocity has been investigated by use of finite element method. In this paper the tube wall thickness is considered to be uniform throughout and small compared to mean radius of the tube. The intensity of the moving pressure as well as the velocity of the front is constant. Various cylinders with different length to diameter ratio are assumed and their dynamic behaviour is compared. Furthermore the influence of orthotropy ratio on dynamic behaviour is investigated. This study shows that dynamic deflection is about 1.8 to 2.55 times the static displacement depending on cylinder length to diameter ratios. For pressure speed lower than 30 m/s and higher than 200 m/s the changing of longitudinal elastic modulus has a little effect on dynamic amplification factor. A new concept of transition ratio is introduced.

A probabilistic approach to fatigue life estimation under biaxial non-proportional random loading
Part I. Methodology

VLADIMÍR KLIMAN

A new method of fatigue life distribution function prediction of the structure has been proposed for the random non-proportional biaxial loading. The method is based
– on the probability approach to respect the non-proportionality between normal (s) and shear (t) stress under random biaxial loading, and
– on the probabilistic interpretation of the loading characteristics and cyclic material properties in fatigue damage calculations.
The suggested methodology (Part I) of the structure fatigue life calculation takes into account the directional nature of fatigue damage, enables to calculate the fatigue life distribution function (FLDF) for an arbitrary plane and, on the base of comparison of fatigue life distribution functions calculated for the individual planes, enables to establish a plane with the maximum fatigue damage. The resulting FLDF (calculated for the most damaged plane and representing the service fatigue life of the structure) respects the random nature of cyclic materials properties, the random nature of the loading process and the random nature of the relation between normal (s) and shear (t) stress during the loading – non-proportionality in loading. The proposed methodology of life calculation is demonstrated and discussed on the concrete model example presented in Part II.

A probabilistic approach to fatigue life estimation under biaxial non-proportional random loading
Part II. Model experiment

VLADIMÍR KLIMAN

Concrete procedure of fatigue-life distribution function estimation for biaxial non-proportional random loading according to the method proposed in Part I is demonstrated on the model example. Straining of a critical spot of the structure is simulated by two independent random processes: sx(t) – time behaviour of normal stress, and tz(t) – time behaviour of shear stress. Computed fatigue-life distribution function for combined loading by the sx(t) and tz(t) processes, using the method proposed in Part I, has been compared with the experiments and with the evaluation of the fatigue life for loading by the sx(t) process only. Model experiment proved that the presented method of life estimation for biaxial non-proportional random loading is simple to apply. Computed representative fatigue-life distribution function enables to assess the fatigue reliability with probability interpretation.