Instructions for Authors - Facultatea de Mecanica Craiova ...

SMAT2008V59THE RESPONSE OF A RANDOM EXCITATION NON-LINEAR SQUEEZE FILMOSCILLATORPetre STANAbstract. Nonlinear dynamic systems subject to random excitations are frequently met in engineering practice. The presentpaper consists of discussion on dynamic response of structures under random vibrations. They are random processes and commonlydescribed by spectral density functions. We present a method for estimating the power spectral density of the stationary response ofoscillator with a nonlinear restoring force under external stochastic wide-band excitation. An equivalent linear system is derived, fromwhich the power spectral density is deduced.The method of the stochastic equivalent linearization is based on the idea that a nonlinear system may be replaced by a linearsystem by minimizing the mean square error of the two systems. The most applied and convenient procedure is used by Yingfang, L.Zhao, Q. Chen [1,3] suggestion to estimate the linearization coefficients in context with Wen’s introduction of an analyticalexpression for the restoring force. This method has seen the broadest application because of their ability to accurately capture theresponse statistics over a wide range of response levels while maintaining relatively light computational burden.The basic idea of the statistical linearization in use here approach is to replace the original nonlinear system by a linear one.Assume that a single-degree of the sferic body with a mass m, caught at end of a spring with a elastic constant given ,when the lenghtof the undeformed spring is known, at random excitations in a liquid with the viscosity cofficient γ . for 20 0 C temperature.The sistem is excited by a force W which is a random process described by the spectral density function. As the force is notdeterministic, the response of the structure is expected to be random. If Gaussian assumption is adopted for the force and the structureis assumed to be nonlinear, the response is expected to be Gaussian distribution as well. As a result, we obtain the standard deviationof the respons,. the velocity variance of the single-degree of freedom system, the natural frequency of the equivalent linearized systemand the spectral density of the response. This is done in such a way that the difference between the two systems is minimised in somestatistical sense. In this way, the parameters of the linearised system are determined. The response of the nonlinear system isapproximated by the response of the equivalent linear system. So, the unknown statistics of the response are evaluated approximatingthe response as a Gaussian process, when the excitation is assumed to be Gaussian.Petre STAN, dipl. engineer, Metallurgical High School, Department of Mechanics, tel.+40 722 888 974, e-mail:petre_stan_marian@yahoo.comSMAT2008V60ANALYSIS OF SINGLE-DEGREE OF FREEDOM NON-LINEAR STRUCTURE UNDERGAUSSIAN WHITE NOISE GROUND EXCITATIONPetre STANAbstract. The present paper consists of discussion on dynamic response of structures under random load. They are randomprocesses and commonly described by spectral density functions. Assume that a single-degree of freedom structure is excited by aforce F which is a random process described by the spectral density function SF( ω ). As the force is not deterministic, the response ofthe structure is expected to be random. If Gaussian assumption is adopted for the force and the structure is assumed to be nonlinear,the response is expected to be Gaussian distribution as well. As a result, to obtain the standard deviation of the respons,. the velocityvariance of the single-degree of freedom system the relative acceleration of this structure and the spectral density of the response.Petre STAN, dipl. engineer, Metallurgical High School, Department of Mechanics, tel.+40 722 888 974, e-mail:petre_stan_marian@yahoo.com34