The Stochastic Vibration Analysis On Rectangular Orthotropic Membranes

Membrane materials have been found increasing applications in structuralengineering, for example, the tension membrane structure. Due to its light weight andlarge flexibility, it can construct large-span spatial structure in the stadium, exhibitionhall and other buildings. Because of its low stiffness, low natural frequency and smalldamping, architectural membrane structure is prone to large deflection vibrationphenomenon. Impact load size of architectural membrane structure is random in naturalconditions, so displacement response of the membrane will be random. Large deflectionvibration will cause natural disaster of the membrane structure, for example tearingfailure, relaxation and so on, which will bring about casualties and property losses. Soit’s necessary and important to accurately calculate deflection response of membranestructures under dynamic load.This paper research random vibration characteristics of building membrane underimpact load and master the law of its random deflection response to provide theoreticalbasis for building membrane structure design. Researching random vibration of buildingmembrane structure in random impact load (such as storms, hail, residue with wind,etc.), and grasping displacement response mean value function, mean square value,autocorrelation and power spectrum function accurately were not only have importanttheoretical significance but also provides the theory basis for design, construction andthe second tensioning in membrane structure engineering. it can ensure the normal useof membrane structure and prevent or reduce engineering accidents.This paper established stochastic governing differential equation of rectangularorthotropic membrane with edges clamped under large deflection, when it is confrontedwith random impact loading. We applied perturbation method and the random vibrationtheory to solve it and obtained displacement response mean value function, meansquare value, autocorrelation and power spectrum function of the membrane surface.Under a certain pretension, stochastic simulation experiment about orthotropic ZZFmembrane chosen which commonly applied in the membrane structural engineeringwas carried out. In trials, the ball with random velocity hit the membrane surface tosimulate random impact load; displacement sensors are used to measure displacementtime history curves of the three measuring points elected and speedometer is used tomeasure the speeds of the ball. At last, a abundant of deflection response sample curves and random velocity of ball were obtained. With the theory of random process to dealwith the data relating to test, the probability density curve of ball speed difference isobtained which obeys gaussian distribution, and the stability of ball speed differencestochastic process is verified by the rounds method. Deflection response mean andautocorrelation function, the mean square value and the power spectrum function ofmeasuring points were obtained by statistical analysis for sample data; and comparedwith the theoretical values, the correctness of the theoretical calculation can be verified.At the same time, we mastered some properties of random vibration of membrane.