MODAL INTERACTIONS OF A RANDOMLY EXCITED HINGED–CLAMPED BEAM

✍ Scribed by D.S. CHO; W.K. LEE

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 180 KB
• Volume: 237
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3030

✦ Synopsis

An investigation into the response statistics of a hinged}clamped beam under broadband random excitation is made. By using Galerkin's method the governing equation is reduced to a system of non-autonomous non-linear ordinary di!erential equations. The Fokker} Planck equation is applied to generate a general "rst order di!erential equation in the dynamic moments of response co-ordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary di!erential equations. The analytical results for two-and three-mode interactions are also compared with results obtained by Monte Carlo simulation.

2000 Academic Press EI *w* *x* # A *w* *t* "!2c* *w* *t* #H* *w* *x* #P*(x*, t*), w*(0, t*)"0, *w*(0, t*) *x* "0, w*(l*, t*)"0, *w*(l*, t*) *x* "0, where E is the Young's modulus, b the width of beam, h the thickness of beam, the density of beam, I("bh/12) the area moment of inertia, c* the damping coe$cient, P* the exciting random force, H*("EA/2l*J * (*w*/*x*) dx*) the tension due to mid-plane stretching,