Parametric resonance of viscoelastic columns

Dynamic stability of a viscoelastic beam with frequency-dependent modulus

“…In the above papers, the complex modulus was considered to be independent of frequency, and the damping was simulated as a hysteretic damping model. Stevens and Evan-Iwanowski (1969) and Stevens (1969) presented analytical and experimental results to discuss the effect of the behavior of a viscoelastic material on the instability regions of a column, when the complex modulus of the viscoelastic material is influenced by frequency. Steidel (1989) pointed out that the damping ratio is a constant for hysteretic damping model; increases with frequency for a viscous damping model, and decreases as the frequency of actual damping increases.…”

“…Accordingly, a model that involves a frequency-dependent complex modulus captures actual damping more accurately than other models. Stevens and Evan-Iwanowski (1969) and Stevens (1969) applied the method of perturbation to determine dynamic instability. Lau et al (1982), presented an incremental harmonic balance (IHB) method to determine the parametric instability of viscous damped columns or beam systems.…”

Parametric Instability of a Beam Under Electromagnetic Excitation

“…Handoo and Sundararajan [15] experimentally investigated the simple resonance of a cantilevered column with an end mass subjected to speci"ed axial motion at its "xed end. Stevens and Evan-Iwanowski [22] observed the principal instability region of a viscoelastic simply supported column under a periodically axial force.…”

“…Chen and Yeh [21] assessed the simple and combination resonances of a general column carrying an axially oscillating mass. Stevens and Evan-Iwanowski [22] and Cederbaum and Mond [23] investigated the instability properties of viscoelastic columns under a periodic axial loading. GuK rgoK ze [24] studied the parameteric behavior of a viscoelastic beam subjected to a steady axial load and a transverse displacement excitation at one end.…”

Axisymmetric parametric resonance of polar orthotropic sandwich annular plates

“…Based on the complex modulus representation, Stevens [13] also investigated on the transverse vibration of initial curvature on the dynamic stability of a viscoelastic column under a periodic axial load. The analytical and experimental results of the effect of the viscoelastic material behavior on the parametric resonance of viscoelastic columns were presented by Stevens and Evan-Iwanowski [14]. Dost and Glockner [15] handled the dynamic stability of simply supported perfect viscoelastic columns by means of Laplace transforms.…”