Parametric Excitation of a Pendulum With Bilinear Hysteresis

1970 ◽  
Vol 37 (4) ◽  
pp. 1061-1068 ◽  
Author(s):  
W. K. Tso ◽  
K. G. Asmis
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Viscous Damping ◽  
Sinusoidal Oscillation ◽  
Effective Mechanism ◽  
Steady State Responses ◽  
The Stability ◽  
State Responses ◽  
Steady State Solutions

The steady-state responses of a simple pendulum with a hinge exhibiting bilinear hysteretic moment-rotation characteristics and parametrically excited by a sinusoidal oscillation at the base is given. The stability of the steady-state solutions is discussed. It is shown that in contrast with viscous damping, the bilinear hysteresis is an effective mechanism to limit the growth of the response during parametric resonance.

NONLINEAR VIBRATION OF A CANTILEVER WITH A DERJAGUIN–MÜLLER–TOPOROV CONTACT END

2008 ◽  
Vol 08 (01) ◽  
pp. 25-40 ◽  
Author(s):  
Q.-Q. HU ◽  
C. W. LIM ◽  
L.-Q. CHEN
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Excitation Amplitude ◽  
Response Curves ◽  
State Response ◽  
Linearized Stability ◽  
Steady State Responses ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
State Responses

In this paper, the principal resonance is investigated for a cantilever with a contact end. The cantilever is modeled as an Euler–Bernoulli beam, and the contact is modeled by the Derjaguin–Müller–Toporov theory. The problem is formulated as a linear nonautonomous partial-differential equation with a nonlinear autonomous boundary condition. The method of multiple scales is applied to determine the steady-state response. The equation of response curves is derived from the solvability condition of eliminating secular terms. The stability of steady-state responses is analyzed by using the Lyapunov-linearized stability theory. Numerical examples are presented to highlight the effects of the excitation amplitude, the damping coefficient, and the coefficients related to the contact.

Estimating the Audiogram Using Multiple Auditory Steady-State Responses

2002 ◽  
Vol 13 (04) ◽  
pp. 205-224 ◽  
Author(s):  
Andrew Dimitrijevic ◽  
Sasha M. John ◽  
Patricia Van Roon ◽  
David W. Purcell ◽  
Julija Adamonis ◽  
...  
Keyword(s):  
Steady State ◽  
Correlation Coefficients ◽  
Behavioral Threshold ◽  
Behavioral Thresholds ◽  
Sensorineural Hearing Impairment ◽  
Steady State Responses ◽  
Auditory Steady State Responses ◽  
Tonal Stimuli ◽  
Conductive Hearing ◽  
State Responses

Multiple auditory steady-state responses were evoked by eight tonal stimuli (four per ear), with each stimulus simultaneously modulated in both amplitude and frequency. The modulation frequencies varied from 80 to 95 Hz and the carrier frequencies were 500, 1000, 2000, and 4000 Hz. For air conduction, the differences between physiologic thresholds for these mixed-modulation (MM) stimuli and behavioral thresholds for pure tones in 31 adult subjects with a sensorineural hearing impairment and 14 adult subjects with normal hearing were 14 ± 11, 5 ± 9, 5 ± 9, and 9 ± 10 dB (correlation coefficients .85, .94, .95, and .95) for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. Similar results were obtained in subjects with simulated conductive hearing losses. Responses to stimuli presented through a forehead bone conductor showed physiologic-behavioral threshold differences of 22 ± 8, 14 ± 5, 5 ± 8, and 5 ± 10 dB for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. These responses were attenuated by white noise presented concurrently through the bone conductor.

Weighted averaging of steady-state responses

2001 ◽  
Vol 112 (3) ◽  
pp. 555-562 ◽  
Author(s):  
M.Sasha John ◽  
Andrew Dimitrijevic ◽  
Terence W Picton
Keyword(s):  
Steady State ◽  
Weighted Averaging ◽  
Steady State Responses ◽  
State Responses
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