Steady‐State Responses of One‐Dimensional Periodic Flexural Systems

1966 ◽  
Vol 39 (5A) ◽  
pp. 887-894 ◽  
Author(s):  
Eric E. Ungar
Keyword(s):  
Steady State ◽  
One Dimensional ◽  
Steady State Responses ◽  
State Responses

Steady-State Responses of a Beam on Idealized Strain-Hardening Foundations for a Moving Load

1973 ◽  
Vol 40 (4) ◽  
pp. 1040-1044 ◽  
Author(s):  
T. M. Mulcahy
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Elastic Foundation ◽  
Moving Load ◽  
Elastic Beam ◽  
Point Load ◽  
One Dimensional ◽  
Wide Range ◽  
Steady State Responses ◽  
State Responses

The steady-state responses to a point load moving with constant velocity on an elastic beam which rests on two types of idealized strain-hardening foundations are considered. The one-dimensional elastic-rigid foundation problem is shown to be equivalent to an elastic foundation with two traveling point loads. The opposing loads produce deflections which remain bounded for all load velocities and less than the corresponding elastic foundation results. The deflections of a one-dimensional elastic-perfectly plastic foundation are shown to be bounded for all load velocities. However, deflections significantly larger than the corresponding elastic foundation results occur over a wide range of velocities which are less than the elastic foundation critical velocity.

A New Spatial and Temporal Incremental Harmonic Balance Method for Obtaining Steady-State Responses of a One-Dimensional Continuous System

2016 ◽  
Author(s):  
X. F. Wang ◽  
W. D. Zhu
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Harmonic Balance ◽  
Jacobian Matrix ◽  
Harmonic Balance Method ◽  
Continuous System ◽  
One Dimensional ◽  
Spatial Coordinate ◽  
Steady State Responses ◽  
State Responses

A new spatial and temporal incremental harmonic balanced (STIHB) method is developed for obtaining steady-state responses of a one-dimensional continuous system. In the STIHB method, Galerkin procedure for a governing partial differential equation (PDE) in the spatial coordinate to obtain a set of ordinary differential equations (ODEs) and the harmonic balance procedure for the set of ODEs in the temporal coordinate to obtain the harmonic balanced residual are combined to be Galerkin procedures for the PDE in the spatial and temporal coordinates to simultaneously obtain the spatial and temporal harmonic balanced residual, and integrations in Galerkin procedures are replaced by the fast discrete sine transform (DST) or fast discrete cosine transform (DCT) in the spatial coordinate and the fast Fouriour transform (FFT) in the temporal coordinate, which is referred to as a DST-FFT or DCT-FFT procedure. The harmonic balanced residual for an arbitrary second-order PDE can be automatically and efficiently obtained by a computer program when the expression of the PDE is given, where numbers of basis functions in the spatial and temporal coordinates can be arbitrarily selected and no more extra derivations are needed. There are two versions of the STIHB method. In the simple version, the DST-FFT or DCT-FFT procedure to calculate the harmonic balanced residual and Broyden’s method that is a quasi-Newton method are combined to find solutions that make the residual vanish, which can be used to construct steady-state solutions of the PDE. In the complex version, the exact Jacobian matrix is derived and used in Newton-Raphson method to achieve faster convergence. While its derivation is complex, the exact Jacobian matrix for the arbitrary PDE can be automatically and efficiently obtained by following a calculation routine when the linearized expression of the PDE is given, and it can be easily implemented by a computer program. The exact Jacobian matrix can also be used to study stability of steady-state responses, where no more extra derivations are needed. The STIHB method is demonstrated by studying the transverse vibration of a string with geometric nonlinearity; its frequency-response curves with weak and strong nonlinearities and different numbers of trial functions are calculated, and stability of solutions on the curves is studied.

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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