Timothy M. Cameron

An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems

A method is proposed for analyzing the steady-state response of nonlinear dynamic systems. The method iterates to obtain the discrete Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there-rather than analytically describing the nonlinear terms in the frequency domain. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the steady-state response. The method is demonstrated by solving a problem with friction damping in which the excitation has multiple discrete frequencies.

Movement and sound generation by the toadfish swimbladder

Abstract. Although sound-producing (sonic) muscles attached to fish swimbladders are the fastest known vertebrate muscles, the functional requirement for such extreme speed has never been addressed. We measured movement of the swimbladder caused by sonic muscle stimulation in the oyster toadfish Opsanus tau and related it to major features of the sound waveform. The movement pattern is complex and produces sound inefficiently because the sides and bottom of the bladder move in opposite in and out directions, and both movement and sound decay rapidly. Sound amplitude is related to speed of swimbladder movement, and slow movements do not produce perceptible sound. Peak sound amplitude overlaps fundamental frequencies of the males mating call because of muscle mechanics and not the natural frequency of the bladder. These findings suggest that rapid muscle speed evolved to generate sound from an inefficient highly damped system.

Robust design optimization of structures through consideration of variation

Abstract Optimal structural design is considered under the presence of variation in loading, geometry and material properties. A Monte Carlo simulation is embedded in a genetic optimization algorithm to produce an output distribution for the objective function and constraint functions at each design evaluation. A hybrid genetic/non-linear-programming algorithm is used with a multi-objective formulation to locate a design that is optimal under the primary design criteria, but is simultaneously insensitive to variation. Cross-sectional, geometric and topological design changes are considered. Specific examples presented include a truss structure and an automotive inner body panel. The goal is to produce optimal designs that map better to the designers intent.

An Integrated Approach for Friction Damper Design

A procedure is outlined for determining the optimal design of friction dampers for high-speed turbomachinery blading. The procedure includes: An integration of bench test results with finite-element analysis and a single-mode blade model to ensure accuracy of the analytical model and improve reliability of the friction damper design; an extension of the single-mode blade model to predict the engine behavior of friction dampers; and a new way of viewing analytical and experimental results in terms of a damper performance curve to determine optimal design parameters, when the levels of excitation and damping in the system are unknown. Unique experiments are performed on a test disk in order to demonstrate and verify the accuracy of the design procedure.

The effect of loading on disturbance sounds of the Atlantic croaker Micropogonius undulatus: Air versus water

Physiological work on fish sound production may require exposure of the swimbladder to air, which will change its loading (radiation mass and resistance) and could affect parameters of emitted sounds. This issue was examined in Atlantic croaker Micropogonius chromis by recording sounds from the same individuals in air and water. Although sonograms appear relatively similar in both cases, pulse duration is longer because of decreased damping, and sharpness of tuning (Q factor) is higher in water. However, pulse repetition rate and dominant frequency are unaffected. With appropriate caution it is suggested that sounds recorded in air can provide a useful tool in understanding the function of various swimbladder adaptations and provide reasonable approximation of natural sounds. Further, they provide an avenue for experimentally manipulating the sonic system, which can reveal details of its function not available from intact fish underwater.

Fundamentals of anti-shudder durability: Part I - Clutch plate study

In automatic transmission technology development the degradation of paper friction plates has often been considered a major failure mechanism by which transmissions lose their anti-shudder characteristics. One of the most common degradation processes for paper friction plates is known as glazing. In this study, we focus on the relationship between friction plate glazing and anti-shudder durability in the Japanese Automobile Standards Organization (JASO) low velocity friction apparatus (LVFA) rig test following the procedure M349-98. We also investigate the impact of used friction plates and used oil on torque capacity durability as measured by an SAE No. 2 machine following the JASO procedure M348-95. We find that friction plate glazing has no correlation with anti-shudder durability. A completely glazed plate can have long anti-shudder durability but a barely glazed plate can have short anti-shudder durability. The basic reason for the lack of correlation is that friction plate glazing does not affect boundary friction coefficients. In almost all the cases studied, changes in fluid properties have a greater influence on boundary friction than does surface glazing.

Acoustical properties of the swimbladder in the oyster toadfish Opsanus tau

SUMMARY Both the swimbladder and sonic muscles of the oyster toadfish Opsanus tau (Linnaeus) increase in size with fish growth making it difficult to distinguish their relative contributions to sound production. We examined acoustics of the swimbladder independent of the sonic muscles by striking it with a piezoelectric impact hammer. Amplitude and timing characteristics of bladder sound and displacement were compared for strikes of different amplitudes. Most of the first cycle of sound occurred during swimbladder compression, indicating that the bladder rapidly contracted and expanded as force increased during the strike. Harder hits were shorter in duration and generated a 30 dB increase in amplitude for a 5-fold or 14 dB range in displacement. For an equivalent strike dominant frequency, damping, bladder displacement and sound amplitude did not change with fish size, i.e. equal input generated equal output. The frequency spectrum was broad, and dominant frequency was driven by the strike and not the natural frequency of the bladder. Bladder displacement decayed rapidly (ζ averaged 0.33, equivalent to an automobile shock absorber), and the bladder had a low Q (sharpness of tuning), averaging 1.8. Sound output of an acoustic source is determined by volume velocity (surface area × velocity), and bladder surface area, muscle dimensions and contraction amplitude increase with fish size. Therefore, larger fish will be capable of producing more intense sound. Because the bladder is a low Q resonator, its output will follow muscle contraction rates independent of its size and natural frequency.

Characterization and Generation of Male Courtship Song in Cotesia congregata (Hymenoptera: Braconidae)

Background Male parasitic wasps attract females with a courtship song produced by rapid wing fanning. Songs have been described for several parasitic wasp species; however, beyond association with wing fanning, the mechanism of sound generation has not been examined. We characterized the male courtship song of Cotesia congregata (Hymenoptera: Braconidae) and investigated the biomechanics of sound production. Methods and Principal Findings Courtship songs were recorded using high-speed videography (2,000 fps) and audio recordings. The song consists of a long duration amplitude-modulated “buzz” followed by a series of pulsatile higher amplitude “boings,” each decaying into a terminal buzz followed by a short inter-boing pause while wings are stationary. Boings have higher amplitude and lower frequency than buzz components. The lower frequency of the boing sound is due to greater wing displacement. The power spectrum is a harmonic series dominated by wing repetition rate ∼220 Hz, but the sound waveform indicates a higher frequency resonance ∼5 kHz. Sound is not generated by the wings contacting each other, the substrate, or the abdomen. The abdomen is elevated during the first several wing cycles of the boing, but its position is unrelated to sound amplitude. Unlike most sounds generated by volume velocity, the boing is generated at the termination of the wing down stroke when displacement is maximal and wing velocity is zero. Calculation indicates a low Reynolds number of ∼1000. Conclusions and Significance Acoustic pressure is proportional to velocity for typical sound sources. Our finding that the boing sound was generated at maximal wing displacement coincident with cessation of wing motion indicates that it is caused by acceleration of the wing tips, consistent with a dipole source. The low Reynolds number requires a high wing flap rate for flight and predisposes wings of small insects for sound production.

ATF Friction Properties and Shift Quality

Multiple plate disk clutches are used extensively for shifting gears in automatic transmissions. In a shift from one gear to another one or more clutches is engaging or disengaging. In these active clutches the automatic transmission fluid (ATF) and friction material experience large changes in pressure P, temperature T, and sliding speed v. The coefficient of friction, μ, of the ATF and friction material depends on v, P and T, and also changes during clutch engagement. Changes in μ can lead to vibration and poor shift quality if the ATF and clutch friction material are improperly selected. An in-depth theoretical understanding of the cause of vibration in shifting clutches is crucial in the development of a suitable ATF to work with a particular friction material. To understand the relationship between ATF friction properties and shifting clutch vibration we present a theoretical model that identifies several possible causes: (1) self-excitation instability, (2) a reduction in friction holding torque during engagement, or (3) resonance caused by periodic pressure oscillations. The ATF and friction material properties that affect these sources of vibration include the friction level, μ, and the friction slopes with respect to sliding speed ∂μ/∂v, pressure ∂μ/∂P, and temperature ∂μ/∂T. These properties must be carefully balanced to ensure that a clutch will deliver good shift quality and high torque capacity with effective vibration suppression.

Sensitivity of structural joint stiffnesses with respect to beam properties: A hybrid approach

Abstract In the optimization of frame structures the sizes of the beam members change, as do the stiffnesses of the joints where such members meet. In this paper a method for calculating the design sensitivities of structural joints to changes in the size of the members, using a finite element formulation, is presented. The method uses the initial joint stiffness, predicted from a more detailed shell finite element model or experimental data, to calculate the design sensitivies for any number of joint members. The method is developed into a computer program that does not require a finite element model of the joint. The formulation of the method and a test case are presented.