Study On Dynamic Vibration And Acoustic Behavior Of Violin

After reviewing the current status of violin study, a number of key issues with regard tothe dynamic vibration, mechanics and acoustics of violin were investigated in this thesis.The interaction between violin bow and strings is very complicated. Through the analysisof the Helmholtz motion of strings, the traditional stick-slip friction string vibration modeland modern string vibration theory, a pendulum frictional vibration model was developed inthis thesis. By taking account of the energy conversion and the vibration period in thebow-string vibration system, the vibration behavior of violin string can be modelled moreaccurately in the proposed model.In order to understand the physics of a bowed violin string and develop an accurate model,experimental measurement of the bowed string motion is crucial. In this thesis, a high-speedphotography based non-contact optical measurement system was designed to measure thestring motion without interference for movement when plucking or bowing a string fitted in aviolin. Through a novel optical system design and setting up an artificial marker on the string,the instantaneous motions of the marker in the X-Y and X-Z planes were simultaneouslyrecorded in every single image. The string vibration was videoed using a single high-speedvideo camera, generating more than10,000sequential images. An image processing algorithmbased on the Hough transform were developed to extract the marker position from a recordedimage at sub-pixel resolution. All the recorded sequential images were processedautomatically using the developed image processing algorithm, to track the three-dimensionalmotion of the marker. Experimental results showed that the proposed measurement systemcan accurately track the violin string motion and trajectory. The tracked motion verified thepredicted Helmholtz motion of the bowed string. The designed measurement system andimage processing algorithm provide a potential experimental tool for studying the mechanismof violin string vibration.The dynamic response of a violin is often divided into a deterministic region and astatistic region. However, the statistic region is not well understood. The bridge role in thedynamic response was firstly analyzed through four theoretical models: thedeterministic-statistical division model, the convolution model, the modal model, and thedynamic contact vibration model. The bridge mobility under in-plane and out-of-planeexcitations was then explored based on the dynamic contact vibration model for a real bridgeand a solid plate bridge. Theoretical analysis and numerical results showed that the bridgemobility is not only affected by the bridge geometrical structure and material, but the interaction among the strings, bridge and the front plate also plays a vital role. Especially, thecontact vibration boundaries in the two contact interfaces: strings-bridge, and bridge feet-topplate, have a great impact on the bridge mobility and as a result on the violin dynamicresponse，helping us gain an further understanding to the statistic region in the dynamicresponse of a violin.In order to verify the theoretical and numerical findings on bridge mobility, a novelexperimental system was designed on the basis of a piezoelectric dynamometer for bridgemobility analysis in this thesis. The dynamic forces in three directions acted on the front plateby the bridge when bowing a string with finger slurring on the finger board were recordedthrough the experiment system, and frequency responses were further analyzed. Experimentalresults confirmed the impact of contact vibration boundaries on the bridge mobility, whichwere discovered in the finite element simulation.Violin corpus plays a key role in the acoustic characteristics of violin. In this thesis,vibration mode analysis and frequency response analysis of the violin corpus were carried outby means of finite element simulation. The impact of the material and geometrical structure ofthe violin front and back plates, the bass bar and the sound-post on the violin vibrationcharacteristics were investigated. An experiment system based on acceleration sensors wasthen designed to measure the frequency response of violin. The experimental results verifiedthe simulated results.Based on the obtained theoretical and experimental findings on the vibration mechanismand mechanics of violin, the influence of the violin structures, materials, and interactionamong different parts on the sound quality were further analyzed, and the ways and methodsto improve the violin sound quality were proposed.