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It considers two beam examples with non-standard dynamic behavior, including layered cross laminated timber and beams with a periodically varying thickness profile. The study links dispersion measurement to practical evaluation of stiffness parameters across a wide frequency range, and discusses how dispersion relations can also address the performance of structural metamaterials with engineered band gaps and wave attenuation.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/measuring-dispersion-curves-for-bending-waves-in-beams-a-comparison-of-spatial-fourier-transform-and-inhomogeneous-wave-correlation/268810/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/measuring-dispersion-curves-for-bending-waves-in-beams-a-comparison-of-spatial-fourier-transform-and-inhomogeneous-wave-correlation/268810.png","ImageObject",300,407,{"name":92,"@type":93},"McGucket","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Which two methods are compared for measuring bending-wave dispersion?","Question",{"text":113,"@type":114},"The paper compares spatial Fourier transform and inhomogeneous wave correlation for acquiring bending-wave dispersion in beams.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What types of beams are used as examples in the comparison?",{"text":118,"@type":114},"Examples include layered cross laminated timber (wood with cross-laminated layers) and beams with a periodically varying thickness profile, described as phononic crystals.",{"name":120,"@type":111,"acceptedAnswer":121},"Why is measuring dispersion useful for evaluating beam properties?",{"text":122,"@type":114},"A direct dispersion measurement supports efficient assessment of stiffness parameters over a wide frequency range, and it also helps analyze structural metamaterials where band gaps attenuate waves.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},268810,1789437437,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":46,"preview_page_count":4},1236954412713,"https://us-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","COVER PAGE  \nDocument downloaded by @DAEL  \nTue Sep 15 01:57:00 2026  \nFor personal use  \nWhen automatic English translation is provided, only the original document  \nis authentic.  \nThe EAA cannot be held responsible of any translation error  \nBibliographical reference  \nMeasuring Dispersion Curves for Bending Waves in Beams: A Comparison of Spatial Fourier Transform and Inhomogeneous Wave Correlation, Bart Van Damme and Armin Zemp, Acta Acustica vol. 104 (Number 2), 2018,  \npp. 228-234  \nDOI  \n[https://doi.org/10.3813/AAA.919164](https://doi.org/10.3813/AAA.919164)  \nMeasuring Dispersion Curves for Bending Waves in Beams: A Comparison of Spatial Fourier Transform and Inhomogeneous Wave Correlation  \nBart Van Damme, Armin Zemp  \nEmpa, Laboratory for Acoustics/Noise Control, Ueberlandstrasse 129, 8600 Dübendorf, Switzerland. [bart.vandamme@empa.ch](bart.vandamme@empa.ch)  \nSummary  \nIn this paper, two methods to acquire the dispersion of bending waves in beams are compared: the spatial Fourier transform and inhomogeneous wave correlation. Two examples of beams with non-standard dynamic properties are given: layered beams made out of wood (cross laminated timber) and beams with a periodically varying thickness profile. Dynamic testing, such as modal analysis or wave speed measurements, can be used to determine the elastic properties of materials. A direct measurement of the dispersion facilitates an easy assessment of the stiffness parameters over a wide frequency range for layered beams made out of orthotropic layers. Theefficiency of structural metamaterials, elastic structures engineered to exhibit band gaps in which waves are quickly attenuated, can also be addressed through the dispersion relation.  \nPACS no. 43.40.At, 43.40.Cw, 43.20.Jr, 43.40.Tm  \n1. Introduction  \nNondestructive evaluation of material parameters can be done in a number of ways. Static testing, such as stressstrain tensile tests [1, 2] or three-point bending tests [3, 4] are widely used to determine stiffness properties such as Young’s modulus, Poisson ratio, and bending stiffness. These methods can only be performed on specified, often small, geometries (tensile tests), or address the stiffness locally between the support points (bending tests) . This is problematic for materials with large local elastic variability such as composites and wood [1, 2, 5] . Dynamic testing employs properties of waves and vibrations to indirectly calculate the underlying material parameters. For large structures, modal analysis is a popular method [3, 6, 7, 8, 9]: After measuring the eigenfrequencies, the results are compared to a model in which the unknown stiffness values are chosen in such a way that the difference between model and measurements is minimized. This model can be analytical for simple geometries, but often requires numerical techniques such as finite elements. Since the eigenfrequencies depend on the specimen’s boundary conditions, these have to be meticulously described in the model. Measuring the wave speed is another popular approach, mostly performed using ultrasound transducers [10] . The wave velocity can also be obtained for lower frequencies, e.g. using time-of-flight measurements [11] or phase measurements [12] . Once the  \nReceived 12 June 2017, accepted 8 August 2017.  \nvelocity of longitudinal, shear, surface and bending waves is known, it can be related to the stiffness. It is in general not straightforward to separate the different wave types, or account for geometrical dispersion effects. Additionally, early reflections in small specimens interact with the source signal, and thus complicate the wave speed measurement.  \nAlternatively, several methods are available to determine the dispersion relation of waves in a large frequency band, such as air-coupled ultrasound [13], waveform imaging [14] or the waveguide finite element method [15] . In this paper, we compare two of these methods for bending wave propagation in complex beams: spatial fast Fourier transf","cbCaiuFFv6coZZWd","https://ap.wps.com/l/cbCaiuFFv6coZZWd","pdf",928752,"English","# 1. Introduction\n# 2. Analysis methods\n## 2.1. Spatial Fourier transform","[{\"question\":\"Which two methods are compared for measuring bending-wave dispersion?\",\"answer\":\"The paper compares spatial Fourier transform and inhomogeneous wave correlation for acquiring bending-wave dispersion in beams.\"},{\"question\":\"What types of beams are used as examples in the comparison?\",\"answer\":\"Examples include layered cross laminated timber (wood with cross-laminated layers) and beams with a periodically varying thickness profile, described as phononic crystals.\"},{\"question\":\"Why is measuring dispersion useful for evaluating beam properties?\",\"answer\":\"A direct dispersion measurement supports efficient assessment of stiffness parameters over a wide frequency range, and it also helps analyze structural metamaterials where band gaps attenuate waves.\"}]","Measuring Dispersion Curves for Bending Waves in Beams - A Comparison of Spatial Fourier Transform and Inhomogeneous Wave Correlation | PDF"]