Changes In Fundamental Frequency Research Articles

Support condition monitoring of monopile-supported offshore wind turbines in layered soil based on model updating

Monopile-supported offshore wind turbines (OWTs) are dynamically sensitive structures whose fundamental frequencies may be close to those of environmental and turbine-related excitations. The changes in fundamental frequencies caused by pile-soil interaction (PSI) may result in unwanted resonance and serious O&M (Operation and Maintenance) issues, which have been identified as major challenges in the research field. Therefore, a novel model updating framework with an implicit objective function is proposed to monitor both the stiffness and damping variation of the OWT system based on the measured vibration characteristics, which is further verified by laboratory tests. In particular, layered soil was considered in the tests to simulate the practical soil conditions of Chinese seas. Different pile lengths were introduced to consider the long-term PSI effects for rigid piles and slender piles. The results showed that the variation in the fundamental frequency is significantly reduced in layered soil compared with the pure sand scenario. For the OWT systems in layered soil, the variation in foundation stiffness is negatively related to the burial depth under cyclic loading. The proposed model updating framework is proven reliable for support condition monitoring of OWT systems in complicated soil conditions.

Effect of Voice Projection Training on Acoustic and Auditory-Perceptual Characteristics of Voice in Tamil-Speaking Imams

Imams are professional voice users at risk of developing voice problems. Speech-Language Pathologists need to provide intervention programs to target risk factors associated with voice disorders and improve the voice quality of Imams. However, studies examining the effect of vocal training for Imams are limited in the literature. This study attempted to document the acoustic and auditory-perceptual changes in the voices of Tamil-speaking Imams with a voice projection training program. Eleven Tamil-speaking Imams participated in a voice projection training program. Voice samples were recorded at four specific time points before, during, and after the voice projection training. These recordings were subjected to various acoustic analyses (AVQI, Dr Speech, and MDVP) and auditory-perceptual analysis (CAPE-V) to determine the changes with the voice projection training. Auditory-Perceptual analysis carried out by five experienced SLPs suggested significant changes in the voice quality of the participants with voice projection training. High inter-rater reliability was observed across the judges as well. We observed positive changes in several acoustic measures indicated within AVQI, Dr Speech, and MDVP software. These primarily included changes in fundamental frequency, noise related measures (HNR, SNR), and perturbation measures. Voice projection training positively impacts the acoustic and auditory-perceptual characteristics of the voices of Tamil-speaking Imams.

Empirical Evaluation of the Role of Vocal Fold Collision on Relative Fundamental Frequency in Voicing Offset

Relative fundamental frequency (RFF) is an acoustic measure of changes in fundamental frequency during voicing transitions. The physiological mechanisms underlying RFF remain unclear. Recent modeling suggests that changes in RFF during voicing offset are due to decreases in overall system stiffness as a direct result of the cessation of vocal fold collision. To evaluate this finding empirically, here we examined whether variable timing between the end of vocal fold collision and the final voicing cycle used to calculate RFF explained the variability in RFF across individual voicing offset utterances. RFF during voicing offset was calculated from /ifi/ utterances produced by 35 participants under endoscopy, with and without vocal effort. RFF was calculated via two methods, in which utterances were aligned by (1) the end of vocal fold collision, or (2) the end of voicing. Analyses of variance were used to determine the effects of vocal effort and RFF method on the mean and standard deviation of RFF. Aligning by vocal fold collision resulted in statistically significantly lower standard deviations. RFF means were statistically higher using the collision method; however, the degree of vocal effort was statistically significant regardless of the method. These results provide empirical evidence to support that decreases in RFF during voicing offset are a result of decreases in system stiffness due to termination of vocal fold collision.

Goat kid recognition of their mothers' calls is not impacted by changes in fundamental frequency or formants

AbstractFeatures varying more between than within individuals are considered as potential cues for individual recognition. According to the source‐filter theory of vocal production, the fundamental frequency of mammals' vocalizations depends on the characteristics of vocal folds, while Formants are determined by the characteristics of the vocal tract. Goat mothers and their kids (Capra hircus) display mutual recognition, and both source‐related parameters (f0) and filter‐related ones (Formants) have been shown to be individualized. Here, we aimed to identify if f0 and Formants are used by goat kids to recognize their mother's vocalizations. To do this, we independently modified these parameters in calls of goat mothers to different degrees (within or exceeding the range of natural intra‐individual variability), and we played back these modified calls to their kids. We found no effect of f0 or Formants modification on the kids' reactions. Further analyses revealed that goat kids emitted fewer calls when modifications to f0 resulted in higher values of the first energy quartile, suggesting a role of the distribution of energy in the spectrum in maternal recognition. We propose that either: (i) f0 and Formants are not involved in goats' maternal recognition; (ii) goat kids have a tolerance for variation when recognizing their mother's calls that exceeds the performed shifts in these parameters; or (iii) goat kid maternal recognition is based on a combination of features and might be more flexible than previously thought, such that when one feature is modified, kids focus on other features. The effect of the spectral energy distribution modification on the kid responses, which depends both on f0 and Formant heights, suggests that (iii) is a likely explanation. Our findings support the hypothesis of complex individual acoustic recognition from the early stages of development in ungulates.

Effects of bolted connections’ properties on natural dynamic characteristics of corner-supported modular steel buildings

Corner-supported modular steel building, made of volumetric units, is an efficient construction system for the next generation of industrialised building construction. The mechanical performance of joints, including inter-modular connections and beam-to-column connections, or so-called intra-modular connections, and their effects on the dynamic behaviour of these structures have remained a research hotspot in the design of modular buildings. This paper studies the effect of bolted vertical inter-module and intra-modular connections’ characteristics on the dynamic properties of a corner-supported modular steel frame using an experimental program and numerical simulations. To that end, a half-scaled vertically stacked 3-storey modular building, instrumented with highly sensitive accelerometers, is used to scrutinise the effect of different configurations of inter- and intra-modular connections on the dynamic characteristics of the structure. The acceleration responses of the system under randomly generated artificial vibrations and pure ambient vibrations are synchronously recorded. Then, dynamic characteristics of the modular building are extracted by employing the Operational Modal Analysis (OMA). Finally, finite element models are developed, and a comprehensive parametric study is conducted to verify the experimental results and evaluate the influence of connections’ behaviour on the frequencies of the structure. The results indicate that while the behaviour of inter-connection has no significant effect on the natural frequency of the building, variation of intra-connections’ properties and their configurations can lead to a change in fundamental frequency of modular buildings. Shear stiffness of connections was found to be the most effective factor influencing the frequencies of modular structures.

A Scoping Literature Review of Relative Fundamental Frequency (RFF) in Individuals with and without Voice Disorders

Relative fundamental frequency (RFF) is an acoustic measure that characterizes changes in voice fundamental frequency during voicing transitions. Despite showing promise as an indicator of vocal disorder and laryngeal muscle tension, the clinical adoption of RFF remains challenging, partly due to a lack of research integration. As such, this review sought to provide summative information and highlight next steps for the clinical implementation of RFF. A systematic literature search was completed across 5 databases, yielding 37 articles that met inclusion criteria. Studies most often included adults with and without tension-based voice disorders (e.g., muscle tension dysphonia), though patient and control groups were directly compared in only 32% of studies. Only 11% of studies tracked therapeutic progress, making it difficult to understand how RFF can be used as a clinical outcome. Specifically, there is evidence to support within-person RFF tracking as a clinical outcome, but more research is needed to understand how RFF correlates to auditory-perceptual ratings (strain, effort, and overall severity of dysphonia) both before and after therapeutic interventions. Finally, a marked increase in the use of automated estimation methods was noted since 2016, yet there remains a critical need for a universally available algorithm to support widespread clinical adoption.

Voice, Speech, and Clinical Aspects During Pregnancy: A Longitudinal Study

Pregnancy involves anatomical, physiological, and metabolic changes in a woman's body. However, the effects of these changes on the voice remains unclear, particularly regarding the clinical characteristics. We aimed to evaluate changes in vocal and speech acoustic measures and the relationship between them and clinical aspects in women during pregnancy. A prospective, longitudinal study was carried out with 41 low risk, adult, pregnant women, followed for prenatal care. Demographic and anthropometric data as well as lifestyle habits and health conditions were collected. Voice recordings of sustained vowels, and automatic and spontaneous speech were held over each trimester and analyzed by PRAAT®to evaluate acoustic, aerodynamic, and articulatory measures. There were no changes in fundamental frequency, jitter, shimmer, and harmony to noise ratio during pregnancy. Maximum phonation time (MPT), pause rate, and pause duration reduced at the end of pregnancy. MPT was lower in sedentary pregnant women. The fundamental frequency peak rate was higher in eutrophic participants and lower in the third trimester in women with BMI ≥25 kg/m2. Pause rate was higher in pregnant women with BMI ≥25 kg/m2. There was no relationship between sleep quality, reflux, and vocal symptoms and acoustic and aerodynamic measures. Differences were shown in MPT and temporal pause measurements during pregnancy. Acoustic measurements did not change. There was a relationship between acoustic and aerodynamic measures and clinical variables (BMI, physical activity, and body mass gain).

The Effects of Intensive Voice Treatment in Mandarin Speakers With Parkinson's Disease: Acoustic and Perceptual Findings.

This study investigated the effects of intensive voice treatment on subjective and objective measures of speech production in Mandarin speakers with hypokinetic dysarthria. Nine Mandarin speakers with hypokinetic dysarthria due to Parkinson's disease received 4 weeks of intensive voice treatment (4 × 60 min per week). The speakers were recorded reading a passage before treatment (PRE), immediately after treatment (POST), and at 6-month follow-up (FU). Listeners (n = 15) rated relative ease of understanding (EOU) of paired speech samples on a visual analogue scale. Acoustic analyses were performed. Changes in EOU, vocal intensity, global and local fundamental frequency (f o) variation, speech rate, and acoustic vowel space area (VSA) were examined. Increases were found in EOU and vocal intensity from PRE to POST and from PRE to FU, with no change found from POST to FU. Speech rate increased from PRE to POST, with limited evidence of an increase from PRE to FU and no change from POST to FU. No changes in global or local f o variation or in VSA were found. Intensive voice treatment shows promise for improving speech production in Mandarin speakers with hypokinetic dysarthria. Vocal intensity, speech rate, and, crucially, intelligibility, may improve for up to 6 months posttreatment. In contrast, f o variation and VSA may not increase following the treatment. https://doi.org/10.23641/asha.19529017.

Interdependencies between Dynamic Response and Crack Growth in a 3D-Printed Acrylonitrile Butadiene Styrene (ABS) Cantilever Beam under Thermo-Mechanical Loads.

Acrylonitrile butadiene styrene (ABS) is the most commonly used thermoplastic printing material for fused deposition modelling (FDM). FDM ABS can be used in a variety of complex working environments. Notably, the thermo-mechanical coupled loads under complex operating conditions may lead to cracking and ultimately catastrophic structural failure. Therefore, it is crucial to determine the crack depth and location before a structural fracture occurs. As these parameters affect the dynamic response of the structure, in this study, the fundamental frequency and displacement amplitude response of a cracked 3D-printed ABS cantilever beam in a thermal environment were analytically and experimentally investigated. The existing analytical model, specifically the torsional spring model used to calculate the fundamental frequency change to determine the crack depth and location was enhanced by the proposed Khan-He model. The analytical relationship between the displacement amplitude and crack was established in Khan-He model and validated for the first time for FDM ABS. The results show that a reduced crack depth and location farther from the fixed end correspond to a higher fundamental frequency and displacement amplitude. An elevated ambient temperature decreases the global elastic modulus of the cracked beam and results in a lower fundamental frequency. Moreover, a non-monotonic relationship exists between the displacement amplitude and ambient temperature. The displacement amplitude is more sensitive to the crack change than the fundamental frequency in the initial stages of crack growth.

Voice emotion recognition by Mandarin-speaking pediatric cochlear implant users in Taiwan.

ObjectivesTo explore the effects of obligatory lexical tone learning on speech emotion recognition and the cross‐culture differences between United States and Taiwan for speech emotion understanding in children with cochlear implant.MethodsThis cohort study enrolled 60 cochlear‐implanted (cCI) Mandarin‐speaking, school‐aged children who underwent cochlear implantation before 5 years of age and 53 normal‐hearing children (cNH) in Taiwan. The emotion recognition and the sensitivity of fundamental frequency (F0) changes for those school‐aged cNH and cCI (6–17 years old) were examined in a tertiary referred center.ResultsThe mean emotion recognition score of the cNH group was significantly better than the cCI. Female speakers' vocal emotions are more easily to be recognized than male speakers' emotion. There was a significant effect of age at test on voice recognition performance. The average score of cCI with full‐spectrum speech was close to the average score of cNH with eight‐channel narrowband vocoder speech. The average performance of voice emotion recognition across speakers for cCI could be predicted by their sensitivity to changes in F0.ConclusionsBetter pitch discrimination ability comes with better voice emotion recognition for Mandarin‐speaking cCI. Besides the F0 cues, cCI are likely to adapt their voice emotion recognition by relying more on secondary cues such as intensity and duration. Although cross‐culture differences exist for the acoustic features of voice emotion, Mandarin‐speaking cCI and their English‐speaking cCI peer expressed a positive effect for age at test on emotion recognition, suggesting the learning effect and brain plasticity. Therefore, further device/processor development to improve presentation of pitch information and more rehabilitative efforts are needed to improve the transmission and perception of voice emotion in Mandarin.Level of evidence3.

The effects of theatre-based vocal empowerment on young Egyptian women's vocal and language characteristics.

This study investigates the impact of a theatre-based vocal empowerment program on the vocal and language characteristics and the self-perceptions of young bilingual Egyptian women. The program used applied theatre, a dramatic practice that promotes civic action by utilizing improvisational techniques to engage participants in exploring solutions to self-identified community concerns. These techniques supported participants’ pursuit of vocal empowerment: the ability to comfortably express their intended content with a clear audible voice, accompanied by the belief that what they had to say was worthwhile. The program was implemented in Alexandria and Aswan, two Egyptian cities in different regions of the country, with distinct socio-economic profiles. Thirty-six young women from Aswan and nineteen from Alexandria participated. The program was facilitated in Arabic, for 90 minutes per day over twelve consecutive days in 2018. Participants in both groups spoke Arabic as a home language and studied English in school settings but differed in their educational experiences and English proficiency. The vocal and language characteristics of each participant were tested in Arabic and English pre- and post- program using a spontaneous speech task and a reading aloud task. Their self-perceptions were evaluated through a vocal self-perception survey. Results indicated that participants responded differently in each city. In Alexandria, participants showed significant improvement in language skills (e.g., mean length of utterance). In contrast, participants in Aswan showed a significant change in fundamental frequency. Overall, the self-surveys indicated that all participants experienced an increased sense of confidence, a stronger belief in self-authorship, and an increased desire to voice their opinions clearly in public; however, there were subtle differences between the groups. In analyzing these results, we conclude that to design effective vocal empowerment outreach programs internationally, it is necessary to consider participants’ cultural backgrounds, language diversity, and socio-economic status.

A Longitudinal Study of Speech Acoustics in Older French Females: Analysis of the Filler Particle euh across Utterance Positions

Aging in speech production is a multidimensional process. Biological, cognitive, social, and communicative factors can change over time, stay relatively stable, or may even compensate for each other. In this longitudinal work, we focus on stability and change at the laryngeal and supralaryngeal levels in the discourse particle euh produced by 10 older French-speaking females at two times, 10 years apart. Recognizing the multiple discourse roles of euh, we divided out occurrences according to utterance position. We quantified the frequency of euh, and evaluated acoustic changes in formants, fundamental frequency, and voice quality across time and utterance position. Results showed that euh frequency was stable with age. The only acoustic measure that revealed an age effect was harmonics-to-noise ratio, showing less noise at older ages. Other measures mostly varied with utterance position, sometimes in interaction with age. Some voice quality changes could reflect laryngeal adjustments that provide for airflow conservation utterance-finally. The data suggest that aging effects may be evident in some prosodic positions (e.g., utterance-final position), but not others (utterance-initial position). Thus, it is essential to consider the interactions among these factors in future work and not assume that vocal aging is evident throughout the signal.

Speech modifications in interactive speech: effects of age, sex and noise type.

When attempting to maintain conversations in noisy communicative settings, talkers typically modify their speech to make themselves understood by the listener. In this study, we investigated the impact of background interference type and talker age on speech adaptations, vocal effort and communicative success. We measured speech acoustics (articulation rate, mid-frequency energy, fundamental frequency), vocal effort (correlation between mid-frequency energy and fundamental frequency) and task completion time in 114 participants aged 8-80 years carrying out an interactive problem-solving task in good and noisy listening conditions (quiet, non-speech noise, background speech). We found greater changes in fundamental frequency and mid-frequency energy in non-speech noise than in background speech and similar reductions in articulation rate in both. However, older participants (50+ years) increased vocal effort in both background interference types, whereas younger children (less than 13 years) increased vocal effort only in background speech. The presence of background interference did not lead to longer task completion times. These results suggest that when the background interference involves a higher cognitive load, as in the case of other speech of other talkers, children and older talkers need to exert more vocal effort to ensure successful communication. We discuss these findings within the communication effort framework. This article is part of the theme issue 'Voice modulation: from origin and mechanism to social impact (Part II)'.

A numerical study on near-field pressure fluctuations of symmetrical and anti-symmetrical flapping modes of twin-jet using a high-resolution shock-capturing scheme

Screeching supersonic jets appears at off-design operating conditions and is perceived as an intense tonal noise. In a twin nozzle configuration, mutual interactions between the two jet plumes may occur with various coupling modes developing depending on the operating conditions and lateral distance between the jets. The investigation of the detailed flow behaviors and near-field pressure fluctuations with relevance to the twin jets system, the analysis of the developed instabilities, will enhance understanding of fundamental features associated with jets located close to each other.In the present study, the single jet is considered first to assess the large eddy simulation (LES) approach used and the near-field pressure fluctuation predictions. Based on the validated solver, twin jets are simulated. Two different twin-nozzle configurations having different separation distance or nozzle-to-nozzle centerline spacing are scrutinized for the same Mach number of 1.358. Notably, the twin jets are screeching by the coupling mode for both set-ups; however, the case of closer inter-nozzle distance presents a symmetrical dominant flapping mode, while the other case shows an anti-symmetrical flapping mode. The strength of the pressure fluctuation at the fundamental frequency changes depending on the location of the observer point (upstream or downstream) and the reference plane (twin-jet and normal to the twin-jet plane). The screech tones of the two cases, observable in the upstream region, are significantly different in the normal to the twin-jet plane direction because of the phase difference of fluctuating pressure. However, the first harmonic component remains strong, regardless of the flapping mode. It is also observed that, at the fundamental frequency, the amplitude of the pressure fluctuation at downstream locations is found to be strong in the normal to the twin-jet plane when the symmetrical flapping mode occurs. This feature is also observed in the twin-jet plane in the case of the opposite mode. By analyzing the developed vertical structures and performing correlation analyses of pressure fluctuations along jet shear layers, the periodicity of the flow in the downstream region with relevance to the fundamental frequency is revealed.

A generalized differential quadrature-based computational model for describing free vibrations behavior of functionally graded circular plates around buckled configuration

In the present article, the vibrational behavior of buckled functionally graded (FG) circular plates with clamped and simply-supported edge conditions is described. Considering von Karman’s assumptions, the geometric nonlinearity is incorporated into the Kirchhoff plate theory and the nonlinear governing equations of motion are then derived using Hamilton’s principle. Critical buckling load and linear natural frequencies are first calculated using the generalized differential quadrature (GDQ) method. Afterward, the postbuckling characteristics of the circular plate are obtained via solving the nonlinear governing equations, directly. By several comparative studies, the reliability of the presented model is revealed. Finally, the fundamental natural frequency of the plate is evaluated for prebuckled and postbuckled configurations. The effects of material property and boundary conditions on the static bifurcation diagram and the natural frequency of the initial undeflected and bucked plate are studied. It is found that the trend of the fundamental natural frequency changes with the applied radial load around the prebuckled configuration is unlike the one around the buckled configuration.

Infant Pitch and Timbre Discrimination in the Presence of Variation in the Other Dimension.

Adult listeners perceive pitch with fine precision, with many adults capable of discriminating less than a 1 % change in fundamental frequency (F0). Although there is variability across individuals, this precise pitch perception is an ability ascribed to cortical functions that are also important for speech and music perception. Infants display neural immaturity in the auditory cortex, suggesting that pitch discrimination may improve throughout infancy. In two experiments, we tested the limits of F0 (pitch) and spectral centroid (timbre) perception in 66 infants and 31 adults. Contrary to expectations, we found that infants at both 3 and 7months were able to reliably detect small changes in F0 in the presence of random variations in spectral content, and vice versa, to the extent that their performance matched that of adults with musical training and exceeded that of adults without musical training. The results indicate high fidelity of F0 and spectral-envelope coding in infants, implying that fully mature cortical processing is not necessary for accurate discrimination of these features. The surprising difference in performance between infants and musically untrained adults may reflect a developmental trajectory for learning natural statistical covariations between pitch and timbre that improves coding efficiency but results in degraded performance in adults without musical training when expectations for such covariations are violated.

Effects of Cognitive Load on the Categorical Perception of Mandarin Tones.

Purpose This study investigated the effect of cognitive load (CL) on the categorical perception (CP) of Mandarin lexical tones to discuss the application of the generalized pulse-skipping hypothesis. This hypothesis assumes that listeners might miss/skip temporal pulses and lose essential speech information due to CL, which consequently affects both the temporal and spectral dimensions of speech perception. Should CL decrease listeners' pitch sensitivity and impair the distinction of tone categories, this study would support the generalized pulse-skipping hypothesis. Method Twenty-four native Mandarin-speaking listeners were recruited to complete a dual-task experiment where they were required to identify or discriminate tone stimuli while concurrently memorizing six Chinese characters or graphic symbols. A no-load condition without a memory recall task was also included as a baseline condition. The position of categorical boundary, identification slope, between- and within-category discrimination, and discrimination peakedness were compared across the three conditions to measure the impact of CL on tone perception. The recall accuracy of Chinese characters and graphic symbols was used to assess the difficulty of memory recall. Results Compared with the no-load condition, both load conditions showed a boundary shift to Tone 3, shallower identification slope, poorer between-category discrimination, and lower discrimination peakedness. Within-category discrimination was negatively affected by CL in the graphic symbol condition only, not in the Chinese character condition. Conclusions CL degraded listeners' sensitivity to subtle fundamental frequency changes and impaired CP of Mandarin lexical tones. This provides support for the generalized pulse-skipping hypothesis. Besides, the involvement of lexical information modulated the effect of CL.

Discomfort-related changes of call rate and acoustic variables of ultrasonic vocalizations in adult yellow steppe lemmings Eolagurus luteus

Potential of ultrasonic vocalizations (USVs) to reflect a degree of discomfort of a caller is mostly investigated in laboratory rats and mice but poorly known in other rodents. We examined 36 (19 male, 17 female) adult yellow steppe lemmings Eolagurus luteus for presence of USVs during 8-min experimental trials including 2-min test stages of increasing discomfort: isolation, touch, handling and body measure. We found that 33 of 36 individuals vocalized at isolation stage, i.e., without any human impact. For 14 (6 male and 8 female) individuals, a repeated measures approach revealed that increasing discomfort from isolation to handling stages resulted in increase of call power quartiles and fundamental frequency, whereas call rate remained unchanged. We discuss that, in adult yellow steppe lemmings, the discomfort-related changes of USV fundamental frequency and power variables follow the same common rule as the audible calls of most mammals, whereas call rate shows a different trend. These data contribute to research focused on searching the universal acoustic cues to discomfort in mammalian USVs.

1 g Shaking table test of segmental tunnel in sand under near-fault motions

A 1 g shaking table test is conducted to investigate seismic responses of a segmental tunnel in sand under near-fault motions. The tunnel model is assembled with segments, bolts and rubber strips and embedded in a shallow sand ground. The test facility, design and preparation of the tunnel model and the sand ground, as well as selected earthquake motions, are presented in detail. Dynamic responses obtained from the experiment include accelerations of the sand ground and the tunnel model, strains of segments, diametric deformations of the tunnel section, as well as bolt tensions and rotation of radial joints. Results show that the ground fundamental frequency changes with different input motions due to sand nonlinearities, and the deformation of the segmental tunnel is concentrated on radial joints. Moreover, near-fault motions would significantly aggravate the seismic response of both the sand ground and the segmental tunnel compared to far-field motions. Physical mechanisms contributed to the observation that near-fault motions would lead to larger shear strains of ground, especially when the ground fundamental frequency decreases, are also discussed.

Research on non-collinear mixing test method of concrete nonlinear ultrasound

ABSTRACT Considering that the nonlinear ultrasonic mixing method is seldom used in concrete detection, for the feasibility of the non-collinear mixing method detecting concrete, this study conducts ultrasonic nonlinear research on sum frequency longitudinal wave scattered by two intersecting ultrasonic transverse waves. Based on non-collinear mixing theory, the paper analyses the angle between two incident fundamental frequency waves and the relationship between incident angle and frequency ratio to form non-collinear mixing testing system. Testing on concrete beams, the relationship between the nonlinear coefficient and the respective frequency and amplitude of the incident fundamental waves have been explored. The results show that mixing wave appeared only when the frequency ratio of two fundamental waves was in the range of 0.54–1.87. The nonlinear coefficient gradually decreases with the increase of frequency and amplitude of the fundamental waves. The amplitudes of the fundamental and the mixing wave increase with the rising of the frequency of the fundamental wave. Compared with the test results of the higher harmonic ratios method, the nonlinear coefficient of non-collinear mixing method is more sensitive to the change of fundamental frequency and amplitude, which verified the feasibility of non-collinear mixing method in detecting concrete damage.