Ce travail de recherche est une contribution à l'étude de la propagation d'ondes élastiques dans les milieux granulaires. L'objectif principal est d'analyser deux aspects particuliers qui influencent la propagation, d'une part le degré de liberté en rotation des grains et d'autre part les non-linéarités de contact. Dans le cadre de ce travail, des structures granulaires périodiques et unidimensionnelles sont étudiées.L'apport principal de ce travail est la mise en évidence expérimentale et la modélisation d'ondes de rotation pures dans une chaîne granulaire composée de billes magnétiques. Le point de départ de la modélisation est la description du contact en torsion entre deux sphères jusqu'au premier ordre de non-linéarité. Pour un moment de torsion oscillant, il est montré un comportement de type purement hystérétique quadratique. Généralement, cette non-linéarité coexiste avec d'autres types de non-linéarités (quadratique, clappement, ...) et certains de ses effets n'ont jamais été observés. Pour la première fois, la distorsion d'ondes impulsionnelles par une non-linéarité hystérétique est mise en évidence et modélisée.D'autres effets liés à la dispersion et aux non-linéarités de contact dans une chaîne diatomique sont étudiés théoriquement et expérimentalement. En particulier, la génération de l'harmonique 2 des ondes de compression présente une richesse intéressante selon leur caractère propagatif, fortement dispersif ou évanescent.Outre les apports fondamentaux, les résultats obtenus peuvent trouver des applications dans le domaine du contrôle des ondes : filtres acoustiques dépendant de l'amplitude, convertisseurs de fréquences, rectificateurs et diodes acoustiques, ... . / This research is a contribution to the study of the propagation of elastic waves in granular media. The main purpose is to analyze two particular aspects that influence the propagation, first the rotation motion of grain and other nonlinearities of contact. As part of this work, the periodic one-dimensional granular structure is studied. The main contribution of this work is the experimental demonstration and modeling purely rotational wave in a granular chain composed of magnetic beads. The starting point of modeling is the description of the pure shear coupling at the contact between two spheres excited in torsion up to the first order of nonlinearity. For a oscillating torque, pure nonlinear quadratic hysteretic behaviour is shown. Generally, this nonlinearity coexists with other types of nonlinearities (quadratic, clapping, ...) and some of its effects have not been observed. For the first time, the transformation of pulse profile in a medium with pure hysteretic quadratic nonlinearity, essentially different from the distortion by classical nonlinearities, is reported.Other effects related to the dispersion and nonlinearity of contact in a diatomic chain are studied theoretically and experimentally. In particular, the generation of the 2nd harmonic wave compression presents an interesting behaviour according to their propagating nature, highly dispersive or evanescent. Apart from the fundamental interests, the results may find applications in the field of wave control: amplitude dependent filtering devices, rectifiers, actuating devices, acoustic diodes, ... .

Ce travail de thèse est l'étude expérimentale de la propagation des ondes acoustiques dans un milieu granulaire sec et confiné. Ces ondes permettent de sonder de manière non invasive les propriétés viscoélastiques et la structure hétérogène du milieu, mais peuvent aussi être utilisées comme perturbation contrôlée pour étudier le réarrangement des réseaux des forces. Dans une première partie, nous nous intéressons à la propagation des ondes cohérentes dans les empilements des billes de verre et aussi dans ceux des grains irréguliers (sable). En régime linéaire, un très bon accord est retrouvé entre les vitesses d'onde de compression mesurées et celles prédites par la théorie des milieux effectifs, ce qui permet d'accéder au nombre de coordinance Z. En régime non linéaire, nous observons à la fois un softening et un hardening de la vitesse d'onde de compression à cause du changement de Z induit pat la forte vibration. La deuxième partie étudie la propagation des ondes multiplement diffusées. Nous montrons que le transport de ces ondes dans un milieu granulaire peut être décrit par le modèle de diffusion. Le coefficient de diffusion et l'absorption inélastique sont déterminés en fonction de la contrainte de confinement et de la fréquence d'onde incidente. Le libre parcours moyen versus la longueur d'onde relèvent deux régimes distincts du transport des ondes diffusées à basse et à haute fréquence. De plus, une décroissance non exponentielle est observée sur le profile d'intensité des ondes diffusées à temps long lorsque la fréquence de l'onde incidente devient importante. Une étude paramétrique basée sur la renormalisation du coefficient de diffusion est effectuée pour comprendre l'origine de ce transport diffusif anomal. Enfin, nous développons un dispositif (MRT) pour effectuer l'opération du retournement temporel dans un milieu granulaire. En régime linéaire, la recompression temporelle et la refocalisation spatiale sont vérifiées. Cependant, en régime non linéaire, nous observons que le processus du retournement temporel est brisé par l'interaction irréversible onde-matière, dû au changement ou réarrangement des réseaux des forces / This experimental work describes sound propagation in dry granular media. These sound waves provide a non invasive method to probe the viscoelastic properties and the heterogeneous structure of the materials. They may also be served as controlled perturbation to study the nonlinear response due to the rearrangements of the contact force networks. In the first part, we investigate the coherent wave propagation both in the packings of glass beads and those of irregular grains such as sands. In the linear regime, measured compressional wave velocities are in good agreement with the effective medium theory, giving access to the coordination umber Z. In the nonlinear regime, we observe both softening and hardening of the sound velocity, likely stemming from the change in Z caused by the strong vibration. In the second part, we study the multiple scattering of short-wavelength elastic waves in granular media. It is shown that the wave transport can be well described by the approximation of diffusion. We determine the diffusion constant and the inelastic absorption time as a function of the confining pressure and the frequency of the incident wave. The plot of the mean transport free path versus the wavelength shows two distinct regimes of transport in low- and high-frequency. Moreover, we find time-resolved intensity profile of multiply scattered waves exhibit a non exponential decay in long time, thus deviated from the classic diffusive transport. A parametric study using the renormalized diffusion constant is performed in order to understand the underlying physics of such anomaly wave transport. Finally, we perform a first experimental study of the time-reversal of ultrasound in glass bead packings. In the linear regime, we obtain by time-reversal processes both a temporal recompression and a spatial refocusing at the source transducer of an ultrasonic pulse transmitting through the disordered force networks. However, in the nonlinear regime, we observe a breakdown of the time-reversal of ultrasound due to the structural change of the materials, i.e. sound-induced rearrangement of the force networks

L'objectif de ce manuscrit est de présenter mes travaux concernant la modélisation des ablations thermiques par ultrasons focalisés. La méthode de simulation du faisceau acoustique, fondée sur l'utilisation de la bibliothèque k-Wave, est appliquée à un cas concret de propagation des ultrasons à travers une couche de tissu superficiel. Des mesures à l'hydrophone réalisées dans différentes configurations sur des échantillons biologiques fournissent une validation en régime linéaire. A partir de ces résultats, l'influence des tissus superficiels sur la focalisation est évaluée en fonction de la géométrie du problème grâce à des simulations non linéaires.La modélisation thermique des traitements est ensuite discutée avec la volonté de réaliser des simulations thermiques réellement quantitatives. En particulier, un modèle équivalent de la déposition de chaleur en présence d'ébullition est proposé et validé grâce à l'utilisation de données expérimentales originales, diversifiées et peu coûteuses à acquérir.Finalement, un algorithme d'optimisation fondé sur le principe du maximum de Pontryagin est proposé afin d'optimiser la durée des traitements. L'approche étudiée consiste à optimiser la trajectoire du point focal pour maximiser l'efficacité de la déposition de chaleur. A travers une série d'exemples, les avantages et les limites de l'algorithme proposé sont discutés. / This manuscript aims at discussing the complex issue of modeling high-intensity focused ultrasound thermal ablations. An acoustical simulation method, based on the use of the k-Wave library, is described and applied to the description of the interaction between the acoustic beam and the superficial tissue layers. It is validated in the linear domain based on hydrophone measurements realized in different configurations with biological samples. Nonlinear simulations are subsequently used to evaluate the influence of the tissue geometry on the beam focusing.The thermal modeling of the treatment is then discussed with intent to design a truly quantitative model. An equivalent model of the modified heat deposition pattern in presence of boiling is presented and validated based on the use of original, diverse and unexpensive data.Finally, an algorithm is proposed to optimize the focal spot trajectory in order to maximize the heat deposition efficiency, thus reducing treatment time. The advantages and the limits of the approach are discussed based on different examples.

Near-field acoustical holography (NAH) has been used extensively for acoustical imaging of infinitesimal-amplitude (or small-amplitude) sources. However, recent interests are in the application of NAH to image finite-amplitude (or high-amplitude) sources such as jets and rockets. Since NAH is based on linear equations and finite-amplitude sources imply nonlinear effects, which cause shock formation and consequently an altered spectral shape, a feasibility study is carried out to determine the effect of nonlinear propagation on NAH. Jet and rocket sources typically have a distinct spectral shape resembling a ‘haystack’ and center frequencies varying from 30 to 300 Hz. To test the effect of nonlinear propagation on jet or rocket noise, several waveforms with varying spectral shapes and center frequencies were created and numerically propagated in one dimension using a nonlinear propagation algorithm. Bispectral methods were used to determine the amount and effect of nonlinearity, showing that higher center frequencies lead to more nonlinearities for a given amplitude. Also, higher-order statistical analysis of the time derivative of the waveforms was used to determine information about the relative amount of waveform steepening and shock coalescence occurring. NAH was then used to reconstruct the original waveform magnitude and the errors were determined. It was found that the ‘haystack’ spectral shape can be preserved by the nonlinear effects leading to low amplitude-reconstruction errors, whereas a narrow-band spectral shape will become altered and reconstruct very poorly. However, if nonlinear effects become strong due to higher center frequencies, longer propagation distances or higher amplitudes, even the ‘haystack’ shape will become altered enough to cause poor reconstruction. Two-dimensional propagation studies were also performed from two point sources, showing differences between linear and nonlinear propagation.

The natural dynamics are not ideal or linear. To understand their complex behavior, we needs to study the nonlinear dynamics in more simple models. This thesis is consist of two main setups. Both setups are simplified models for the behavior occurs in the complex systems. We studied in both systems the same nonlinear dynamics such as higher-harmonics, sub-harmonics, solitary waves,...etc. In Chapter (2), the propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly in influenced by dispersion. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of FPU equation, describing a chain of masses connected by nonlinear quadratic springs. The results can be extrapolated to other systems described by this equation. We studied theoretically and experimentally the generation and propagation of kinks in the system. We excite pulses at one boundary of the system and demonstrate the existence of kinks, whose properties are in very good agreement with the theoretical predictions, that is the equation that approaches, under the conditions of our experiments, the one corresponding to full model describing a chain of masses connected by magnetic forces. The results can be extrapolated to other systems described by this equation. Also, In the case of a lattice of finite length, where standing waves are formed, we report the observation of subharmonics of the driving wave. In chapter (3), we studied the propagation of intense acoustic waves in a multilayer crystal. The medium consists in a structured fluid, formed by a periodic array of fluid layerswith alternating linear acoustic properties and quadratic nonlinearity coefficient. We presents the results for different mathematicalmodels (NonlinearWave Equation,Westervelt Equation and Constitutive equations). We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media. In chapter (4), the oscillatory behavior of a microbubble is investigated through an acousto-mechanical analogy based on a ring-shaped chain of coupled pendula. Observation of parametric vibration modes of the pendula ring excited at frequencies between 1 and 5 Hz is considered. Simulations have been carried out and show spatial mode, mixing and localization phenomena. The relevance of the analogy between a microbubble and the macroscopic acousto-mechanical setup is discussed and suggested as an alternative way to investigate the complexity of microbubble dynamics. / La dinámica natural no es ideal ni lineal. Para entender su comportamiento complejo, necesitamos estudiar la dinámica no lineal en modelos más simples. Esta tesis consta de dos configuraciones principales. Ambas configuraciones son modelos simplificados de el comportamiento que se produce en los sistemas complejos. Estudiamos en ambos sistemas la misma dinámica no lineal como son la generación de armónicos superiores, los sub-armónicos, las ondas solitarias, etc. En elCapítulo (2), se estudia, tanto teórica comoexperimentalmente, la propagación de ondas no lineales en sistemas periodicos de partículas acopladas mediante fuerzas repulsivas. Se propone una configuración experimental simple, que consiste en una matriz de dipolos magnéticos acoplados. Inyectando armónicamente la señal en un extremo, excitamos ondas de propagación y demostramos diferentes regímenes de conversión de modos en armónicos, fuertemente influenciados por la dispersión. También se predice y se discute el fenómeno de dilatación acústica de la cadena. Los resultados se comparan con las predicciones teóricas de la ecuación FPU, describiendo una cadena de masas conectadas por muelles cuadráticos no lineales. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Estudiamos también teórica y experimentalmente la generación y propagación de kinks. Excitamos pulsos en la frontera del sistema y demostramos la existencia de kinks cuyas propiedades están en muy buen acuerdo con las predicciones teóricas, es decir, con la ecuación que aproxima bajo las condiciones de nuestros experimentos la correspondiente al modelo completo que describe un cadena de masas conectadas por fuerzas magnéticas. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Además, en el caso de una red finita, donde se forman ondas estacionarias, describimos la observación de subarmónicos del armónico principal. En el capítulo (3), estudiamos la propagación de ondas acústicas intensas en un cristal multicapa. El medio consiste en un fluido estructurado, formado por un conjunto periódico de capas fluidas con propiedades acústicas lineales alternas y coeficiente de no linealidad cuadrática. Presentamos los resultados de diferentes modelos matemáticos (ecuación de ondas no lineal, ecuación de Westervelt y ecuaciones constitutivas). Mostramos que la interacción entre la fuerte dispersión y la no linealidad conduce a nuevos escenarios de propagaciónde ondas. El proceso de distorsión de la onda clásica, típico de las ondas acústicas intensas en medios homogéneos, puede ser alterado de forma importante cuando los armónicos generados no linealmente se encuentran dentro o cerca del gap. Esto permite la posibilidad de diseñar un medio con el fin de obtener una forma de onda en particular. Ejemplos de esto incluyen el diseño demedios con no linealidad efectiva (por ejemplo, cúbica) o medios extremadamente lineales. En el capítulo (4), el comportamiento oscilatorio de una microburbuja se investiga a través de una analogía acusto-mecánica basada en una cadena en forma de anillo de péndulos acoplados. Se estudian los modos de vibración paramétrica del anillo pendular excitado a frecuencias entre 1 y 5 Hz. Se han llevado a cabo simulaciones que muestran la presencia de modos espaciales, mixtos y fenómenos de localización. Se discute la relevancia de la analogía entre una microburbuja y la configuración macroscópica acústico-mecánica y se sugiere como una vía alternativa para investigar la complejidad de la dinàmica de microburbujas. / La dinàmica natural no és ideal ni tampoc lineal. Per entendre el seu comportament complex, es necessita estudiar la dinàmica no lineal dels models més simples. Aquesta tesi consisteix en l'estudi de dues configuracions principals, que són models simplificats del comportament que es produeix en els sistemes complexos. Estudiem en ambdós sistemes la mateixa dinàmica no lineal, com és la generació d'harmònics superiors, sub-harmònics, ones solitàries, etc. En el capítol (2), estudiem, tant teòrica com experimentalment, la propagació de les ones no lineals en sistemes periòdics de partícules acoblades mitjançant forces repulsives. Es proposa una configuració experimental simple, que consisteixen en una matriu de dipols magnètics acoblats. En conduint harmònicament la xarxa en un límit, excitemla propagació de les ones i demostrem diferents règims de conversió de modes en harmònics més alts, força influenciada per la dispersió. El fenomen de la dilatació acústica de la cadena també es prediu i es discuteix. Els resultats es comparen amb les prediccions teòriques que descriu una cadena de masses conectades per molls quadràtics no lineals. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. Hem estudiat teòrica i experimentalment la generació i propagació de Kinks. Excitem polsos a la frontera del sistema i demostrem l'existència d'Kinks, les propietats desl quals estan en molt bon acord amb les prediccions teòriques, és a dir, de l'equació que aproxima sota les condicions dels nostres experiments la corresponent al model complet que descriu un cadena demasses connectades per forcesmagnètiques. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. A més, en el cas d'una xarxa finita, on es formen ones estacionàries, descrivim l'observació de subarmónicos de l'harmònic principal. En el capítol (3), s'estudia la propagació d'ones acústiques intenses en un medi multicapa. El medi consisteix en un fluid estructurat, format per una matriu periòdica de capes de fluid amb l'alternança de propietats acústiques lineals i coeficient de no linealitat de segon grau. Es presenten els resultats per a diferents models matemàtics no lineals (equació d'ones no lineal, equació de Westervelt i les equacions constitutives). Es demostra que la interacciò entre la forta dispersió i no linealitat condueix a nous escenaris de propagació de l'ona. El procés de distorsió en formad'ona clàssica, típica de les ones acústiques intenses en medis homogenis, es pot alterar de manera significativa quan els harmònics generats de forma no lineal es troben dins o a prop del gap. Això obri la possibilitat de dissenyar unmedi per tal d'obtenir una forma d'ona particular. Exemples d'això inclouen el disseny delsmedis amb una no linealitat efectiva (per exemple cúbica), o medis extremadament lineals. En el capítol (4), el comportament oscilatori d'una micro-bombolla és investigat a través d' una analogia acústica-mecànica basada en una cadena en forma d'anell de pèndols acoblats. Es considera l'observació dels modes de vibració paramètriques de l'anell pendular excitat amb freqüències entre 1 i 5 Hz. S'han dut a terme simulacions que mostren la presència de moes espacilas, mixtes i fenòmens de localització. Es discuteix la relevància de l'analogia entre les microbambolles i la configuració macroscòpica acústica-mecànica i es suggereix una formaalternativa per a investigar la complexitat de la dinàmica demicrobombolles. / Mehrem Issa Mohamed Mehrem, A. (2017). Nonlinear acoustics in periodic media: from fundamental effects to applications [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/80289

Sensitive nonlinear acoustic methods are suitable for material characterization. This thesis describes three nonlinear acoustic methods that are proven useful for detection of defects like cracks and delaminations in solids. They offer the possibility to use relatively low frequencies which is advantageous because attenuation and diffraction effects are smaller for low frequencies. Therefore large and multi-layered complete objects can be investigated in about one second. Sometimes the position of the damage is required. But it is in general difficult to limit the geometrical extent of low-frequency acoustic waves. A technique is presented that constrains the wave field to a localized trapped mode so that damage can be located.

Finite amplitude perturbations in compressible media are ubiquitous in scientific and engineering applications such as gas-turbine engines, rocket propulsion systems, combustion instabilities, inhomogeneous solids, and traffic flow prediction models, to name a few. Small amplitude waves in compressible fluids propagate as sound and are very well described by linear theory. On the other hand, the theory of nonlinear acoustics, concerning high-amplitude wave propagation (Mach<2) is relatively underdeveloped. Most of the theoretical development in nonlinear acoustics has focused on wave steepening and has been centered around the Burgers' equation, which can be extended to nonlinear acoustics only for purely one-way traveling waves. In this dissertation, theoretical and computational developments are discussed with the objective of advancing the multi-fidelity modeling of nonlinear acoustics, ranging from quasi one-dimensional high-amplitude waves to combustion-induced detonation waves. <br> <br> We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order in perturbation variables is derived. The exact energy corollary of such second-order system of equations is then formulated and used to elucidate the spectral energy dynamics of nonlinear acoustic waves. We then extend this analysis to thermoacoustically unstable waves -- i.e. amplified as a result of thermoacoustic instability. We drive such instability up until the generation of shock waves. We further study the nonlinear wave propagation in geometrically complex case of waves induced by the spark plasma between the electrodes. This case adds the geometrical complexity of a curved, three-dimensional shock, yielding vorticity production due to baroclinic torque. Finally, detonation waves are simulated by using a low-order approach, in a periodic setup subjected to high pressure inlet and exhaust of combustible gaseous mixture. An order adaptive fully compressible and unstructured Navier Stokes solver is currently under development to enable higher fidelity studies of both the spark plasma and detonation wave problem in the future. <br>

Ce travail de thèse est une contribution au développement des méthodes d’acoustique non linéaire pour le contrôle non destructif et l’imagerie de défauts de type contact dans les solides.Dans ce travail, des modifications sont proposées pour deux méthodes récentes de contrôle non destructif par acoustique non linéaire : l’interférométrie de coda couplée au retournement temporel, et l’imagerie non linéaire par ultrasons aériens. Le principal avantage de la première méthode est sa sensibilité extrême liée à l’accumulation des effets induits par des changements, même faibles, des propriétés de l’échantillon durant la formation de la coda. La deuxième méthode apporte une approche complémentaire en permettant de réaliser un contrôle sans contact. Les techniques développées ont été testées sur des échantillons présentant des défauts artificiels à des emplacements connus. Les performances de chacune des méthodes ont été étudiées.La deuxième partie de ce travail porte sur la description théorique des non-linéarités acoustiques de contact et leur utilisation pour le développement d’une boite à outils numériques permettant la simulation d’ondes acoustiques dans des structures complexes contenant des contacts internes. Un model physique décrivant le décalage tangentiel de deux corps en contact en présence de friction est proposé. Il aboutit à une solution analytique pour la relation présentant une hystérésis entre les déplacements de contact normal et tangentiel et les chargements. Ce modèle est utilisé comme condition aux frontières pour les surfaces de contact internes (défauts) dans un modèle de propagation d’ondes acoustiques utilisant un logiciel d’éléments finis commercial / This PhD thesis work contributes to the development of nonlinear elastic methods for non-destructive testing and imaging of contact-type defects in solids.In this work, two modifications of recent nonlinear nondestructive testing methods are suggested: the coda wave interferometry combined with the nonlinear time reversal principle and air-coupled nonlinear ultrasonic imaging. The principal advantage of former technique is in its extremely high sensitivity owing to the fact that weak changes in sample's parameters are accumulated and finally greatly amplified during the formation of the coda wave. The other technique has a complimentary strength and offers a possibility of a remote detection. The developed techniques are tested on samples with artificially fabricated defects at known locations. The performance of each method is accessed and the potential for obtaining robust nonlinear images is demonstrated.The second part of the work is concerned with a theoretical description of contact acoustical nonlinearity and its use for creating of a numerical toolbox capable of simulating wave propagation in complex structures containing internal contacts. A physical model describing the tangential shift of two contacting bodies in the presence of friction has been proposed. Its result is an analytical computer-assisted solution for hysteretic relationships between normal and tangential contact displacements and loads. The contact model and derived load-displacement relationships are used as boundary conditions posed at the internal boundaries (contact surfaces) in a finite element wave propagation model programmed via commercial software

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

This research deals with the second harmonic generation of Lamb waves in nonlinear elastic, homogeneous, isotropic plates. These waves find current applications in the field of ultrasonic, nondestructive testing and evaluation of materials. The second harmonic Lamb wave generation is investigated analytically in order to provide information on suitable excitation modes maximizing the second harmonic amplitude. Using an existing solution for the problem of second harmonic generation in wave guides, the solution is explained for the plate and examined as to the symmetry properties of the second harmonic wave, since published results are contradictory. It is shown that the cross-modal generation of a symmetric secondary mode by an antisymmetric primary mode is possible. Modes showing internal resonance, whose conditions are nonzero power flux from the primary wave and phase velocity matching, are shown to be most useful for measurements. In addition, group velocity matching is required. A material-independent analysis of the linear Lamb mode theory provides mode types satisfying all three requirements. Using the example of an aluminum plate, the found internally resonant modes are evaluated with regard to the rate of second harmonic generation and practical issues such as excitability and ease of measurement. Pros and cons of each mode type are presented.