Pub Date : 2024-11-06DOI: 10.1016/j.ijnonlinmec.2024.104940
Zsolt Iklodi , Petri T. Piiroinen , Oier Franco , Xavier Beudaert , Zoltan Dombovari
This paper deals with mechanical modelling and numerical bifurcation analysis of stick–slip oscillations that plague extremely low feed grinding operations. Based on experimental observations, a novel two degree of freedom mechanical model of a grinding machine feed drive system is formulated, which incorporates Stribeck-type dry friction, position and velocity controller dynamics, and actuator backlash. Loss and re-establishment of contact between the feed drive elements is modelled through both rigid-body impacts and a contact-stiffness model. The resulting piecewise-smooth equations of motion are subjected to detailed stability and bifurcation analysis with the help of shooting and collocation based numerical continuation tools. Major focus is attributed to the influence of the feed velocity and the control-loop parameters as well as the identification of stable, stick–slip free parameter regimes. Finally, a controller enhancement strategy is proposed, based on event-driven integrator reset rules, to help limit the amplitude of arising limit-cycle oscillations.
{"title":"Stick–slip oscillations in the low feed linear motion of a grinding machine due to dry friction and backlash","authors":"Zsolt Iklodi , Petri T. Piiroinen , Oier Franco , Xavier Beudaert , Zoltan Dombovari","doi":"10.1016/j.ijnonlinmec.2024.104940","DOIUrl":"10.1016/j.ijnonlinmec.2024.104940","url":null,"abstract":"<div><div>This paper deals with mechanical modelling and numerical bifurcation analysis of stick–slip oscillations that plague extremely low feed grinding operations. Based on experimental observations, a novel two degree of freedom mechanical model of a grinding machine feed drive system is formulated, which incorporates Stribeck-type dry friction, position and velocity controller dynamics, and actuator backlash. Loss and re-establishment of contact between the feed drive elements is modelled through both rigid-body impacts and a contact-stiffness model. The resulting piecewise-smooth equations of motion are subjected to detailed stability and bifurcation analysis with the help of shooting and collocation based numerical continuation tools. Major focus is attributed to the influence of the feed velocity and the control-loop parameters as well as the identification of stable, stick–slip free parameter regimes. Finally, a controller enhancement strategy is proposed, based on event-driven integrator reset rules, to help limit the amplitude of arising limit-cycle oscillations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104940"},"PeriodicalIF":2.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.ijnonlinmec.2024.104950
Haojie Ma , Xiao Kang , Shengyu Duan , Ying Li
Currently, there is a lack of structural optimization methods when a structure is suffering transient impact load, considering nonlinear factors such as material plasticity and strain rate effect. The utilization of derivative-free algorithms also increases computational expenses. Accordingly, this paper presents a novel structure transient optimization approach based on multilayer perceptron combined with a derivative-free optimization method, which can efficiently solve the transient structure dynamics optimization problem with multiple optimization objects. In this approach, the area to be optimized is cut by several closed B-spline curves whose shapes are controlled by several parameters and can be varied and merged at each optimization iteration step. The structure's transient analysis process is replaced by a machine learning based surrogate model, which is trained by thousands of results from the FEM explicit transient simulation. Additionally, nearly orthogonal Latin hypercube sampling is utilized to simplify parameter dimensionality, reduce the training data set, save calculation time, and give the training data set a more comprehensive range of design parameters. In our optimization process, our design target is to minimize the peak reaction force while with the constrain of ensuring enough stiffness and mass. The results demonstrate our proposed methods could efficiently handle transient optimization problems without sensitivity calculations, exhibiting strong generalization capabilities.
{"title":"Efficient structural optimization under transient impact loads using multilayer perceptron and genetic algorithms","authors":"Haojie Ma , Xiao Kang , Shengyu Duan , Ying Li","doi":"10.1016/j.ijnonlinmec.2024.104950","DOIUrl":"10.1016/j.ijnonlinmec.2024.104950","url":null,"abstract":"<div><div>Currently, there is a lack of structural optimization methods when a structure is suffering transient impact load, considering nonlinear factors such as material plasticity and strain rate effect. The utilization of derivative-free algorithms also increases computational expenses. Accordingly, this paper presents a novel structure transient optimization approach based on multilayer perceptron combined with a derivative-free optimization method, which can efficiently solve the transient structure dynamics optimization problem with multiple optimization objects. In this approach, the area to be optimized is cut by several closed B-spline curves whose shapes are controlled by several parameters and can be varied and merged at each optimization iteration step. The structure's transient analysis process is replaced by a machine learning based surrogate model, which is trained by thousands of results from the FEM explicit transient simulation. Additionally, nearly orthogonal Latin hypercube sampling is utilized to simplify parameter dimensionality, reduce the training data set, save calculation time, and give the training data set a more comprehensive range of design parameters. In our optimization process, our design target is to minimize the peak reaction force while with the constrain of ensuring enough stiffness and mass. The results demonstrate our proposed methods could efficiently handle transient optimization problems without sensitivity calculations, exhibiting strong generalization capabilities.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104950"},"PeriodicalIF":2.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.ijnonlinmec.2024.104938
Ying Wang , Zhixiang Wang , Chun Zhang , Qinsheng Bi
This paper aims to investigate the non-smooth bifurcations and to uncover the underlying dynamics that lead to bursting patterns within a two-scale piecewise-smooth system. The system is established by applying a modification scheme to a fourth-order Chua’s circuit, with a periodic external excitation current acting as the slow state variable. Several smooth as well as non-smooth bifurcations are discovered within the fast subsystem by utilizing theoretical and numerical methods. Two special non-smooth bifurcations have been discussed. The first is the multiple crossing bifurcation involving the boundary equilibrium, which exhibits the behavior of both the turning point and Hopf bifurcation. The second arises from an encounter between a saddle-focus and the trajectory of a non-smooth chaotic solution, which can result in the vanishing or appearance of a non-smooth chaotic attractor. Four typical bursting patterns associated with these two non-smooth bifurcations in the established slow–fast system are observed, and the mechanisms behind them are revealed based on bifurcation analysis.
{"title":"Bursting oscillations with multiple crossing bifurcations in a piecewise-smooth system","authors":"Ying Wang , Zhixiang Wang , Chun Zhang , Qinsheng Bi","doi":"10.1016/j.ijnonlinmec.2024.104938","DOIUrl":"10.1016/j.ijnonlinmec.2024.104938","url":null,"abstract":"<div><div>This paper aims to investigate the non-smooth bifurcations and to uncover the underlying dynamics that lead to bursting patterns within a two-scale piecewise-smooth system. The system is established by applying a modification scheme to a fourth-order Chua’s circuit, with a periodic external excitation current acting as the slow state variable. Several smooth as well as non-smooth bifurcations are discovered within the fast subsystem by utilizing theoretical and numerical methods. Two special non-smooth bifurcations have been discussed. The first is the multiple crossing bifurcation involving the boundary equilibrium, which exhibits the behavior of both the turning point and Hopf bifurcation. The second arises from an encounter between a saddle-focus and the trajectory of a non-smooth chaotic solution, which can result in the vanishing or appearance of a non-smooth chaotic attractor. Four typical bursting patterns associated with these two non-smooth bifurcations in the established slow–fast system are observed, and the mechanisms behind them are revealed based on bifurcation analysis.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104938"},"PeriodicalIF":2.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Blended wing–body configurations are anticipated to dominate future transport and military aerospace designs. The departure of the conventional tube-wing configuration has opened several areas of investigation. These designs are susceptible to lateral instability during landing, takeoff, and maneuvering flight despite having improved aerodynamics because of their tailless nature. One of these instabilities, Wing-Rock, poses significant performance and operational difficulties and can potentially cause crashes. Though experimental and numerical studies of the aerodynamics and stability of blended wing–body configurations have been conducted, wing-rock characteristics still need to be identified in the literature. This research aims to investigate these characteristics at low subsonic speeds with varying outboard sweep and geometric twist angles. The study includes a numerical approach based on the rigid body free-vibration method in single roll degree of motion, which uses three-dimensional unsteady Reynolds’ Average Navier Stokes equations, and an analytical approach based on the multiple time scale method, which captures the crucial aspect of the wing rock system. The findings show that the geometrical parameters significantly impact the wing rock characteristics, which are unique to such novel tailless designs.
{"title":"Effect of geometric variations on the wing rock of blended wing–body aircraft","authors":"Waseeq Siddiqui , Adnan Maqsood , Shuaib Salamat , Hongyi Xu , Dan Xie","doi":"10.1016/j.ijnonlinmec.2024.104934","DOIUrl":"10.1016/j.ijnonlinmec.2024.104934","url":null,"abstract":"<div><div>Blended wing–body configurations are anticipated to dominate future transport and military aerospace designs. The departure of the conventional tube-wing configuration has opened several areas of investigation. These designs are susceptible to lateral instability during landing, takeoff, and maneuvering flight despite having improved aerodynamics because of their tailless nature. One of these instabilities, Wing-Rock, poses significant performance and operational difficulties and can potentially cause crashes. Though experimental and numerical studies of the aerodynamics and stability of blended wing–body configurations have been conducted, wing-rock characteristics still need to be identified in the literature. This research aims to investigate these characteristics at low subsonic speeds with varying outboard sweep and geometric twist angles. The study includes a numerical approach based on the rigid body free-vibration method in single roll degree of motion, which uses three-dimensional unsteady Reynolds’ Average Navier Stokes equations, and an analytical approach based on the multiple time scale method, which captures the crucial aspect of the wing rock system. The findings show that the geometrical parameters significantly impact the wing rock characteristics, which are unique to such novel tailless designs.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104934"},"PeriodicalIF":2.8,"publicationDate":"2024-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Identification of bifurcation diagrams in nonlinear systems is of great importance for resilient design and stability analysis of dynamical systems. Data-driven identification of bifurcation diagrams has a significant advantage for large dimensional systems where analysis of the equations is not possible, and for experimental systems where accurate system equations are not available. In this work, a novel forecasting approach to predict bifurcation diagrams in nonlinear systems is presented using system trajectories before instabilities occur. Unlike previous techniques, the proposed method considers a varying bifurcation parameter during the system response to perturbations. Combined with an asymptotic analysis provided by the method of multiple scales eliminates the requirement of using multiple measurements and allows the novel technique to predict the bifurcation diagram using a single system recovery. The proposed approach allows stability analyses of nonlinear systems with limited access to experimental or surrogate data. The novel technique is demonstrated through its application to a Hopf bifurcation, highlighting its inherent advantages. Subsequently, the method is employed in the analysis of an aeroelastic system that shows both supercritical and subcritical Hopf bifurcations. The findings reveal great accuracy, achieved with a reduced number of measurements, while enhancing versatility.
{"title":"Data-driven bifurcation analysis using parameter-dependent trajectories","authors":"Jesús García Pérez , Leonardo Sanches , Amin Ghadami , Guilhem Michon , Bogdan Epureanu","doi":"10.1016/j.ijnonlinmec.2024.104937","DOIUrl":"10.1016/j.ijnonlinmec.2024.104937","url":null,"abstract":"<div><div>Identification of bifurcation diagrams in nonlinear systems is of great importance for resilient design and stability analysis of dynamical systems. Data-driven identification of bifurcation diagrams has a significant advantage for large dimensional systems where analysis of the equations is not possible, and for experimental systems where accurate system equations are not available. In this work, a novel forecasting approach to predict bifurcation diagrams in nonlinear systems is presented using system trajectories before instabilities occur. Unlike previous techniques, the proposed method considers a varying bifurcation parameter during the system response to perturbations. Combined with an asymptotic analysis provided by the method of multiple scales eliminates the requirement of using multiple measurements and allows the novel technique to predict the bifurcation diagram using a single system recovery. The proposed approach allows stability analyses of nonlinear systems with limited access to experimental or surrogate data. The novel technique is demonstrated through its application to a Hopf bifurcation, highlighting its inherent advantages. Subsequently, the method is employed in the analysis of an aeroelastic system that shows both supercritical and subcritical Hopf bifurcations. The findings reveal great accuracy, achieved with a reduced number of measurements, while enhancing versatility.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104937"},"PeriodicalIF":2.8,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.ijnonlinmec.2024.104939
Vignesh Palani, Ashirbad Swain
Owing to the improved mechanical properties of composites and functionally graded materials (FGMs), their applications have been realised in various engineering domains, such as aerospace, marine, automobile, and defence. Materials’ property plays a crucial role in dictating the dynamics of shell structure. Although much research has been conducted in structural dynamics, researchers are still working to develop new theories for structure and materials for composite shell structures to investigate their dynamic behaviour with various computational approaches involving different shell theories and experimental techniques. Apart from the linear analysis, researchers have also focused on the nonlinear dynamic behaviour of the shell structure with various shell theories. But still, this field of research remains vibrant for many researchers. This review encapsulates some critical articles in the field of the dynamics of both composite and FGM shell structures involving nanocomposite, viscoelastic and hyperelastic material systems. The motive of the study is also to highlight the analyses of the shear deformation theories employed for the development of formulations of shell structures, including geometrical and material nonlinearity, for the analysis of the dynamics involved in closed shells, panels, and such structures under fluid-structure interaction.
{"title":"Nonlinear vibration analysis of composite and functionally graded material shell structures: A literature review from 2013 to 2023","authors":"Vignesh Palani, Ashirbad Swain","doi":"10.1016/j.ijnonlinmec.2024.104939","DOIUrl":"10.1016/j.ijnonlinmec.2024.104939","url":null,"abstract":"<div><div>Owing to the improved mechanical properties of composites and functionally graded materials (FGMs), their applications have been realised in various engineering domains, such as aerospace, marine, automobile, and defence. Materials’ property plays a crucial role in dictating the dynamics of shell structure. Although much research has been conducted in structural dynamics, researchers are still working to develop new theories for structure and materials for composite shell structures to investigate their dynamic behaviour with various computational approaches involving different shell theories and experimental techniques. Apart from the linear analysis, researchers have also focused on the nonlinear dynamic behaviour of the shell structure with various shell theories. But still, this field of research remains vibrant for many researchers. This review encapsulates some critical articles in the field of the dynamics of both composite and FGM shell structures involving nanocomposite, viscoelastic and hyperelastic material systems. The motive of the study is also to highlight the analyses of the shear deformation theories employed for the development of formulations of shell structures, including geometrical and material nonlinearity, for the analysis of the dynamics involved in closed shells, panels, and such structures under fluid-structure interaction.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104939"},"PeriodicalIF":2.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.ijnonlinmec.2024.104930
Benedetta Calusi
In this paper, we investigate the linear stability of a gravity-driven fluid with pressure-dependent viscosity flowing down an inclined plane. The linear stability analysis is formulated using the long-wave approximation method. We show that the onset of instability occurs at a critical Reynolds number that depends on the material and geometrical parameters. Our results suggest that the dependence of the viscosity on pressure can influence the stability characteristics of the flow down an incline.
{"title":"Flow of fluids with pressure-dependent viscosity down an incline: Long-wave linear stability analysis","authors":"Benedetta Calusi","doi":"10.1016/j.ijnonlinmec.2024.104930","DOIUrl":"10.1016/j.ijnonlinmec.2024.104930","url":null,"abstract":"<div><div>In this paper, we investigate the linear stability of a gravity-driven fluid with pressure-dependent viscosity flowing down an inclined plane. The linear stability analysis is formulated using the long-wave approximation method. We show that the onset of instability occurs at a critical Reynolds number that depends on the material and geometrical parameters. Our results suggest that the dependence of the viscosity on pressure can influence the stability characteristics of the flow down an incline.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104930"},"PeriodicalIF":2.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.ijnonlinmec.2024.104932
Phuc L.H. Ho , Changkye Lee , Canh V. Le , Jurng-Jae Yee
Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.
{"title":"Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach","authors":"Phuc L.H. Ho , Changkye Lee , Canh V. Le , Jurng-Jae Yee","doi":"10.1016/j.ijnonlinmec.2024.104932","DOIUrl":"10.1016/j.ijnonlinmec.2024.104932","url":null,"abstract":"<div><div>Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104932"},"PeriodicalIF":2.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.ijnonlinmec.2024.104933
Safvan Palathingal , Dominic Vella
The shift in the backbone of the frequency–response curve and the ‘jump-down’ observed at a critical frequency observed in nano-resonators are caused by their nonlinear mechanical response. The shift and jump-down point are therefore often used to infer the mechanical properties that underlie the nonlinear response, particularly the resonator’s stretching modulus. To facilitate this, the resonators’ dynamics are often modelled using a Galerkin-type numerical approach or lumped ordinary differential equations like the Duffing equation, that incorporate an appropriate nonlinearity. To understand the source of the problem’s nonlinearities, we first develop an axisymmetric but spatially-varying model of a membrane resonator subject to a uniform oscillatory load with linear damping. We then derive asymptotic solutions for the resulting partial differential equations (PDEs) using the Method of Multiple Scales (MS), which allows a systematic reduction to a Duffing-like equation with analytically determined coefficients. We also solve the PDEs numerically via the method of lines. By comparing the numerical solutions with the asymptotic results, we demonstrate that the numerical approach reveals a non-constant maximum compliance with increasing load, which contradicts the predictions of the MS analysis. In contrast, we show that combining a Galerkin decomposition with the Harmonic Balance Method accurately captures the non-constant maximum compliance and reliably predicts jump-down behaviour. We analyse the resulting frequency–response predictions derived from these methods. We also argue that fitting based on the jump-down point may be sensitive to noise and discuss strategies for fitting frequency–response curves from experimental data to theory that are robust to this.
{"title":"Axisymmetric membrane nano-resonators: A comparison of nonlinear reduced-order models","authors":"Safvan Palathingal , Dominic Vella","doi":"10.1016/j.ijnonlinmec.2024.104933","DOIUrl":"10.1016/j.ijnonlinmec.2024.104933","url":null,"abstract":"<div><div>The shift in the backbone of the frequency–response curve and the ‘jump-down’ observed at a critical frequency observed in nano-resonators are caused by their nonlinear mechanical response. The shift and jump-down point are therefore often used to infer the mechanical properties that underlie the nonlinear response, particularly the resonator’s stretching modulus. To facilitate this, the resonators’ dynamics are often modelled using a Galerkin-type numerical approach or lumped ordinary differential equations like the Duffing equation, that incorporate an appropriate nonlinearity. To understand the source of the problem’s nonlinearities, we first develop an axisymmetric but spatially-varying model of a membrane resonator subject to a uniform oscillatory load with linear damping. We then derive asymptotic solutions for the resulting partial differential equations (PDEs) using the Method of Multiple Scales (MS), which allows a systematic reduction to a Duffing-like equation with analytically determined coefficients. We also solve the PDEs numerically via the method of lines. By comparing the numerical solutions with the asymptotic results, we demonstrate that the numerical approach reveals a non-constant maximum compliance with increasing load, which contradicts the predictions of the MS analysis. In contrast, we show that combining a Galerkin decomposition with the Harmonic Balance Method accurately captures the non-constant maximum compliance and reliably predicts jump-down behaviour. We analyse the resulting frequency–response predictions derived from these methods. We also argue that fitting based on the jump-down point may be sensitive to noise and discuss strategies for fitting frequency–response curves from experimental data to theory that are robust to this.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104933"},"PeriodicalIF":2.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-25DOI: 10.1016/j.ijnonlinmec.2024.104931
Mohammed Daher Albalwi
The flow of a density stratified fluid over obstacles has been intensively explored from a natural and scientific point of view. This flow has been successfully governed by using the forced Korteweg–de Vries-Burgers equation that generated solitons in a viscous flow. This is done by adding the viscous term beyond the Korteweg–de Vries approximation. It is based on the conservation laws of the Korteweg–de Vries-Burgers equation for mass and energy, and assumes that the upstream wavetrains are composed of solitary waves. Our results show that the influence of viscosity plays a key role in determining the upstream solitary wave amplitude of the bore. A good comparison is obtained between the numerical and analytical solutions.
{"title":"Uniform solitary wave theory for viscous flow over topography","authors":"Mohammed Daher Albalwi","doi":"10.1016/j.ijnonlinmec.2024.104931","DOIUrl":"10.1016/j.ijnonlinmec.2024.104931","url":null,"abstract":"<div><div>The flow of a density stratified fluid over obstacles has been intensively explored from a natural and scientific point of view. This flow has been successfully governed by using the forced Korteweg–de Vries-Burgers equation that generated solitons in a viscous flow. This is done by adding the viscous term beyond the Korteweg–de Vries approximation. It is based on the conservation laws of the Korteweg–de Vries-Burgers equation for mass and energy, and assumes that the upstream wavetrains are composed of solitary waves. Our results show that the influence of viscosity plays a key role in determining the upstream solitary wave amplitude of the bore. A good comparison is obtained between the numerical and analytical solutions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104931"},"PeriodicalIF":2.8,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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