{"title":"Nonlinear Longitudinal Oscillations of the Wall of a Wedge-Shaped Channel Filled with a Pulsating Viscous Fluid","authors":"V. S. Popov, L. I. Mogilevich, A. A. Popova","doi":"10.1007/s11141-026-10505-8","DOIUrl":null,"url":null,"abstract":"<p>We present the formulation and solution of a hydroelasticity problem to determine the nonlinear response for the wall of a wedge-shaped channel filled with a pulsating viscous fluid. A plane problem is considered for the channel formed by rigid walls that are rectangular in plan view. The upper wall is fixed and has a wedge shape, while the bottom one has a nonlinear elastic fixation at the ends and performs steady forced oscillations due to pressure pulsation at the end of the channel. Nonlinear-elastic fixation of the bottom wall is represented by weightless springs with a symmetric hardening stiffness characteristic with cubic nonlinearity. For the fluid in the channel, a model of a Newtonian fluid of constant density is adopted, and its motion is studied as creeping one. A boundary-value problem of mathematical physics was formulated, including the equations of creeping motion for a viscous fluid, the equation of motion of the rigid wall on a nonlinear elastic suspension, as well as boundary conditions for fluid pressure at the ends of the channel and velocities at the contact boundaries between the channel walls and the fluid. Asymptotic analysis of this problem allowed us to find the laws of distribution for the velocities and pressure of a viscous fluid in a wedge-shaped channel and reduce the initial problem to considering the generalized Duffing equation describing nonlinear hydroelastic oscillations of the channel wall. The solution of this equation, carried out using the Krylov–Bogolyubov averaging method for the primary resonance, made it possible to determine the nonlinear hydroelastic amplitude response and phase response, which are implicit functions of the amplitude of oscillations and frequency. A numerical study of these responses was carried out, showing a significant influence of the wedge shape of the channel, the thickness of the fluid layer, and the amplitude of pressure pulsation at the channel end on the amplitude of oscillations, resonance frequencies, and the possibility of unstable oscillations of the bottom wall of the wedge-shaped channel.</p>","PeriodicalId":748,"journal":{"name":"Radiophysics and Quantum Electronics","volume":"68 11","pages":"890 - 902"},"PeriodicalIF":0.8000,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Radiophysics and Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11141-026-10505-8","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
We present the formulation and solution of a hydroelasticity problem to determine the nonlinear response for the wall of a wedge-shaped channel filled with a pulsating viscous fluid. A plane problem is considered for the channel formed by rigid walls that are rectangular in plan view. The upper wall is fixed and has a wedge shape, while the bottom one has a nonlinear elastic fixation at the ends and performs steady forced oscillations due to pressure pulsation at the end of the channel. Nonlinear-elastic fixation of the bottom wall is represented by weightless springs with a symmetric hardening stiffness characteristic with cubic nonlinearity. For the fluid in the channel, a model of a Newtonian fluid of constant density is adopted, and its motion is studied as creeping one. A boundary-value problem of mathematical physics was formulated, including the equations of creeping motion for a viscous fluid, the equation of motion of the rigid wall on a nonlinear elastic suspension, as well as boundary conditions for fluid pressure at the ends of the channel and velocities at the contact boundaries between the channel walls and the fluid. Asymptotic analysis of this problem allowed us to find the laws of distribution for the velocities and pressure of a viscous fluid in a wedge-shaped channel and reduce the initial problem to considering the generalized Duffing equation describing nonlinear hydroelastic oscillations of the channel wall. The solution of this equation, carried out using the Krylov–Bogolyubov averaging method for the primary resonance, made it possible to determine the nonlinear hydroelastic amplitude response and phase response, which are implicit functions of the amplitude of oscillations and frequency. A numerical study of these responses was carried out, showing a significant influence of the wedge shape of the channel, the thickness of the fluid layer, and the amplitude of pressure pulsation at the channel end on the amplitude of oscillations, resonance frequencies, and the possibility of unstable oscillations of the bottom wall of the wedge-shaped channel.
期刊介绍：
Radiophysics and Quantum Electronics contains the most recent and best Russian research on topics such as:
Radio astronomy;
Plasma astrophysics;
Ionospheric, atmospheric and oceanic physics;
Radiowave propagation;
Quantum radiophysics;
Pphysics of oscillations and waves;
Physics of plasmas;
Statistical radiophysics;
Electrodynamics;
Vacuum and plasma electronics;
Acoustics;
Solid-state electronics.
Radiophysics and Quantum Electronics is a translation of the Russian journal Izvestiya VUZ. Radiofizika, published by the Radiophysical Research Institute and N.I. Lobachevsky State University at Nizhnii Novgorod, Russia. The Russian volume-year is published in English beginning in April.
All articles are peer-reviewed.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
