Acoustic Frequency Splitting in Thermoacoustically Driven Coupled Oscillators with Fibrous Stacks

ORAL

Abstract

Frequency splitting or level repulsion occurs near the point where the two resonant modes coupled oscillators intersect as one parameter is varied that allows the resonance of one to pass through the resonance of the other. A thermacoustic stack, which provides internal self-sustained oscillations, placed inside the neck of a closed bottle-shaped resonator can set up standing waves of the coupled neck-cavity system. A simplified model for using a fibrous stack is presented. A one dimensional wave equation with appropriately applied boundary conditions of the bottle system reveal the mode splitting between the neck and cavity modes. Thermoacoustic engines with bottle-shaped resonators were tested while varying one of three geometric parameters. All exhibit frequency splitting in good agreement with the model. Graphs of the solutions of the wave equation readily illustrate the mode splitting of the coupled oscillator system.

–

Authors

  • Bonnie Andersen

    Utah Valley University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University