Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers
Transfer functions are often employed to evaluate the vibration characteristics of mechanical and electrical systems. Within a group of transfer functions, some particular ones have the property that swapping the coefficients of the two terms in the equation does not change the properties of the ori...
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| Format: | Article |
| Language: | English |
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The Japan Society of Mechanical Engineers
2022-02-01
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| Series: | Mechanical Engineering Journal |
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| Online Access: | https://www.jstage.jst.go.jp/article/mej/9/1/9_21-00362/_pdf/-char/en |
| _version_ | 1797985215603277824 |
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| author | Toshihiko ASAMI |
| author_facet | Toshihiko ASAMI |
| author_sort | Toshihiko ASAMI |
| collection | DOAJ |
| description | Transfer functions are often employed to evaluate the vibration characteristics of mechanical and electrical systems. Within a group of transfer functions, some particular ones have the property that swapping the coefficients of the two terms in the equation does not change the properties of the original function. Such functions are said to have a reciprocity property. Mechanical vibratory systems typically have three transfer functions; namely, compliance, mobility, and accelerance. For a single-degree-of-freedom system, the mobility transfer function has the reciprocity property; for a two-degree-of-freedom system, no transfer function has the reciprocity property; and for a three-degree-of-freedom system, one transfer function has the reciprocity property. This paper shows that the presence of transfer functions with the reciprocity property is extremely important for obtaining simple optimal design formulas for dynamic vibration absorbers. |
| first_indexed | 2024-04-11T07:13:45Z |
| format | Article |
| id | doaj.art-c0798b867c584054be0ee3a104c46ada |
| institution | Directory Open Access Journal |
| issn | 2187-9745 |
| language | English |
| last_indexed | 2024-04-11T07:13:45Z |
| publishDate | 2022-02-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| spelling | doaj.art-c0798b867c584054be0ee3a104c46ada2022-12-22T04:38:04ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452022-02-019121-0036221-0036210.1299/mej.21-00362mejRelationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbersToshihiko ASAMI0Department of Mechanical Engineering, University of HyogoTransfer functions are often employed to evaluate the vibration characteristics of mechanical and electrical systems. Within a group of transfer functions, some particular ones have the property that swapping the coefficients of the two terms in the equation does not change the properties of the original function. Such functions are said to have a reciprocity property. Mechanical vibratory systems typically have three transfer functions; namely, compliance, mobility, and accelerance. For a single-degree-of-freedom system, the mobility transfer function has the reciprocity property; for a two-degree-of-freedom system, no transfer function has the reciprocity property; and for a three-degree-of-freedom system, one transfer function has the reciprocity property. This paper shows that the presence of transfer functions with the reciprocity property is extremely important for obtaining simple optimal design formulas for dynamic vibration absorbers.https://www.jstage.jst.go.jp/article/mej/9/1/9_21-00362/_pdf/-char/endynamic vibration absorberdamped primary systemh∞ optimizationh2 optimizationformula manipulationexact algebraic solutionmobility transfer functionreciprocity |
| spellingShingle | Toshihiko ASAMI Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers Mechanical Engineering Journal dynamic vibration absorber damped primary system h∞ optimization h2 optimization formula manipulation exact algebraic solution mobility transfer function reciprocity |
| title | Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| title_full | Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| title_fullStr | Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| title_full_unstemmed | Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| title_short | Relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| title_sort | relationship between the reciprocity of transfer functions for mechanical vibration systems and optimal design formulas of dynamic vibration absorbers |
| topic | dynamic vibration absorber damped primary system h∞ optimization h2 optimization formula manipulation exact algebraic solution mobility transfer function reciprocity |
| url | https://www.jstage.jst.go.jp/article/mej/9/1/9_21-00362/_pdf/-char/en |
| work_keys_str_mv | AT toshihikoasami relationshipbetweenthereciprocityoftransferfunctionsformechanicalvibrationsystemsandoptimaldesignformulasofdynamicvibrationabsorbers |