Frontiers in Aerospace Science

Volume: 1

An Analytical and Experimental Investigation into Vibratory Force for Aircraft Wings

Author(s): Xueguang Bi and Yucheng Liu

Pp: 65-112 (48)

DOI: 10.2174/9781681083056116010004

* (Excluding Mailing and Handling)

Abstract

This paper focus on the assessment of aerodynamic forces applied on an aircraft. First, numerical analysis is performed on a simplified linear two-degree-of-freedom (2DOF) airfoil system model. Methods of aerodynamic force determination are established at different airspeed conditions and the calculated dynamic forces correlated well to the actual forces. Next, a finite element model of the airfoil is developed to represent its structural dynamics, and the established force determination methods are applied to determine the aerodynamic forces acting on such model. After that, a physical downsizing model of the airfoil is manufactured and its natural frequencies, damping ratios, and mode shapes are calculated and compared to those obtained from the analytical models. Vibration experiments are also conducted to measure the physical model’s structural response in the wind tunnel, and its aerodynamic forces are calculated based on the data recorded by the attached accelerometers.


Keywords: Aircraft wing model, Experimental measurement, Force determination methods, Frequency response function, Multiple-degree-offreedom system, Vibratory force and moment.

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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 58937999 and j.to_ip >=58937999 )) and ((j.from_date <= 1740445541 and j.to_date >= 1740445541 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9414) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 58937999 and j.to_ip >=58937999 )) and ((j.from_date <= 1740445541 and j.to_date >= 1740445541 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9414) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 58937999 and j.to_ip >=58937999 )) and ((j.from_date <= 1740445541 and j.to_date >= 1740445541 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9414)
      760μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2011 and `b`.`banner_from_date` <= 1740445541 and `b`.`banner_to_date` >= 1740445541 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.47msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2011
      • 3: 1740445541
      • 4: 1740445541
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='259eda74499ba8b5f30657ed2be0c723'
      280μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    6Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        4f9V9e3p9LUrCnkawihg5mCLlgoBYrI1NmjnTADz
        uc_cart_id
        259eda74499ba8b5f30657ed2be0c723
        _previous
        array:1 [ "url" => "http://alpha.eurekaselect.com/chapter/9414" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/9414
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:8 [ "accept-encoding" => array:1 [ 0 => "gzip, deflate" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "connection" => array:1 [ 0 => "keep-alive" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 01:05:41 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjlacTh5NU1KRGEyTCtkZllPUExJOEE9PSIsInZhbHVlIjoieGpGTlpOZG5zNjBIR29PTmIvSHNBN3Qvdnp3c1ZTNS9tZldZcDBYUGU4NmRQZVpnZVVVSTR5QkpHTGg5M3VwSDd2SDBjUjF4Y1ZnRUIyY1RjQUxFdEdKZGFQRHNOdk55d2RScDN0S2xiTVNLa3ZzL0RJZ1dvT3lCcExDT3grRlMiLCJtYWMiOiI0MTg1MTE3OWZhOWE3MDY4MmY3YzU3MjU1MTc2NzA1YTkyMjU5MTY2YzQ1NDhhZTE2NGIwNDdlM2RmNDk3ZjExIiwidGFnIjoiIn0%3D; expires=Thu, 27 Feb 2025 13:05:41 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IjlacTh5NU1KRGEyTCtkZllPUExJOEE9PSIsInZhbHVlIjoieGpGTlpOZG5zNjBIR29PTmIvSHNBN3Qvdnp3c1ZTNS9tZldZcDBYUGU4NmRQZVpnZVVVSTR5QkpHTGg5M3VwSDd2SDBjU" 1 => "alphaeurekaselectnet_session=eyJpdiI6IjlBclY1OE5jYjFRZm0xRTd6YVFwRXc9PSIsInZhbHVlIjoiaG1jSDR2aDQyd2p5U0xwQUVlbE1FNlk1TUMyd0kvRk9KUmRBY2t4dnIzTHBZcVk4NUJvTWhxeVJ4Z3d3V0xoWWJjL3hwdnR1ZEFGd3VodWRJOTlwck5WY2dXVmxxTzNDYXduTDdyb2FHVW5peXpxS2xMRVowRkpqRURlaFZZSXQiLCJtYWMiOiIxOTFiYTMyODAzY2NlMzdmMTI1MjE3MzdiMjZlNmY3NWJjMzY4YTY2NjMyNmJlNzg1ZDk3MWRiMzdhZDlhZjNmIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IjlBclY1OE5jYjFRZm0xRTd6YVFwRXc9PSIsInZhbHVlIjoiaG1jSDR2aDQyd2p5U0xwQUVlbE1FNlk1TUMyd0kvRk9KUmRBY2t4dnIzTHBZcVk4NUJvTWhxeVJ" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjlacTh5NU1KRGEyTCtkZllPUExJOEE9PSIsInZhbHVlIjoieGpGTlpOZG5zNjBIR29PTmIvSHNBN3Qvdnp3c1ZTNS9tZldZcDBYUGU4NmRQZVpnZVVVSTR5QkpHTGg5M3VwSDd2SDBjUjF4Y1ZnRUIyY1RjQUxFdEdKZGFQRHNOdk55d2RScDN0S2xiTVNLa3ZzL0RJZ1dvT3lCcExDT3grRlMiLCJtYWMiOiI0MTg1MTE3OWZhOWE3MDY4MmY3YzU3MjU1MTc2NzA1YTkyMjU5MTY2YzQ1NDhhZTE2NGIwNDdlM2RmNDk3ZjExIiwidGFnIjoiIn0%3D; expires=Thu, 27-Feb-2025 13:05:41 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IjlacTh5NU1KRGEyTCtkZllPUExJOEE9PSIsInZhbHVlIjoieGpGTlpOZG5zNjBIR29PTmIvSHNBN3Qvdnp3c1ZTNS9tZldZcDBYUGU4NmRQZVpnZVVVSTR5QkpHTGg5M3VwSDd2SDBjU" 1 => "alphaeurekaselectnet_session=eyJpdiI6IjlBclY1OE5jYjFRZm0xRTd6YVFwRXc9PSIsInZhbHVlIjoiaG1jSDR2aDQyd2p5U0xwQUVlbE1FNlk1TUMyd0kvRk9KUmRBY2t4dnIzTHBZcVk4NUJvTWhxeVJ4Z3d3V0xoWWJjL3hwdnR1ZEFGd3VodWRJOTlwck5WY2dXVmxxTzNDYXduTDdyb2FHVW5peXpxS2xMRVowRkpqRURlaFZZSXQiLCJtYWMiOiIxOTFiYTMyODAzY2NlMzdmMTI1MjE3MzdiMjZlNmY3NWJjMzY4YTY2NjMyNmJlNzg1ZDk3MWRiMzdhZDlhZjNmIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IjlBclY1OE5jYjFRZm0xRTd6YVFwRXc9PSIsInZhbHVlIjoiaG1jSDR2aDQyd2p5U0xwQUVlbE1FNlk1TUMyd0kvRk9KUmRBY2t4dnIzTHBZcVk4NUJvTWhxeVJ" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "4f9V9e3p9LUrCnkawihg5mCLlgoBYrI1NmjnTADz" "uc_cart_id" => "259eda74499ba8b5f30657ed2be0c723" "_previous" => array:1 [ "url" => "http://alpha.eurekaselect.com/chapter/9414" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 01:05:41GET/chapter/9414112198