Solutions to Problems of Controlling Long Waves with the Help of Micro-Structure Tools

Acoustical Sources of One-sided Radiation

Author(s): Vladimir V. Arabadzhi

Pp: 139-165 (27)

DOI: 10.2174/978160805275211101010139

* (Excluding Mailing and Handling)

Abstract

In monochromatic description (sections 5.1, 5.2), the results of the studies of the physical characteristics of unidirectional acoustic sources used in active sound control systems are presented. A discrete unidirectional source in the form of two phased monopoles (section 5.1) and a planar array of such unidirectional sources is considered (section 5.2.1). One-dimensional boundary-value problems with two (the two-point problem) and three (the three-point problem) controlled parallel planar boundaries between homogeneous media with arbitrary impedances are studied (sections 5.2.2-5.2.6). The boundaries (two or three) are subjected to the action of external forces. The case of the zero sum of external forces applied to the controlled boundaries corresponds to a supportless unidirectional source (SUS). It is shown that a unidirectional source can be created within the twopoint boundary-value problem, whereas a supportless unidirectional source can be created within the three-point problem (sections 5.2.5, 5.2.6). Such parameters such as transparency, small size, absence of support, and broad frequency band can be achieved for a unidirectional source in the form of two piezoelectric layers with the same impedance and velocity of sound as those of the surrounding medium (5.2.7-5.2.9). The aspects of linearity of the transparent SUS and its application to active sound control problems are described (sections 5.2.10, 5.2.11). A spatially one-dimensional model of a plane active double layer between two homogeneous elastic half-spaces is studied analytically in temporal representation (section 5.3). The layer synthesizes a preset smooth trajectory of the controlled boundary between the media without any mechanical support. The outer layer of the coating is piezoelectric, and the inner layer is a polymer that is transparent for low-frequency sound and opaque for highfrequency sound because of dissipation. An algorithm for controlling the piezoelectric elements of the layer on the basis of signals from surface particle velocity sensors is proposed (section 5.3.6), and a method for measuring the particle velocity is developed simultaneously (section 5.3.9). Conditions of stability and efficiency of the synthesis are formulated (section 5.3.7). It is shown that the active layer thickness can be much smaller than the wavelength corresponding to the minimal time scale of the boundary trajectory to be formed. The accuracy of the trajectory synthesis depends on the accuracy of measuring, computing, and actuating elements of the system but does not depend on the vibroacoustic characteristics of the half-spaces separated by the active layer or on the presence of smooth waves in these half-spaces. For the synthesis to be efficient, the operating frequency band and the dynamic range of sensors and actuators should be many times greater than the frequency band and the dynamic range of the trajectory to be formed.

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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 <= 51368230 and j.to_ip >=51368230 )) and ((j.from_date <= 1740460081 and j.to_date >= 1740460081 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 2417) 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 <= 51368230 and j.to_ip >=51368230 )) and ((j.from_date <= 1740460081 and j.to_date >= 1740460081 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 2417) 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 <= 51368230 and j.to_ip >=51368230 )) and ((j.from_date <= 1740460081 and j.to_date >= 1740460081 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 2417)
      670μsalphaeurekaselec_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` = 958 and `b`.`banner_from_date` <= 1740460081 and `b`.`banner_to_date` >= 1740460081 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.51msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 958
      • 3: 1740460081
      • 4: 1740460081
      • 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='c8aae4ae3ce0a3d5c9e5280daeb5100e'
      250μsalphaeurekaselec_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\Chapter
    1Chapter.php#?
    App\Models\Keywords
    1Keywords.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        oNrVjKtetiEgHx0JfHQACm2gpkIdeilgfUgNnxyV
        uc_cart_id
        c8aae4ae3ce0a3d5c9e5280daeb5100e
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/2417" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/2417
        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:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IjdkT0NUOENCdFBKNjZkbXRpYU5waGc9PSIsInZhbHVlIjoiNTQ1NndlMEFseUN4MW90cUtEb3lwZWZTZVd1d3hHSVZTOGtNL1FJMXdRRT0iLCJtYWMiOiJiZWFiOGY2Y2RjZmZjZGUxMWI5ZWJhOTUxY2M1ZmZhMDYxNjEwNTQ1NTk4YjRhZTk3NDJlYzQxNGM3NjdhZjM4IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IjdkT0NUOENCdFBKNjZkbXRpYU5waGc9PSIsInZhbHVlIjoiNTQ1NndlMEFseUN4MW90cUtEb3lwZWZTZVd1d3hHSVZTOGtNL1FJMXdRRT0iLCJtYWMiOiJiZWFiOGY2Y2RjZmZj" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "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" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        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 05:08:01 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IkNIcmxzeTJpZXZvVVZwRmduNWVnT2c9PSIsInZhbHVlIjoiVFBFWkJEdVE2bkgxQ2NxQ2x3T1Z3VGFDcWs3OVZtb0l5OHlqTWdYUytkUUhtRTVZM3Z6d1Roa215T0ROMnNRWGtSMmRZbWxrK21qVGQ0WDZUcjNWNzVyU3NkZjZjbVFJTDVZaUV0NzVlWXpzUmhQZ05uV1hHMmFwZmc5RGlFVXEiLCJtYWMiOiJhOGZjNThhMDRkYmFhZmU4MTRjMDlmZjc1NzBmNjZjMjZiZWRlY2JkOGE0Mjc1MGE3ZTI2MGMzMGNiMTIxMjkwIiwidGFnIjoiIn0%3D; expires=Thu, 27 Feb 2025 17:08:01 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IkNIcmxzeTJpZXZvVVZwRmduNWVnT2c9PSIsInZhbHVlIjoiVFBFWkJEdVE2bkgxQ2NxQ2x3T1Z3VGFDcWs3OVZtb0l5OHlqTWdYUytkUUhtRTVZM3Z6d1Roa215T0ROMnNRWGtSMmRZb" 1 => "alphaeurekaselectnet_session=eyJpdiI6InBJZmlIbGNLNkh1SmdCYlZoUUxOTXc9PSIsInZhbHVlIjoiN01KQXF2UFlwMVYyRzhpU3FacUlrL0I5MjFtejZiaS94S1lYc25hT2lGNHlJaUNYd2xTWTZHOTRYRkYraXFTWGxKM1M5c2NXcnFYVGxrWXoyRWx4bGNmZ1BWd1lSVWxyQWVUclpHR0JXYWZoYkJ0WXFEdFc0MEErck1YU2lzQkYiLCJtYWMiOiJiYjAzMWNmZDc3NTgwMGY1ZDY3NWUwMGRiMjkyNGQwMmNlYjg1ZGVkNjU4YTI3YTZmMmZiOTlmMjc0OGZiYjEwIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6InBJZmlIbGNLNkh1SmdCYlZoUUxOTXc9PSIsInZhbHVlIjoiN01KQXF2UFlwMVYyRzhpU3FacUlrL0I5MjFtejZiaS94S1lYc25hT2lGNHlJaUNYd2xTWTZHOTR" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IkNIcmxzeTJpZXZvVVZwRmduNWVnT2c9PSIsInZhbHVlIjoiVFBFWkJEdVE2bkgxQ2NxQ2x3T1Z3VGFDcWs3OVZtb0l5OHlqTWdYUytkUUhtRTVZM3Z6d1Roa215T0ROMnNRWGtSMmRZbWxrK21qVGQ0WDZUcjNWNzVyU3NkZjZjbVFJTDVZaUV0NzVlWXpzUmhQZ05uV1hHMmFwZmc5RGlFVXEiLCJtYWMiOiJhOGZjNThhMDRkYmFhZmU4MTRjMDlmZjc1NzBmNjZjMjZiZWRlY2JkOGE0Mjc1MGE3ZTI2MGMzMGNiMTIxMjkwIiwidGFnIjoiIn0%3D; expires=Thu, 27-Feb-2025 17:08:01 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IkNIcmxzeTJpZXZvVVZwRmduNWVnT2c9PSIsInZhbHVlIjoiVFBFWkJEdVE2bkgxQ2NxQ2x3T1Z3VGFDcWs3OVZtb0l5OHlqTWdYUytkUUhtRTVZM3Z6d1Roa215T0ROMnNRWGtSMmRZb" 1 => "alphaeurekaselectnet_session=eyJpdiI6InBJZmlIbGNLNkh1SmdCYlZoUUxOTXc9PSIsInZhbHVlIjoiN01KQXF2UFlwMVYyRzhpU3FacUlrL0I5MjFtejZiaS94S1lYc25hT2lGNHlJaUNYd2xTWTZHOTRYRkYraXFTWGxKM1M5c2NXcnFYVGxrWXoyRWx4bGNmZ1BWd1lSVWxyQWVUclpHR0JXYWZoYkJ0WXFEdFc0MEErck1YU2lzQkYiLCJtYWMiOiJiYjAzMWNmZDc3NTgwMGY1ZDY3NWUwMGRiMjkyNGQwMmNlYjg1ZGVkNjU4YTI3YTZmMmZiOTlmMjc0OGZiYjEwIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6InBJZmlIbGNLNkh1SmdCYlZoUUxOTXc9PSIsInZhbHVlIjoiN01KQXF2UFlwMVYyRzhpU3FacUlrL0I5MjFtejZiaS94S1lYc25hT2lGNHlJaUNYd2xTWTZHOTR" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "oNrVjKtetiEgHx0JfHQACm2gpkIdeilgfUgNnxyV" "uc_cart_id" => "c8aae4ae3ce0a3d5c9e5280daeb5100e" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/2417" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 05:08:01GET/chapter/2417112193