{"id":831,"date":"2026-10-03T05:51:21","date_gmt":"2026-10-03T02:51:21","guid":{"rendered":"https:\/\/wpcalc.com\/fr\/?p=831"},"modified":"2026-10-03T05:51:21","modified_gmt":"2026-10-03T02:51:21","slug":"frequence-de-resonance-ressort-2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/fr\/ingenierie\/frequence-de-resonance-ressort-2\/","title":{"rendered":"Calculateur de fr\u00e9quence de r\u00e9sonance d'un ressort (module de cisaillement)"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Estimation de la r\u00e9sonance d&#039;un ressort \u00e0 l&#039;aide du module de cisaillement<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"831\" data-favorite-title=\"Fr\u00e9quence de r\u00e9sonance d&#039;un ressort\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/ingenierie\/frequence-de-resonance-ressort-2\/\" data-favorite-excerpt=\"Ce calculateur estime la fr\u00e9quence de r\u00e9sonance d&#039;un ressort \u00e0 partir des param\u00e8tres g\u00e9om\u00e9triques, de la densit\u00e9 du mat\u00e9riau et du module de cisaillement (G). Il est id\u00e9al pour \u00e9valuer la dynamique des ressorts h\u00e9lico\u00efdaux dans les syst\u00e8mes m\u00e9caniques de pr\u00e9cision, automobiles et vibratoires.\" aria-label=\"Ajouter aux favoris\" data-favorite-icon=\"icon icon-electrical\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/fr\/ingenierie\/frequence-de-resonance-ressort-2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-831\" data-post=\"831\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Diam\u00e8tre moyen des spires<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"diamtre_moyen_des_spires\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"0.05\"\/><div class=\"unit\" id=\"calc-unit-1\">m<\/div><small id=\"calc-info-1\">Diam\u00e8tre moyen de la bobine<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Diam\u00e8tre du fil<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"diamtre_du_fil\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"0.002\"\/><div class=\"unit\" id=\"calc-unit-2\">m<\/div><small id=\"calc-info-2\">Diam\u00e8tre du fil<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Nombre de spires<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"nombre_de_spires\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"6\"\/><small id=\"calc-info-3\">Nombre de spires actives<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Masse volumique du mat\u00e9riau<\/label><div class=\"term\">\u03c1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"masse_volumique_du_matriau\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"7850\"\/><div class=\"unit\" id=\"calc-unit-4\">kg\/m\u00b3<\/div><small id=\"calc-info-4\">Masse volumique du mat\u00e9riau du ressort (par ex. 7850 pour l&#039;acier)<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Module de cisaillement<\/label><div class=\"term\">G<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"module_de_cisaillement\" id=\"field-5\" aria-describedby=\"calc-unit-5 calc-info-5\" step=\"any\" value=\"79000000000\"\/><div class=\"unit\" id=\"calc-unit-5\">Pa<\/div><small id=\"calc-info-5\">Module de cisaillement du mat\u00e9riau<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"831\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Vos r\u00e9sultats<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Fr\u00e9quence de r\u00e9sonance<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"Hz\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copier le lien vers ce calcul<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Laisser un commentaire<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"831\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">J\u2019aime <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Utile <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confus <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">D\u00e9\u00e7u <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inexact <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<p><style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Fr\u00e9quence de r\u00e9sonance d'un ressort avec le module de Young ou de cisaillement<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formule<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$f_{\\text{res}} = \\frac{d}{D^2} \\cdot \\sqrt{ \\frac{9 \\cdot G}{n \\cdot \\rho} }$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>O\u00f9&nbsp;:<\/strong><\/p>\n<ul>\n<li>$$f_{\\text{res}}$$ = fr\u00e9quence de r\u00e9sonance (Hz)  <\/li>\n<li>$$d$$ = diam\u00e8tre du fil (m)  <\/li>\n<li>$$D$$ = diam\u00e8tre de la spire (m)  <\/li>\n<li>$$n$$ = nombre de spires actives  <\/li>\n<li>$$\\rho$$ = masse volumique du mat\u00e9riau (kg\/m\u00b3)  <\/li>\n<li>$$G$$ = module de cisaillement (Pa)<\/li>\n<\/ul>\n<p>Cette formule d\u00e9coule de la dynamique ressort-masse et de l'\u00e9lasticit\u00e9 du mat\u00e9riau, en supposant l'absence d'amortissement.<br \/>\r\n<\/section><br \/>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Fr\u00e9quence de r\u00e9sonance d'un ressort (module de Young) \u2013 Exemple de calcul<\/h2><\/div>\r\n\r\n<\/p>\n<h3>Donn\u00e9es&nbsp;:<\/h3>\n<ul>\n<li>$$d$$ = 0,003 m  <\/li>\n<li>$$D$$ = 0,03 m  <\/li>\n<li>$$n$$ = 8  <\/li>\n<li>$$\\rho $$ = 7850 kg\/m\u00b3 (acier)  <\/li>\n<li>$$G$$ = 79,3 \u00d7 10\u2079 Pa<\/li>\n<\/ul>\n<h3>Calcul&nbsp;:<\/h3>\n<ol>\n<li>$$f_{\\text{res}} = \\frac{0.003}{0.03^2} \\cdot \\sqrt{ \\frac{9 \\cdot 79.3 \\cdot 10^9}{8 \\cdot 7850} }$$<\/li>\n<li>$$= \\frac{0.003}{0.0009} \\cdot \\sqrt{ \\frac{713.7 \\cdot 10^9}{62800} }$$<\/li>\n<li>$$\u2248 3.33 \\cdot \\sqrt{1136226.11} \u2248 3.33 \\cdot 1065.2 \u2248 3547~\\text{Hz}$$<\/li>\n<\/ol>\n<p>\n\r\n<\/section><br \/>\nLa fr\u00e9quence de r\u00e9sonance d'un ressort h\u00e9lico\u00efdal peut \u00eatre mod\u00e9lis\u00e9e avec pr\u00e9cision \u00e0 partir de la g\u00e9om\u00e9trie du fil, de la masse volumique et du module de cisaillement. Ce calculateur est indispensable pour les ing\u00e9nieurs qui con\u00e7oivent des syst\u00e8mes de suspension, des isolateurs de vibrations et des r\u00e9sonateurs m\u00e9caniques n\u00e9cessitant un contr\u00f4le pr\u00e9cis de la fr\u00e9quence. Il permet aux concepteurs d'explorer comment la modification du diam\u00e8tre du fil, du nombre de spires ou du mat\u00e9riau influence les performances dynamiques.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ce calculateur estime la fr\u00e9quence de r\u00e9sonance d'un ressort \u00e0 partir des param\u00e8tres g\u00e9om\u00e9triques, de la densit\u00e9 du mat\u00e9riau et du module de cisaillement (G). Il est id\u00e9al pour \u00e9valuer la dynamique des ressorts h\u00e9lico\u00efdaux dans les syst\u00e8mes m\u00e9caniques de pr\u00e9cision, automobiles et vibratoires.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[9],"class_list":["post-831","post","type-post","status-publish","format-standard","hentry","category-ingenierie","tag-electricite"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/831","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/comments?post=831"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/831\/revisions"}],"predecessor-version":[{"id":5006,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/831\/revisions\/5006"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/media?parent=831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/categories?post=831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/tags?post=831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}