{"id":165,"date":"2025-10-31T00:25:51","date_gmt":"2025-10-31T00:25:51","guid":{"rendered":"https:\/\/vibromera.eu\/glossary\/mode-shape\/"},"modified":"2026-05-23T23:04:15","modified_gmt":"2026-05-23T23:04:15","slug":"mode-shape","status":"publish","type":"glossary","link":"https:\/\/vibromera.eu\/tt\/glossary\/mode-shape\/","title":{"rendered":"What is Mode Shape in Rotor Dynamics?"},"content":{"rendered":"<h1>Understanding Mode Shapes in Rotor Dynamics<\/h1>\n\t\t<section class=\"woocommerce hestia-shop products is-shortcode\" id=\"products\" data-sorder=\"hestia_shop\" >\n\t\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<div class=\"hestia-shop-content\">\n\t\t\t<div class=\"row\" data-aos=\"fade-up\" >\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" title=\"Portable balancer &#038; Vibration analyzer Balanset-1A\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A full kit portable balancer and vibration analyzer\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-272x182.webp 272w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/devices\/\" rel=\"tag\">Devices<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\" title=\"Portable balancer &#038; Vibration analyzer Balanset-1A\">Portable balancer &#038; Vibration analyzer Balanset-1A<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>1,975.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=986\" data-quantity=\"1\" data-product_id=\"986\" data-product_sku=\"BS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=986\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_986\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"986\" data-product_sku=\"BS-1\" aria-label=\"Add to cart: \u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d\" rel=\"nofollow\" data-success_message=\"\u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_986\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" title=\"Vibration sensor\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A vibration sensor close-up\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/vibration-sensor\/\" title=\"Vibration sensor\">Vibration sensor<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>90.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1820\" data-quantity=\"1\" data-product_id=\"1820\" data-product_sku=\"VS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1820\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1820\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1820\" data-product_sku=\"VS-1\" aria-label=\"Add to cart: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1820\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Optical Sensor (Laser Tachometer)\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Optical Sensor (Laser Tachometer)\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1536x1023.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU.webp 1600w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Optical Sensor (Laser Tachometer)\">Optical Sensor (Laser Tachometer)<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>124.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1832\" data-quantity=\"1\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1832\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1832\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" aria-label=\"Add to cart: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1832\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" title=\"Balanset-4\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Vibromera rotor balancing kit: carry case, multi-channel signal conditioner, handheld analyzer, magnetic base, vibration sensors, and coiled cables.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4.webp 640w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/devices\/\" rel=\"tag\">Devices<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-4\/\" title=\"Balanset-4\">Balanset-4<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>6,803.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1833\" data-quantity=\"1\" data-product_id=\"1833\" data-product_sku=\"BS-4\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=1833\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1833\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1833\" data-product_sku=\"BS-4\" aria-label=\"Add to cart: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1833\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div><!-- \/.row --><div class=\"row\">\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" title=\"Magnetic Stand Insize-60-kgf\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Magnet base.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/parts\/\" rel=\"tag\">Parts<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/magnet-stand\/\" title=\"Magnetic Stand Insize-60-kgf\">Magnetic Stand Insize-60-kgf<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span 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https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-e1732998877834.webp 708w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/tt\/product-category\/devices\/\" rel=\"tag\">Devices<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/tt\/product\/dynamic-balancer-balanset-1a\/\" title=\"Dynamic balancer \u201cBalanset-1A\u201d OEM\">Dynamic balancer \u201cBalanset-1A\u201d OEM<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>1,735.00<\/span> + VAT (if applicable)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=4193\" data-quantity=\"1\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/tt\/wp-json\/wp\/v2\/glossary\/165?add-to-cart=4193\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_4193\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" aria-label=\"Add to cart: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_4193\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t\n<p>A <strong>mode shape<\/strong> \u2014 also called a vibration mode or natural mode \u2014 is the characteristic spatial pattern of deformation that a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/rotor\/\">rotor<\/a> system takes on when it vibrates at one of its <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/natural-frequency\/\">natural frequencies<\/a>. It describes the relative amplitude and <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/phase\/\">phase<\/a> of motion at every point along the shaft when the system oscillates freely at that specific <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/resonance\/\">resonant<\/a> frequency. Each mode shape is paired with one natural frequency, and together the set of them forms a complete description of the system&#8217;s dynamic behaviour. Understanding mode shapes is fundamental to <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/rotor-dynamics\/\">rotor dynamics<\/a>, because they determine where <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/critical-speed\/\">critical speeds<\/a> occur and how the rotor responds to the forces that excite it.<\/p>\n<h2>1. Definition and Physical Meaning<\/h2>\n<p>When a structure is disturbed and left to vibrate on its own, it does not move arbitrarily. It settles into a small number of preferred patterns, each ringing at its own frequency, exactly as a guitar string sounds a fundamental and a series of overtones. For a rotor those preferred patterns are its mode shapes, and the frequencies at which they appear are its natural frequencies. The danger in rotating machinery is that a rotor&#8217;s running speed can coincide with one of these natural frequencies; when it does, the matching mode shape is driven into <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/resonance\/\">resonance<\/a> and vibration amplitudes climb sharply. Knowing the shapes in advance tells the engineer where the rotor will flex most, where it will barely move, and therefore where to intervene.<\/p>\n<h2>2. Visualising the Mode Shapes<\/h2>\n<p>Mode shapes are best pictured as the deflection curves of the rotor shaft.<\/p>\n<h3>First Mode (Fundamental)<\/h3>\n<ul>\n<li><strong>Shape:<\/strong> a simple arc or bow, like a skipping rope with a single hump.<\/li>\n<li><strong>Node points:<\/strong> none internally \u2014 the shaft is supported at the bearings, which act as approximate nodes.<\/li>\n<li><strong>Maximum deflection:<\/strong> typically near mid-span between the bearings.<\/li>\n<li><strong>Frequency:<\/strong> the lowest natural frequency of the system.<\/li>\n<li><strong>Critical speed:<\/strong> the first critical speed corresponds to this mode.<\/li>\n<\/ul>\n<h3>Second Mode<\/h3>\n<ul>\n<li><strong>Shape:<\/strong> an S-curve with one node in the middle.<\/li>\n<li><strong>Node points:<\/strong> one internal node, where shaft deflection is zero.<\/li>\n<li><strong>Maximum deflection:<\/strong> at two locations, one each side of the node.<\/li>\n<li><strong>Frequency:<\/strong> higher than the first mode, often three to five times its frequency.<\/li>\n<li><strong>Critical speed:<\/strong> the second critical speed.<\/li>\n<\/ul>\n<h3>Third Mode and Higher<\/h3>\n<ul>\n<li><strong>Shape:<\/strong> increasingly complex wave patterns.<\/li>\n<li><strong>Node points:<\/strong> two for the third mode, three for the fourth, and so on.<\/li>\n<li><strong>Frequency:<\/strong> progressively higher.<\/li>\n<li><strong>Practical importance:<\/strong> usually relevant only for very high-speed or very <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/flexible-rotor\/\">flexible rotors<\/a>.<\/li>\n<\/ul>\n<h2>3. Key Characteristics of Mode Shapes<\/h2>\n<h3>Orthogonality<\/h3>\n<p>Different mode shapes are mathematically orthogonal \u2014 that is, independent. In an ideal linear system, energy fed in at one modal frequency does not excite the others, which is precisely what lets engineers treat and correct each mode separately.<\/p>\n<h3>Normalisation<\/h3>\n<p>Mode shapes are usually normalised, with the maximum deflection scaled to a reference value (often 1.0) so that shapes can be compared. The actual deflection magnitude in service depends on the forcing amplitude and the system <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/damping\/\">damping<\/a>.<\/p>\n<h3>Node Points<\/h3>\n<p><strong>Nodes<\/strong> are locations along the shaft where deflection stays zero during vibration in that mode. The number of internal nodes equals the mode number minus one:<\/p>\n<ul>\n<li>first mode: 0 internal nodes;<\/li>\n<li>second mode: 1 internal node;<\/li>\n<li>third mode: 2 internal nodes.<\/li>\n<\/ul>\n<p>A <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/nodal-point\/\">nodal point<\/a> is a position of stillness in a given mode \u2014 a fact with direct consequences for both sensor placement and balancing.<\/p>\n<h3>Antinode Points<\/h3>\n<p><strong>Antinodes<\/strong> are the locations of maximum deflection in a mode shape. They are the points of greatest bending stress and therefore the most likely sites of fatigue and failure during resonant vibration.<\/p>\n<h2>4. Why Mode Shapes Matter<\/h2>\n<h3>Critical-Speed Prediction<\/h3>\n<p>Each mode shape corresponds to a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/critical-speed\/\">critical speed<\/a>. When running speed matches a natural frequency, that mode is excited, the rotor deflects into the mode-shape pattern, and <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/unbalance\/\">unbalance<\/a> forces produce their greatest vibration where they align with the antinodes. A <a href=\"https:\/\/vibromera.eu\/tt\/calculators\/rotor-critical-speed\/\">rotor critical-speed calculator<\/a> gives a quick first estimate of where these speeds fall relative to the operating range.<\/p>\n<h3>Balancing Strategy<\/h3>\n<p>Mode shapes guide the choice of <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/balancing\/\">balancing<\/a> approach:<\/p>\n<ul>\n<li><strong><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/rigid-rotor\/\">Rigid rotors<\/a><\/strong> run below the first critical speed; simple <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/two-plane-balancing\/\">two-plane balancing<\/a> is sufficient.<\/li>\n<li><strong><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/flexible-rotor\/\">Flexible rotors<\/a><\/strong> run above the first critical and may need <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/modal-balancing\/\">modal balancing<\/a> aimed at specific mode shapes.<\/li>\n<li><strong>Correction-plane location<\/strong> is most effective at antinodes, where a given mass has the greatest influence on the mode.<\/li>\n<li><strong>Node locations<\/strong> are the opposite case: a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/correction-weight\/\">correction weight<\/a> placed at a node has almost no effect on that mode.<\/li>\n<\/ul>\n<h3>Failure Analysis<\/h3>\n<p>Mode shapes also explain where damage appears. Fatigue cracks typically form at antinodes, where bending stress peaks; bearing distress is more likely where deflection is high; and <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/rotor-rub\/\">rubs<\/a> occur where shaft deflection brings the rotor close to stationary parts.<\/p>\n<h2>5. Determining Mode Shapes<\/h2>\n<h3>Analytical Methods<\/h3>\n<h4>Finite Element Analysis (FEA)<\/h4>\n<ul>\n<li>The most common modern approach.<\/li>\n<li>The rotor is modelled as a chain of beam elements carrying mass, stiffness and inertia.<\/li>\n<li>An eigenvalue analysis returns the natural frequencies and their corresponding mode shapes.<\/li>\n<li>It can account for complex geometry, material properties and bearing characteristics.<\/li>\n<\/ul>\n<h4>Transfer Matrix Method<\/h4>\n<ul>\n<li>A classical analytical technique.<\/li>\n<li>The rotor is divided into stations of known properties.<\/li>\n<li>Transfer matrices propagate deflection and force along the shaft.<\/li>\n<li>Efficient for relatively simple shaft configurations.<\/li>\n<\/ul>\n<h4>Continuous Beam Theory<\/h4>\n<ul>\n<li>For uniform shafts, closed-form analytical solutions exist.<\/li>\n<li>Provides exact expressions for simple cases.<\/li>\n<li>Useful for teaching and for preliminary design.<\/li>\n<\/ul>\n<h3>Experimental Methods<\/h3>\n<h4>Modal Testing (Impact Testing)<\/h4>\n<ul>\n<li>Strike the shaft with an instrumented hammer at several locations \u2014 a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/bump-test\/\">bump test<\/a>.<\/li>\n<li>Measure the response with <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/accelerometer\/\">accelerometers<\/a> at multiple points.<\/li>\n<li>The resulting <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/frequency-response-function\/\">frequency response functions<\/a> reveal the natural frequencies.<\/li>\n<li>The mode shape is extracted from the relative response amplitudes and phases.<\/li>\n<\/ul>\n<h4>Operating Deflection Shape (ODS) Measurement<\/h4>\n<ul>\n<li>Measure vibration at many locations during normal operation.<\/li>\n<li>Near a critical speed, the <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/ods-analysis\/\">operating deflection shape<\/a> approximates the mode shape.<\/li>\n<li>It can be performed with the rotor in situ.<\/li>\n<li>It needs either multiple sensors or a roving-sensor technique.<\/li>\n<\/ul>\n<h4>Proximity Probe Arrays<\/h4>\n<ul>\n<li>Non-contact <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/proximity-probe\/\">proximity probes<\/a> at several axial locations.<\/li>\n<li>Measure shaft deflection directly.<\/li>\n<li>During <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/coastdown-analysis\/\">startup or coastdown<\/a>, the deflection pattern reveals the mode shapes.<\/li>\n<li>The most accurate experimental method for machinery that is actually running.<\/li>\n<\/ul>\n<h2>6. What Changes a Mode Shape<\/h2>\n<h3>Bearing Stiffness Effects<\/h3>\n<ul>\n<li><strong>Rigid bearings:<\/strong> nodes form at the bearing locations and the mode shapes are more constrained.<\/li>\n<li><strong>Flexible bearings:<\/strong> significant motion occurs at the bearings and the mode shapes are more distributed.<\/li>\n<li><strong>Asymmetric bearings:<\/strong> the mode shapes differ between the horizontal and vertical directions.<\/li>\n<\/ul>\n<h3>Speed Dependence<\/h3>\n<p>For rotating shafts the mode shapes can shift with speed because of:<\/p>\n<ul>\n<li><strong><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/gyroscopic-effect\/\">Gyroscopic effects<\/a>:<\/strong> they split modes into forward and backward whirl.<\/li>\n<li><strong>Bearing-stiffness changes:<\/strong> fluid-film <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/journal-bearing\/\">journal bearings<\/a> stiffen as speed rises.<\/li>\n<li><strong>Centrifugal stiffening:<\/strong> at very high speeds, centrifugal forces add stiffness to slender components.<\/li>\n<\/ul>\n<h3>Forward versus Backward Whirl<\/h3>\n<p>In rotating systems each mode can take two forms. In <strong>forward whirl<\/strong> the shaft <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/orbit\/\">orbit<\/a> rotates in the same direction as the shaft itself; in <strong>backward whirl<\/strong> it rotates the opposite way. Gyroscopic effects cause the forward and backward versions to occur at different frequencies \u2014 a frequency split that a <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/campbell-diagram\/\">Campbell diagram<\/a> displays clearly.<\/p>\n<h2>7. Practical Applications<\/h2>\n<h3>Design Optimisation<\/h3>\n<p>Engineers use mode-shape analysis to position bearings so that antinodes do not fall at bearing locations, to size shaft diameters that move critical speeds clear of the operating range, to select bearing stiffness that shapes the modal response favourably, and to add or remove mass at strategic points to shift natural frequencies.<\/p>\n<h3>Troubleshooting<\/h3>\n<p>When excessive vibration appears, the analyst compares operating speed with the predicted critical speeds, identifies whether the machine is running near a resonance, determines which mode is being excited, and selects a modification that shifts the problematic mode away from operating speed.<\/p>\n<h3>Modal Balancing<\/h3>\n<p><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/modal-balancing\/\">Modal balancing<\/a> of flexible rotors depends entirely on knowing the mode shapes: each mode is balanced independently, correction weights are distributed to match the mode-shape pattern, weights placed at nodes have no effect on that mode, and the optimal correction planes sit at the antinodes.<\/p>\n<h2>8. Visualisation and Communication<\/h2>\n<p>Mode shapes are presented in several forms \u2014 2D deflection curves of lateral deflection against axial position; animations of the oscillating shaft; 3D renderings for complex or coupled geometries; colour maps that encode deflection magnitude; and tabular data giving numerical deflection at discrete stations.<\/p>\n<h2>9. Coupled and Complex Mode Shapes<\/h2>\n<h3>Lateral\u2013Torsional Coupling<\/h3>\n<p>In some systems the bending (lateral) and twisting (<a href=\"https:\/\/vibromera.eu\/tt\/glossary\/torsional-vibration\/\">torsional<\/a>) motions couple together \u2014 a behaviour seen with non-circular cross-sections or offset loads. The mode shape then includes both lateral deflection and angular twist, and the analysis required is correspondingly more involved.<\/p>\n<h3>Coupled Bending Modes<\/h3>\n<p>In systems with asymmetric stiffness, the horizontal and vertical modes couple; the mode shapes become elliptical rather than planar. This is common where bearings or supports are anisotropic.<\/p>\n<h2>10. Standards and Guidelines<\/h2>\n<p>Several standards address mode-shape analysis. <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/api-684\/\">API 684<\/a> provides guidelines for rotor-dynamics analysis, including mode-shape calculation; <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/iso-21940-11\/\">ISO 21940-11<\/a> (the modern successor to ISO 1940-1) references mode shapes in the context of flexible-rotor balancing; and the German VDI 3839 addresses modal considerations for flexible rotors.<\/p>\n<h2>11. Relationship to Campbell Diagrams and Field Measurement<\/h2>\n<p>A <a href=\"https:\/\/vibromera.eu\/tt\/glossary\/campbell-diagram\/\">Campbell diagram<\/a> plots natural frequencies against speed, each curve representing one mode. The mode shape behind each curve determines how strongly unbalance at various locations excites that mode, where sensors should sit for maximum sensitivity, and which type of balancing correction will work best. In the field, the practical link between mode shapes and corrective action is the analyser on the bench: once mode-shape analysis identifies the antinodes as the effective correction planes, a portable two-channel instrument such as the <a href=\"https:\/\/vibromera.eu\/tt\/product\/balanset-1\/\">Balanset-1A<\/a> measures the 1\u00d7 amplitude and phase at the bearings and computes the correction weights, letting the engineer act on the very planes the mode shape highlighted. Understanding mode shapes in this way turns rotor dynamics from abstract mathematical prediction into physical insight about how real machinery behaves \u2014 enabling better design, sharper troubleshooting and more effective balancing for every kind of rotating equipment.<\/p>\n<hr>\n<p><a href=\"https:\/\/vibromera.eu\/tt\/glossary\/\">\u2190 Back to Main Index<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Learn about mode shapes, the characteristic deflection patterns of rotating shafts at natural frequencies, essential for understanding critical speeds and flexible rotor behavior.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[109,111],"tags":[],"class_list":["post-165","glossary","type-glossary","status-publish","hentry","category-glossary","category-rotor-balancing"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/165","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary"}],"about":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/types\/glossary"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/165\/revisions"}],"predecessor-version":[{"id":101438,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/glossary\/165\/revisions\/101438"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/media?parent=165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/categories?post=165"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/tt\/wp-json\/wp\/v2\/tags?post=165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}