title: ÐÐµÑÐ¾Ð´ ÐÐ°Ð»Ð°Ð¼Ð±ÐµÑÐ° Ð¿ÑÐ¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¼ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¸
title: Dalembert method for nonlinear interaction
Creators: name: ÐÐ²Ð³ÑÐ°ÑÐ¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
name: ÐÐ°ÑÐ°Ð·Ð¸Ð½, ÐÐ»Ð°Ð´Ð¸Ð¼Ð¸Ñ
name: Ð¢ÐµÑÐµÑÐ¸Ð½, ÐÐ°Ð»ÐµÑÐ¸Ð¹
name: Ð¥Ð»ÐµÐ±Ð¾ÑÐ¾Ð»Ð¾Ð², ÐÐ³Ð¾ÑÑ
name: "Ð¡Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð°ÑÐ¸Ð½Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ: Ð½Ð°ÑÐºÐ° Ð¸ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (13; 2024; Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³)
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2024
Subjects: ÐÑÐ¿ÑÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ ÑÑÐµÐ½Ð´Ñ
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Dalembert method
nonlinear shaper

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ð¹ Ð¸ÑÐ¿ÑÑÑÐµÐ¼ÑÑ Ð¸Ð·Ð´ÐµÐ»Ð¸Ð¹ Ð½Ð° ÑÐ´Ð°ÑÐ½ÑÑ ÑÑÐµÐ½Ð´Ð°Ñ. ÐÐ»Ñ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐµÐ±ÑÐµÐ¼ÑÑ Ð·Ð°ÐºÐ¾Ð½Ð¾Ð² Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð¼ÐµÐ¶Ð´Ñ Ð±Ð¾Ð¹ÐºÐ¾Ð¼ Ð¸ ÑÑÐ¾Ð»Ð¾Ð¼ ÑÑÐµÐ½Ð´Ð° ÑÑÑÐ°Ð½Ð°Ð²Ð»Ð¸Ð²Ð°ÑÑ Ð¿ÑÐ¾ÐºÐ»Ð°Ð´ÐºÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð¹ ÑÐ¾Ð»ÑÐ¸Ð½Ñ Ñ ÑÐ°Ð·Ð½ÑÐ¼Ð¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ Ð½Ð°Ð³ÑÑÐ·Ð¾ÑÐ½ÑÐ¼Ð¸ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ°Ð¼Ð¸. Ð£ÑÐºÐ¾ÑÐµÐ½Ð¸Ðµ ÑÑÐ¾Ð»Ð° Ñ Ð¸ÑÐ¿ÑÑÑÐµÐ¼ÑÐ¼ Ð¸Ð·Ð´ÐµÐ»Ð¸ÐµÐ¼ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ ÑÐ¿ÑÑÐ³Ð¾-Ð¸Ð½ÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐ¼Ð¸ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð°Ð¼Ð¸ ÑÐ¾ÑÐ´Ð°ÑÑÑÑÐ¸ÑÑÑ ÑÐµÐ», Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÑÑ Ð¿ÑÐ¾ÐºÐ»Ð°Ð´Ð¾Ðº Ð¸ Ð½Ð°Ð»Ð¾Ð¶ÐµÐ½Ð¸ÐµÐ¼ Ð¿Ð°Ð´Ð°ÑÑÐ¸Ñ Ð¸ Ð¾ÑÑÐ°Ð¶ÐµÐ½Ð½ÑÑ Ð²Ð¾Ð»Ð½. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½Ð¸ÑÑ ÑÐ°ÑÑÐµÑ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ ÑÑÐ¾Ð»Ð° Ð² Ð´Ð²Ð° ÑÑÐ°Ð¿Ð°. ÐÐ° Ð¿ÐµÑÐ²Ð¾Ð¼ ÑÑÐ°Ð¿Ðµ Ð¸Ð· ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐ³Ð¾Ð³Ð¾ ÑÐ¾ÑÐ´Ð°ÑÐµÐ½Ð¸Ñ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾ ÑÐ²ÐµÑÐ´ÑÑ ÑÐµÐ» Ð´Ð¾Ð»Ð¶Ð½Ð° Ð±ÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð° Ð¼ÐµÐ´Ð»ÐµÐ½Ð½Ð°Ñ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÐ°Ñ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð´Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð¿ÑÐ¸Ð±Ð¾ÑÐ½Ð¾Ð³Ð¾ ÑÑÐ¾Ð»Ð°. ÐÐ° Ð²ÑÐ¾ÑÐ¾Ð¼ ÑÑÐ°Ð¿Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐµÑÑÑ ÑÐ°ÑÑÐµÑ Ð±ÑÑÑÑÐ¾Ð¹ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÐµÐ¹ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ ÐºÐ°Ðº ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ ÑÑÐ¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð°Ð´Ð°ÑÑÐ¸Ñ Ð¸ Ð¾ÑÑÐ°Ð¶ÐµÐ½Ð½ÑÑ Ð²Ð¾Ð»Ð½. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ
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description: The work is devoted to determination of acceleration of tested articles on impact stands. To form the required laws of motion between the striker and the bench table, shims of different thickness with different nonlinear loading characteristics are installed. The acceleration of the table with the test piece is determined by the elastic-inertial properties of the colliding bodies, nonlinearity of the pads and the superposition of incident and reflected waves. The paper proposes to perform the calculation of table acceleration in two stages. At the first stage, the slow component of the acceleration of the longitudinal motion of the instrument table should be determined from the consideration of nonlinear elastic collision of absolutely solid bodies. At the second stage, the fast component of the acceleration is calculated as a result of the summation of incident and reflected waves. A homogeneous rod is taken as a dynamic model of the table.