CHEKSIZ SOHADAGI BALKA TEBRANISH TENGLAMASI UCHUN TESKARI MASALA

Ushbu tadqiqotda bir jinsli elastik balkaning tebranish jarayoni matematik modellashtirish asosida o‘rganildi. Balka tebranishi to‘rtinchi tartibli xususiy hosilali differensial tenglama yordamida ifodalandi va cheksiz balka uchun Koshi masalasi ko‘rib chiqildi. Tenglama yechimi Fourier integral usuli yordamida qurildi hamda fundamental yechimlar orqali umumiy yechim hosil qilindi. Tadqiqot davomida balkaning vaqt va fazo bo‘yicha tebranish xususiyatlari grafik usulda tahlil qilindi. Natijalar balkaning markaziy qismida maksimal siljish hosil bo‘lishini, tebranish jarayoni davriy xarakterga ega ekanligini va tebranish chastotalari material parametrlariga bog‘liqligini ko‘rsatdi. Shuningdek, teskari masala yordamida material xususiyatlarini aniqlash imkoniyati ko‘rsatildi. Olingan natijalar qurilish konstruksiyalari va mexanik tizimlarning dinamik holatini baholashda qo‘llanilishi mumkin.

In this study, the vibration process of a homogeneous elastic beam was studied based on mathematical modeling. The beam vibration was expressed using a fourth order partial differential equation and the Cauchy problem for an infinite beam was considered. The solution of the equation was constructed using the Fourier integral method, and a general solution was obtained using fundamental solutions. During the study, the vibration characteristics of the beam in time and space were analyzed graphically. The results showed that the maximum displacement occurs in the central part of the beam, the vibration process is periodic, and the vibration frequencies depend on the material parameters. It was also shown that the possibility of determining the material properties using the inverse problem was demonstrated. The results obtained can be used to assess the dynamic state of building structures and mechanical systems.