A method for shifting natural frequencies of a dynamic system to desired values with concentrated mass modifications

Abstract

In this study, shifting a certain number of natural frequencies of a dynamic system to the desired values with the concentrated mass modifications is considered. A new method is proposed in order to determine the necessary mass modifications. The method proposed is based on the Sherman-Morrison formula and uses the receptances that are related to the modification coordinates of the original system. The system is sequentially modified at the predefined locations by a number of unknown masses which equal the number of frequencies that will be shifted. The method yields a set of nonlinear equations which equal the number of shifting frequencies, then the necessary masses are estimated by solving these equations numerically. The efficiency of the proposed method is shown by various numerical and experimental applications. It is shown that the method is very effective and can be used for real applications.

Modifikasi Perilaku Dinamik Struktur dengan Massa Terkonsentrasi

“…McMillan dan Keane [12] melakukan penelitian untuk menggeser frekuensi natural dengan menambahkan massa terkonsentrasi pada sebuah pelat baja. Pada makalah ini di sajikan suatu metode yang dikembangkan oleh Orhan Cakar [3] dengan menggeser beberapa frekuensi natural sehingga diperoleh frekuensi natural yang diinginkan dengan menambahkan massa terkonsentrasi. Metode ini berdasarkan rumus Sherman-Morrison [21] dan dapat mengestimasi massa yang dimodifikasi dengan menyelesaikan beberapa persamaan non linier yang jumlahnya sama dengan massa yang di modifikasi pada persamaan getaran tidak terkopel.…”

“…Metode ini adalah berdasarkan rumus "Structural Modification" [21], pada metode ini dilakukan perhitungan invers matriks modifikasi dengan menggunakan invers dari matriks original dan modifikasi. Modifikasi struktur berdasarkan rumus SM telah dijelaskan pada refrensi [3] dan [21].…”

“…Tujuan dari penelitian ini adalah untuk mendemonstrasikan penelitian yang dilakukan oleh Orhan Cakar [3] yaitu menggeser sejumlah frekuensi natural tertentu pada sejumlah frekuensi natural yang di inginkan. Untuk melakukan perhitungan modifikasi massa dengan menggunakan persamaan (8).…”

Assignment of Natural Frequencies and Mode Shapes Based on FRFs

“…The solution to the problem required only a small linear system and a few unwanted eigenvalues with related eigenvectors. One year later, in order to assign a certain number of natural frequencies, a numerical method based on the Sherman-Morrison formula was proposed [28]. This method required the receptance values related to the modified coordinates of the original system structure.…”

Torsional Vibration Attenuation Characteristics and Stiffness Identification of Flexible Coupling in Vehicle Power Train

“…(1) Torsional vibration modeling and analysis: the torsional vibration model of power train is simplified as one multi-degree-of-freedom analysis model with concentrated mass-stiffness-damping parameters in the previous researches, which has been verified by large quantity of calculation and test data [1][2][3][4][5]. And sensitivities characteristics of main free and forced vibration parameters are important.…”