FRF Based Structural Modification of a Mechanical System by Adding Masses and Utilizing the Grey Wolf Optimization Technique

Yıl 2023, Cilt: 18 Sayı: 1, 1 - 10, 29.03.2023

Murat Şen Osman Yiğid Orhan Çakar

https://doi.org/10.55525/tjst.1148713

Öz

Resonance and anti-resonance frequencies are important parameters that determine the dynamic behavior of mechanical systems. Changes in these parameters, which depend on the system's physical properties such as mass and stiffness, also affect the system's dynamic behavior. Finding the necessary structural modifications to adjust the resonance and anti-resonance frequencies of a system to the desired values is a study area of inverse structural modification. In this study, an inverse structural modification method for one and multi-rank modifications is presented. With the presented method some resonance or anti-resonance frequencies of mechanical systems can be shifted to prescribed values by calculating the necessary modifications. The presented method is based on Sherman-Morrison (SM) formula and uses the frequency response functions (FRF) of the original system directly. For one modification an exact solution is obtained on the other hand for two or more modifications some nonlinear set of equations has to be solved. A meta-heuristic optimization technique known as Grey Wolf Optimizer (GWO) is applied for the solution of the nonlinear equations. The method is applied to a six-degrees-of-freedom mass-spring system. Some resonance and anti-resonance frequencies in the frequency bandwidth of the system are selected as target frequencies. The necessary modification masses are calculated to match these frequencies. After applying the calculated masses to the system the target frequencies are obtained successfully.

Anahtar Kelimeler

Frequency response function, frequency shifting, grey wolf optimization, structural modification

Kaynakça

• Braun SG, Ram YM. Modal modification of vibrating systems: some problems and their solutions. Mech Syst Signal Process 2001; 15(1): 101–119.
• Kyprianou A, Mottershead JE, Ouyang H. Assignment of natural frequencies by an added mass and one or more springs. Mech Syst Signal Process 2004; 18(2): 263–289.
• Ram YM. Dynamic Structural Modification. The Shock and Vibration Digest 2000; 32(1): 11-17.
• Sivan DD, Ram YM. Mass and stiffness modifications to achieve desired natural frequencies. Commun Numer Methods Eng. 1996; 12(9): 531–542.
• Mottershead JE, Kyprianou A, Ouyang H. Structural modification. Part 1: Rotational receptances. J Sound Vib 2005; 284(1–2): 249–265.
• Kyprianou A, Mottershead JE, Ouyang H. Structural modification. Part 2: Assignment of natural frequencies and anti-resonances by an added beam J Sound Vib 2005; 284(1–2): 267–281.
• Bucher I, Braun S. The Structural modification inverse problem: An exact solution. Mech Syst Signal Process 1993; 7(3): 217-238.
• Zhu J, Mottershead JE, Kyprianou A. An inverse method to assign receptances by using classical vibration absorbers. J Vib Control 2009; 15(1): 53–84.
• Mottershead JE, Mares C, Friswell MI. An inverse method for the assignment of vibration nodes. Mech Syst Signal Process 2001; 15(1): 87-100.
• Sanliturk KY. An efficient method for linear and nonlinear structural modifications. Proceedings of ESDA 2002: 6th Biennial Conference on Engineering Systems Design and Analysis 2002; İstanbul, Turkey, 028-040.
• Mottershead JE, Lallement G. Vibration nodes, and the cancellation of poles and zeros by unit-rank modifications to structures. J Sound Vib 1999; 222(5): 833-851.
• Park YH, Park YS. Structural modification based on measured frequency response functions: an exact eigenproperties reallocation. J Sound Vib 2000; 237(3): 411–426.
• Mottershead J. Structural modification for the assignment of zeros using measured receptances. Journal of Applied Mechanics 2001; 68(5): 791-798.
• Prells U, Mottershead JE, Friswell MI. On pole–zero placement by unit-rank modification. Mech Syst Signal Process 2003; 17(3): 611-633.
• Çakar O, Şanlıtürk KY. Elimination of suspension effects from measured frequency response functions. 9th International Research/Expert Conference, Trends in the Development of Machinery and Associated Technology 2005; Antalya, Turkey.
• Mottershead JE. On the zeros of structural frequency response functions and their sensitivities. Mech Syst Signal Process 1998; 12 (5): 591-597.
• Şanlıtürk KY, Çakar O. Noise elimination from measured frequency response functions. Mech Syst Signal Process 2005; 19 (3): 615-631.
• Cakar O, Sanliturk KY. Elimination of transducer mass loading effects from frequency response functions. Mech Syst Signal Process 2005; 19(1): 87–104.
• Tsuei YG, Yee EKLA. method for modifying dynamic properties of undamped mechanical systems. ASME J Dyn Syst Meas Control 1989; 111: 403-408.
• Yee EKL, Tsuei YG. Method for shifting natural frequencies of damped mechanical systems. AIAA Journal 1991; 29(11).
• Ouyang H, Zhang J. Passive modifications for partial assignment of natural frequencies of mass–spring systems. Mech Syst Signal Process 2015; 50-51: 214–226.
• Liu Z, Li W, Ouyang H, Wang D. Eigenstructure assignment in vibrating systems based on receptances. Arch Appl Mech 2015; 85(6): 713–724.
• Mottershead JE, Ram YM. Inverse eigenvalue problems in vibration absorption: Passive modification and active control. Mech Syst Signal Process 2006; 20: 5–44.
• Ouyang H, Richiedei D, Trevisani A, Zanardo G. A convex-constrained modification method based on receptances. Mech Syst Signal Process 2012; 27: 397–409.
• Sherman J, Morrison WJ. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann Math Stat 1950; 21 (1): 124–127.
• Çakar O. Bir konsol kirişin belirli bir doğal frekansını değiştirmeksizin kütle ve ay eklenmesi. 14. Ulusal Makine Teorisi Sempozyumu (UMTS 2009); 2009; Kıbrıs; 183-190.
• Çakar O. Mass and stiffness modifications without changing any specified natural frequency of a structure. J Vib Control 2011; 17(5): 769–776.
• Huseyinoglu M, Çakar O. Determination of stiffness modifications to keep certain natural frequencies of a system unchanged after mass modifications. Arch Appl Mech 2017; 87(10): 1629–1640.
• Çakar O. Bir Sistemin Doğal Frekanslarının Kütle Eklenerek Kaydırılması Üzerine Bir Çalışma. 18. Ulusal Makine Teorisi Sempozyumu (UMTS 2017); 2017; Trabzon, Turkey; 380-386.
• Çakar O. A method for shifting natural frequencies of a dynamic system to desired values with concentrated mass modifications. J Vibroeng 2018; 20(1): 1–12.
• Çakar O. Mekanik bir sistemin bir ters rezonans frekansının kütle eklenerek değiştirilmesi. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 2018; 30(2): 127–134.
• Şen M, Çakar O. Bir sistemin ters rezonans frekanslarının kütle eklenerek istenilen değerlere kaydırılması. 19. Ulusal Makine Teorisi Sempozyumu (UMTS 2019); 2019; İskenderun, Turkey; 321-328.
• Stojanovi I, Brajevi I, Stanimirovi PS, Kazakovtsev LA, Zdravev Z. Application of heuristic and metaheuristic algorithms in solving constrained weber problem with feasible region bounded by arcs. Math Probl Eng 2017: 1-13.
• Cuevas E, Cienfuegos M. A new algorithm inspired in the behavior of the social-spider for constrained optimization. Expert Systems with Applications 2014; 41: 412–425.
• Baydogan C, Alatas B. Sentiment analysis in social networks using social spider optimization algorithm. Technical Gazette 2021; 28(6): 1943-1951.
• Mirjalili S, Mirjalili SM, Lewis A. Grey Wolf Optimizer. Adv Eng Software 2014; 69: 46–61. ptimizer. Advances in Engineering Software 2014; 69: 46–61.