تخمين جرم و سختي سازه با به‌روزرساني مستقيم الگوي سازه‌

Estimation of Mass and Stiffness Matrices by the Direct Model Updating Method

هدف از اين پژوهش، تخمين پارامترهاي ديناميكي سازه شامل ماتريس‌هاي جرم و سختي، با استفاده از روش به‌روزرساني الگوي سازه است. در اين راستا، با در نظر گرفتن اطلاعات اوليه‌ي الگوي نظري و استفاده از داده‌هاي مودال همچون فركانس‌هاي طبيعي و شكل مودها، ماتريس‌هاي جرم و سختي شناسايي مي‌‌شوند. در بخش رابطه‌سازي، توابع هدف به‌صورت اختلاف بين الگوهاي نظري و تجربي تعريف، و با بهره‌‌گيري از بسط مسيله‌ي‌ مقدار ويژه و تعامد مودها، تخمين پارامترهاي ديناميكي سازه رابطه‌سازي مي‌شود. پارامترهاي آزمايشگاهي مودال طي آزمايش تجربي مودال روي يك قاب سه‌طبقه تعيين شده‌‌ است. درستي رابطه‌هاي ارايه‌‌شده ابتدا با حل مسيله‌ي‌‌ عددي بررسي، و سپس با داده‌هاي آزمايشگاهي، جرم و سختي قاب سه‌طبقه استخراج مي‌شود. در نهايت، با مقايسه‌ي فركانس‌هاي طبيعي الگوي تخمين زده شده با الگوي آزمايشگاهي، مي‌توان همگرايي مناسبي بين آن‌ها مشاهده كرد و از درستي تخمين پارامترهاي ديناميكي اطمينان حاصل كرد.

Identification of structural dynamic parameters has received much attention in regard to health monitoring and damage detection over recent years. Within these objectives, assessment of the dynamic behaviour and determination of structural vibration responses are related to dynamic properties, which can be defined as mass, damping and stiffness matrices. This paper presents a new approach for estimation of dynamic parameters, including mass and stiffness matrices, by a model updating technique. These matrices are estimated based on the initial dynamic properties of the analytical model and utilizing modal data such as natural frequencies and mode shapes. Modal parameters are identified by numerical simulation of modal testing or based on signal processing and data acquisition in the experimental modal analysis. In the numerical simulation, these data are determined by the solution of generalized eigenvalue problems. Furthermore, in all parts of the formulation, the damping matrix is assumed as proportional. Therefore, the results of the simulation method are calculated as real data. The proposed approach is introduced based on the general objective function that is defined by the difference between analytical and experimental models. Once the objective function is evaluated, the dynamic parameters are estimated via expanding mass and stiffness orthogonality conditions. The dynamic properties are identified at two stages. In the first stage, the complete modal parameters are used. Then, in the second stage, the mass and stiffness matrices are determined by the first mode of vibration. Measured modal data are obtained by experimental modal analysis on a three story, simple, laboratory frame. It can be noted that the algorithm of identification of dynamic parameters is sensitized to accurate and pure modal data, which are originally extracted from experimental testing or simulation techniques. Investigation of the proposed formulation is verified by a numerical solution on a simulated four story shear frame building as an experimental model. Eventually, comparison of the natural frequency between estimated and experimental models can provide reliable results to accurately identify the dynamic parameters as mass and stiffness matrices.