研究目的
To develop an alternative formulation for optimum Tuned Mass Damper (TMD) parameters based on equal Eigen value criteria, eliminating the need for trial and error methods used in previous studies.
研究成果
The study successfully derives closed-form expressions for optimum TMD parameters by equating Eigen values, identifying regions with one or two optimum solutions and fully damped modes. The optimum TMD (Solution I) is robust, effective over a wide frequency range, and reduces TMD displacement significantly compared to previous methods, making it suitable for seismic applications.
研究不足
The study is limited to single degree of freedom systems; extension to multi-degree of freedom systems is suggested but not implemented. The approach assumes linear behavior and may not account for nonlinear effects. The region of fully damped modes restricts the applicability for very high mass ratios.
1：Experimental Design and Method Selection:
The study uses a theoretical approach based on equating Eigen values of a single degree of freedom system with TMD. The characteristic polynomial is derived from equations of motion for free vibration, and optimum parameters are obtained by solving quartic polynomials analytically.
2：Sample Selection and Data Sources:
No specific samples or datasets are used; the analysis is purely mathematical and theoretical, based on system parameters like mass ratio (μ) and damping ratio (β).
3：List of Experimental Equipment and Materials:
No experimental equipment or materials are mentioned; the study is computational and analytical.
4：Experimental Procedures and Operational Workflow:
The procedure involves deriving the characteristic equation, assuming equal Eigen values, equating coefficients to form polynomials, and solving them to find optimum frequency and damping ratios. Numerical examples are provided for validation.
5：Data Analysis Methods:
Analytical solutions of quartic polynomials using closed-form expressions; comparison with existing studies through frequency response functions and displacement calculations under harmonic and earthquake loadings.
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