Optimal stiffness distribution Chương này là có liên quan với bước đầu tiên trong điều khiển chuyển động thụ động, thiết lập một phân phối của độ cứng cấu trúc trong đó sản xuất mong muốn chuyển hồ sơ. Khi tải thiết kế là bán tĩnh, độ cứng tham số được xác định bằng cách giải các phương trình cân bằng trong một nghịch đảo cách. Nạp năng động được xử lý bằng cách chọn các thông số độ cứng như vậy mà hình dạng chế độ cơ bản có hồ sơ cá nhân chuyển mong muốn. tiềm ẩn giả định ở đây là người ta. | 51 Part I Passive Control Chapter 2 Optimal stiffness distribution Introduction This chapter is concerned with the first step in passive motion control establishing a distribution of structural stiffness which produces the desired displacement profile. When the design loading is quasi-static the stiffness parameters are determined by solving the equilibrium equations in an inverse way. Dynamic loading is handled by selecting the stiffness parameters such that the fundamental mode shape has the desired displacement profile. The implicit assumptions here are that one can incorporate sufficient damping to minimize the contributions of the higher modes and the fundamental mode shape is independent of damping. The latter assumption is reasonable for lightly damped structures. Discrete systems are governed by algebraic equations and the problem reduces to finding the elements of the system stiffness matrix. The static case involves solving K U P for K where U and P are the prescribed displacement and loading vectors. Some novel numerical procedures for solving eqn are presented in a later section. 52 Chapter 2 Optimal Stiffness Distribution In the dynamic case the equilibrium equation for undamped periodic excitation of the fundamental mode is used K o 2 MO where M is the discrete mass matrix o is a scaled version of the desired displacement profile and 1 is the fundamental frequency. Taking K -1- K 1 P MO reduces eqn to K o P The solution technique for eqn also applies for eqn . Once K is known the stiffness can be scaled by specifying the frequency 1 . An appropriate value for 1 is established by converting the system to an equivalent one degree-of-freedom system and using the SDOF design approaches discussed in the introduction. Continuous systems such as beams are governed by partial differential equations and the degree of complexity that can be dealt with analytically is limited. The general strategy of working with .
