Advanced Methods of Structural Analysis

14.1 Fundamental Concepts 515 Table 14.1 Types of elastic members and their characteristics Design diagram CharacteristicP-y Des ...

516 14 Dynamics of Elastic Systems From mathematical point of view, the difference between the two types of sys- tems is the fol ...

14.1 Fundamental Concepts 517 stiffnessEAD1), then the mass can move only in vertical direction and the struc- ture has one degr ...

518 14 Dynamics of Elastic Systems of freedom will be 2 and 6, respectively. Forgently slopingarches, the horizontal displacemen ...

14.1 Fundamental Concepts 519 members AB and BC with distributed massesmand absolutely rigid member CD .EID1/. The simplest form ...

520 14 Dynamics of Elastic Systems 14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method Behavior ...

14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method 521 Each equation of (14.2) presents the com ...

522 14 Dynamics of Elastic Systems The equations (14.4) are homogeneous algebraic equations with respect to un- known amplitudes ...

14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method 523 If a structure has ndegrees of freedom, ...

524 14 Dynamics of Elastic Systems Let D 1 ı 0 m!^2 D 6 EI m!^2 l^3 : In this case equation (a) may be rewritten .13/ A 1 C12 ...

14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method 525 Example 14.2.Design diagram of structure ...

526 14 Dynamics of Elastic Systems Frequency equation DD  4:7320 1:2679 1:2679 6:1961 D 0 Roots of frequency equation and ...

14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method 527 aaaa a EI m 1 m 2 m 3 P 1 =1 P 2 =1 P 3 ...

528 14 Dynamics of Elastic Systems ı 12 Dı 21 D Z M 1 M 2 EI dxD 11 768 l^3 EI ; ı 13 Dı 31 D Z M 1 M 3 EI dxD 7 768 l^3 EI ;ı 2 ...

14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method 529 Frequencies of the free vibration in inc ...

530 14 Dynamics of Elastic Systems Solution is 2 D 0:0;  3 D1:0, and second eigenvector becomes® 2 D 1:0 0:0 1 ̆T ; this mod ...

14.3 Free Vibrations of Systems with Finite Number Degrees of Freedom 531 constraints which prevent each displacement of the mas ...

532 14 Dynamics of Elastic Systems where the mass and stiffness matricesas well as displacement vector are MD 2 6 6 4 m 1 0 ::: ...

14.3 Free Vibrations of Systems with Finite Number Degrees of Freedom 533 can find the ratios between different amplitudes. If a ...

534 14 Dynamics of Elastic Systems The introduced constraints 1, 2, 3which prevent to displacementyiare shown in Fig.14.12a. For ...