Abstract
On the basis of the Eq. (1.3.1) of the present paper, determining the proper transform of a product of two functions, general solution is given for steady-state vibration, stability and equilibrium of straight bars and plates with concentrated masses and a continuous mass. In addition to several algebraic equations, a numerical example is quoted concerning the determination of the fundamental frequency of free vibration of a square isotropic plate clamped along the entire contour and having a concentrated mass in the middle.References
[1] [in Russian]
[2] R. SOLECKI, Rozwiązanie ogólne płyty trójkątnej 30°-60°-90° za pomocą transformacji właściwej, Arch. Inzyn. Ladow., 1960.
[3] [in Russian]
[4] [in Russian]
[5] W. F. STOKEY, C.F. ZOROWSKI, Normal Vibrations of a Uniform Plate Carrying Any Number of Finite Masses, Trans. ASME J. Appl. Mech, 2, 1959.
[6] [in Russian]
[7] R. E. ROBERSON, Transversal Vibrations of a Free Circular Plate Carrying Concentrated Mass J. Appl. Mech., 3, 1951.
[8] R. E. ROBERSON, Vibrations of a Clamped Circular Plate Carrying Concentrated Mass J. Appl. Mech., 4, 1951.
[9] Z. MAZURKIEWICZ, Bending Vibration and Buckling of a Rectangular Plate Resting on a Non-Homogeneous Foundation, Bull. Acad. Pol. Sci. Série Sci. Tech., 3, 1960.
[10] S. KALISKI, The Dynamical Problem of the Rectangular Parallelepiped, Arch. Mech. Stos., 3, 10 (1958).
[11] R. SOLECKI, Rozwiązanie ogólne płyty o kształcie trójkąta prostokątnego, Rozpr. Inzyn., 2, 8 (1960).
[12] [in Russian]
[13] [in Russian]
[14] P. WILDE, The General Solution for a Rectangular Orthotropic Plate Expressed by Double Trigonometric Series, Arch. Mech. Stos., 5, 10 (1958).
[15] [in Russian]
[16] Z. KĄCZKOWSKI, Ortotropowe płyty prostokątnej o brzegach swobodnych, Arch. Mech. Stos., 4, 7, (1955).
[17] Z. KĄCZKOWSKI, Orthotropic Rectangular Plates with Arbitrary Boundary Conditions, Arch. Mech. Stos., 2, 8 (1956).
[2] R. SOLECKI, Rozwiązanie ogólne płyty trójkątnej 30°-60°-90° za pomocą transformacji właściwej, Arch. Inzyn. Ladow., 1960.
[3] [in Russian]
[4] [in Russian]
[5] W. F. STOKEY, C.F. ZOROWSKI, Normal Vibrations of a Uniform Plate Carrying Any Number of Finite Masses, Trans. ASME J. Appl. Mech, 2, 1959.
[6] [in Russian]
[7] R. E. ROBERSON, Transversal Vibrations of a Free Circular Plate Carrying Concentrated Mass J. Appl. Mech., 3, 1951.
[8] R. E. ROBERSON, Vibrations of a Clamped Circular Plate Carrying Concentrated Mass J. Appl. Mech., 4, 1951.
[9] Z. MAZURKIEWICZ, Bending Vibration and Buckling of a Rectangular Plate Resting on a Non-Homogeneous Foundation, Bull. Acad. Pol. Sci. Série Sci. Tech., 3, 1960.
[10] S. KALISKI, The Dynamical Problem of the Rectangular Parallelepiped, Arch. Mech. Stos., 3, 10 (1958).
[11] R. SOLECKI, Rozwiązanie ogólne płyty o kształcie trójkąta prostokątnego, Rozpr. Inzyn., 2, 8 (1960).
[12] [in Russian]
[13] [in Russian]
[14] P. WILDE, The General Solution for a Rectangular Orthotropic Plate Expressed by Double Trigonometric Series, Arch. Mech. Stos., 5, 10 (1958).
[15] [in Russian]
[16] Z. KĄCZKOWSKI, Ortotropowe płyty prostokątnej o brzegach swobodnych, Arch. Mech. Stos., 4, 7, (1955).
[17] Z. KĄCZKOWSKI, Orthotropic Rectangular Plates with Arbitrary Boundary Conditions, Arch. Mech. Stos., 2, 8 (1956).
