A rotor support structure for controlling non-synchronous vibrations of rotating machinery, the rotor support structure comprising: a foil bearing (114a, 114b, 114c) adapted to be disposed around a journal of a rotating rotor shaft, the foil bearing (114a, 114b, 114c) comprising: a bearing sleeve (20, 120) comprising an inner bore therethrough having a diameter to define a sway space between an inner circumferential surface of the bearing sleeve (20, 120) and an outer surface of the journal; and at least three foils (22, 24, 36) radially disposed within the sway space, each foil (22, 24, 36) having a foil stiffness, the at least three foils (22, 24, 36) comprise a top foil, a bump foil having a series of bumps, and at least one intermediate foil disposed between the top foil and the bump foil; wherein the at least one intermediate foil comprises a wavy shim having a series of waves, each wave having a cross-sectional shape, a wave height, and a wave pitch, a bearing housing (202, 402) disposed around the foil bearing (114a, 114b, 114c), wherein the foil bearing (114a, 114b, 114c) is configured to be anisotropic, exhibiting a stiffness in a first support direction that varies in magnitude from that in a second support direction that is substantially orthogonal to the first support direction, wherein at least one foil of the at least three foils (22, 24, 36) has a foil thickness, a foil height, a foil pitch, which refers to the center-to-center distance between adjacent bumps of the bump foil and/or the center-to-center distance between adjacent waves of the wavy shim, a foil pitch ratio, which refers to the bump foil pitch/wavy shim pitch, or combinations thereof in the first support direction that is different from that in the second support direction, and wherein the bump foil has the foil thickness in the first support direction that is different from the foil thickness in the second support direction. a foil bearing (114a, 114b, 114c) adapted to be disposed around a journal of a rotating rotor shaft, the foil bearing (114a, 114b, 114c) comprising: a bearing sleeve (20, 120) comprising an inner bore therethrough having a diameter to define a sway space between an inner circumferential surface of the bearing sleeve (20, 120) and an outer surface of the journal; and at least three foils (22, 24, 36) radially disposed within the sway space, each foil (22, 24, 36) having a foil stiffness, the at least three foils (22, 24, 36) comprise a top foil, a bump foil having a series of bumps, and at least one intermediate foil disposed between the top foil and the bump foil; wherein the at least one intermediate foil comprises a wavy shim having a series of waves, each wave having a cross-sectional shape, a wave height, and a wave pitch, a bearing housing (202, 402) disposed around the foil bearing (114a, 114b, 114c), wherein the foil bearing (114a, 114b, 114c) is configured to be anisotropic, exhibiting a stiffness in a first support direction that varies in magnitude from that in a second support direction that is substantially orthogonal to the first support direction, wherein at least one foil of the at least three foils (22, 24, 36) has a foil thickness, a foil height, a foil pitch, which refers to the center-to-center distance between adjacent bumps of the bump foil and/or the center-to-center distance between adjacent waves of the wavy shim, a foil pitch ratio, which refers to the bump foil pitch/wavy shim pitch, or combinations thereof in the first support direction that is different from that in the second support direction, and wherein the bump foil has the foil thickness in the first support direction that is different from the foil thickness in the second support direction. a bearing sleeve (20, 120) comprising an inner bore therethrough having a diameter to define a sway space between an inner circumferential surface of the bearing sleeve (20, 120) and an outer surface of the journal; and at least three foils (22, 24, 36) radially disposed within the sway space, each foil (22, 24, 36) having a foil stiffness, the at least three foils (22, 24, 36) comprise a top foil, a bump foil having a series of bumps, and at least one intermediate foil disposed between the top foil and the bump foil; wherein the at least one intermediate foil comprises a wavy shim having a series of waves, each wave having a cross-sectional shape, a wave height, and a wave pitch, a bearing housing (202, 402) disposed around the foil bearing (114a, 114b, 114c), wherein the foil bearing (114a, 114b, 114c) is configured to be anisotropic, exhibiting a stiffness in a first support direction that varies in magnitude from that in a second support direction that is substantially orthogonal to the first support direction, wherein at least one foil of the at least three foils (22, 24, 36) has a foil thickness, a foil height, a foil pitch, which refers to the center-to-center distance between adjacent bumps of the bump foil and/or the center-to-center distance between adjacent waves of the wavy shim, a foil pitch ratio, which refers to the bump foil pitch/wavy shim pitch, or combinations thereof in the first support direction that is different from that in the second support direction, and wherein the bump foil has the foil thickness in the first support direction that is different from the foil thickness in the second support direction.