According to the present invention, there is provided a vibration damping device (10) including a first bracket (11) and a second bracket (12), a first attachment member (14), a second attachment member (15), and an elastic body (16). The second attachment member (15) includes an insertion cylinder portion (22) in which the second bracket (12) is inserted. The insertion cylinder portion (22) is provided with a stopper portion (56) which faces a stopper wall (55) provided in the first bracket (11), in a radial direction (Y) in a side wall portion (57) oriented outward in the radial direction (Y) of the insertion cylinder portion (22). The stopper portion (56) includes a first stopper portion (61) and a second stopper portion (62) which are disposed in a manner of being displaced in an axial direction (X) of the insertion cylinder portion (22). The first stopper portion (61) is constituted by a first elastic portion (58). The second stopper portion (62) includes a rigid member (25). A first distance (D1) between the first stopper portion (61) and the stopper wall (55) in the radial direction (Y) is equal to or shorter than a second distance (D2) between the second stopper portion (62) and the stopper wall (55) in the radial direction (Y).

A hydraulically damping assembly bearing has two fluid-filled chambers which lie axially opposite each other and are hydraulically connected by a channel. A first chamber forms a working chamber enclosed by a bearing spring body and a second chamber forms a compensating chamber enclosed by a bellows. The compensating chamber has an axially extending inner wall encircling an interior. The bearing includes an annular body axially between the working and compensating chambers, enclosing an axial throughopening opening into the working chamber and closed by a membrane integrally formed with the inner wall of the bellows. The membrane has a central region defined by the inner wall and together with the inner wall delimits the interior. The membrane has a collar region encircling the central region and integrally formed with the central region. The outer circumference of the collar is rigidly connected to the annular body and/or the spring body.

A vehicle engine mount structure includes a motor mount assembly, a motor bracket and a heat shield. The motor mount assembly has a first attachment part with a fastener receiving aperture, a vibration absorbing section and a second attachment part spaced apart from the first attachment part. The motor bracket has a first flange portion configured to support a vehicle engine and a second flange portion configured to attach to the second attachment part of the motor mount assembly. The heat shield is dimensioned to at least partially overlay the vibration absorbing section of the motor mount assembly and overlay the fastener receiving aperture with the heat shield being disposed between the motor mount assembly and the second flange portion of the motor bracket, and with the second flange portion of the motor bracket attached to the second attachment part of the motor mount assembly.